TECHNICAL CORNER by Greg Sitek Introducing the …...Five forward gears.An additional forward speed is provided between the normal working and hauling ranges. Softer steps between

Five forward gears. An additional forwardspeed is provided between the normal workingand hauling ranges. Softer steps between 2nd, 3rd,and 4th gears enhance shift quality and power-train durability while reducing wheel slip. Reversegear ratios have been improved to better matchapplication needs and increase loading cycle performance.

Auto-Shift. With 4th forward gear selected,the Power Shift control systemautomatically shifts between 4thand 5th gears to maintain roadspeed. However, when higherspeeds are not needed, a manual5th-gear lockout switch preventsautomatic shifts - especially desir-able during such applications asload and carry.

Transmission Disconnect. Theloader control does not changewith the Power Shift option. Atransmission disconnect button isprovided to divert full enginepower to the main hydraulicpump.

Torque Converter. Single stage,2.63:1 stall ratio.

Travel Speeds. Travel speeds at afull throttle when equipped with16.9 x 24 rear tires, 3.6 to 20 mph.

Caterpillar Model Availability.The new Power Shift transmissionis available as an option on the fol-lowing C-Series backhoe loaders —416C (80 hp), 426C and 436C. ■

The new Caterpillar® Power Shift transmissionincreases productivity and operator comfortby providing a single lever to control both

speed and direction.The best keeps getting better. The Cat backhoe

loader continues to be the best in its class - nowwith optional Power Shift. Change gears anddirections effortlessly, while maintaining continu-ous traction throughout the work cycle. You’llwork faster with greater operator comfort.

One lever does it all. The conventional shifterhas been replaced by a twist-grip on the forward-reverse shuttle. This improves operator comfortand productivity by allowing direction and speedchanges to be made with a single lever. There’s nofloor-mounted gear shift lever, so the operator hasmore cab floor space. A neutral start provisionprevents starting while directional clutches areengaged.

TECHNICAL CORNER by Greg Sitek

A singlelever controlsboth speedand direction.

Introducing theCat C-seriesPower Shift

22 • ON YOUR OWN

Backhoe Loaders416C • 426C • 436C • 446B

Track-Type Tractors and LoadersD3C III • D4C III • D5C III • 933C • 939C

Wheel Loaders914G • 924F • 928G

THE CAT EQUIPMENT LINEBuilding Construction Products Division

Telescopic HandlersTH62 • TH63 • TH82 • TH83 • TH103

Integrated ToolcarriersIT14G • IT24F • IT28G

Hydraulic Excavators307 • 311B • 312B • 315B • M318

POWER SHOVEL

• To excavate the earth and load it into the trucks or other hauling equipments.

• Suitable for all class of earth except solid rocks.

TYPE: By its mounting

• Crawler-mounted power shovel

• Wheel-mounted power shovel

SIZE: By the size of dipper

3/8, ½, ¾, 1, 1.25, 1.5, 2, 2.5 m3 etc.

PARTS: Cab, Dipper, Boom, Hoist line, Dipper stick, Mounting- Crawler or Wheel

OPERATION: Release hoist line à Position Shovel à Boom apply downward force

by dipper stick àPull by hoisting line à Empty the dipper by opening the door.

PDF created with FinePrint pdfFactory Pro trial version http://www.fineprint.com

Basic Parts of Power Shovel



DRAGLINE

• Excavate earth and load it into hauling equipments or deposit it to site.

• Boom is light and long.

• Function same as Power shovelTYPE: By its mounting

• Crawler-mounted Dragline – 2 kmph

• Wheel-mounted Dragline – 50 kmph

• Truck-mounted Dragline – 50 kmphSIZE: By the size of bucket

Advantages• A Dragline does not have to go into the pit – useful in removing the earth from

a ditch, canal or pit.

• When excavating earth is to be deposited on nearby banks.

• Good for trenching


DisadvantagesOutput in terms of excavating earth is 70 to 80 % of power shovel.



CLAMSHELLS

• Consists of a bucket of two halves, which are hinged together at top.

• Buckets are attached to the shovel Crane units or at the boom of a Dragline.

• Digging is done like a Dragline and once the bucket is filled, it works like a Crane.

• Suitable for loose material.

• Suitable for vertical lifting of materials.

TYPE: Bucket is classified as

• Light bucket – for handling loose materials

• Heavy bucket – used for digging purposes and has long and sharp teeth.




HOE

• Excavating equipment of the power shovel group.

• Exert greater tooth pressure.

• Generally used in quarries which have tough digging conditions.

• Dig trenches, footings or basements.

• Operate on close-range work and dump into trucks.

OPERATION: Place boom at the desired angle à Dipper moves at desired position

à Release hoist Cable to lower down the boom à Pull Cableà

Raise boom and swing to the dumping position.


HOE






SCRAPERS

• Tractor-pulled Scrappers are Self-sufficient and self operating construction

equipment designed to scrape the ground, load it simultaneously, transport it

over the required distance, dump and spread..

• Used in a wide range of material types

• Economical over a wide rage of haul lengths and haul conditions.

• Best suited for haul distances greater than 500 ft but less than 3000 ft.

PRODUCTION CYCLE:

(1) Loading (2) haul travel (3) dumping and spreading (4) turning (5) return travel,

and (6) turning and positioning to pick up another load.

NOTE: Since Scrapers are a compromise between machines designed exclusively

for either loading or hauling, they are not superior to function-specific equipments

in either hauling or loading.lease hoist



DOZERS

• Effective and versatile earth moving m/c.• Is a tractor-power unit that has a blade attached to the machine’s front.• The blade is used to push, shear, cut and roll material ahead of dozer.• Used for

¤ Moving earth or rock for short haul distances.¤ Spreading earth or rock fills¤ Back-filling trenches.¤ Clearing land of trees and stumps including roots and of vegetation.¤ Opening of temporary roads through rocky areas.¤ Helping load tractor-pulled scrappers.¤ Clearing the construction sites of debris and rubbish.¤ Maintaining haul roads.¤ Stripping of the top soil that is not usable etc.

Bulldozer : Blade is set perpendicular to the direction of travel.

Angledozer : If set at an angle.


Types of Dozers1. Crawler type2. Wheel type

Crawler Type• Can work on variety of soil – travel over very rough surfaces.• Good for short work distance.• Can handle light soils• Slow return speeds• Can push large blade load

Wheel Type• Best for level and downhill work.• Good for long travel distances• Best in handling loose soil• Can only handle moderate blade loads• Travel on paved soil without damaging the surfaces.






Wheel Excavators


Crawler Excavator


HOE



HOE


DRAGLINE


Scrapers: Reynolds International


PULL-TYPE SCRAPERS Bell


Clamshell Buckets


CRAWLER DOZER


DOZERKomatsu


EXCAVATOR AND BULLDOZERKobelco


Pavers


“LA NUEVA MEDIANA MINERIA”

PALAS HIDRÁULICAS

12 DE AGOSTO DE 2008

INDICE

• Modelos disponibles de palas hidráulicas

• Comparación Palas vs Cargador sobre ruedas

• Operación

• Capacidad de Carga

• Especificaciones

• Movilidad

• Match Pala – Camión

• Pala Frontal y Retro (producción)

• Caracteristicas Generales de Palas

• Preguntas

282 t1008 kW16,5 m³ (SAE 2:1)

RH 120-ERH 120-E

525 t1680-1880 kW26.0 m³ (SAE 2:1)

RH 200RH 200

380 t1516 kW22.0 m³ (SAE 2:1)

RH 170BRH 170B

180 t730 kW10.0 m³ (SAE 2:1)

RH 90-CRH 90-C

84-90 t392 kW7,0 m³ (SAE 1:1)

RH 40-ERH 40-E102-112 t477 kW8.0 m³ (SAE 2:1)

RH 70RH 70

1000 t-class3280 kW50.0 m³ (SAE 2:1)

RH 400RH 400

553 t2240 kW34.0 m³ (SAE 2:1)

RH 340BRH 340B

Palas Hidráulicas Terex O&K

Comparasión

Excavadora Hidráulica O&K RH 40 E

vs.

Cargador sobre Ruedas

Suelto, material tronado Rango de Material Compacto, aún sin tronarGran área de carga (25 m) Area de Carga Area de carga reducidaNivelado, estable, seco Condición de Piso Deformado, húmedo, sueltoAprox. 16 pies (5 m) Altura de Banco Aprox. 38 pies (12 m)Siempre de abajo hacia arriba Selectividad Carga selectivaBaja: 480 lbf/in (0.85 kN/cm) Fuerza de Penetración Alta: 960 lbf/in (1.7 kN/cm)Aprox. 45 segundos Tiempo de Ciclo Aprox. 30 segundosAlta: 21.8 mph (35 km/h) Velocidad de Traslado Baja: 1.56 mph (2.5 km/h)60 - 80 psi Presión sobre el suelo 15 - 30 psiDescarga descontrolada Carga de Camiones Descarga ControladaVisibilidad Limitada Carga de Camiones Buena visibilidadNo Equipos de Apoyo Pala: No, Retro: Si

Operación General

Cargador Frontal O&K RH 40 E

Pila

4 ft

Cat 773 D39’ 1”

(11.90 m)

Operación Cargador Frontal

OptimoCiclo Total: 177.5 ft (54.08 m)

OptimoCiclo Total: 177.5 ft (54.08 m)

2 m

Radio de Giro Cargador: 24’ 10” (7.57 m)

39’ 1”(11.90 m)

50’ 6”each

(15.14 m)

Operación Pala Hidráulica

4 ft

2 m

O&K RH 40 E

Frente

Cargador sobre Ruedas:

Capacidad del Balde: 6.0 m3

Tiempo de Ciclo (favorable): 36-39 segundos

Ciclos por hora: 92 - 100

Factor de llenado: 100%

Máxima Producción: 957 - 1,040 t/hr

Excavadora Hidráulica: RH 40 E

Capacidad del Balde : 7.0 m3

Tiempo de Ciclo (favorable): 23-26 segundos

Ciclos por hora: 138 - 156

Factor de llenado: 95%

Máxima Producción: 1,468 - 1,660 t/hr

Máxima Capacidad de Carga

Producción de la excavadora es hasta un 60% mayor

Especificaciones de las Máquina

101,000 lb (46.1 t) Peso de Operación 220,000 lb (100 t)300 hp (224 kW) Potencia Motor 607 hp (453 kW)8.0 yd3 (6.0 m3) Capacidad del Balde para Densidad 1,8 t/m3 9.2 yd3 (7.0 m3)5 ciclos Ciclos de Carga para Cat 773D (52.3 t) 4 ciclos3.2 min. Tiempo de carga de camión 1.67 min.18.8 Número max. de camiones por hora 35.91.040 t/hr Máxima Producción por hora 1,660 t/hr

487 lb/in (0.855 kN/cm) Fuerza de desgarramiento 1,042 lb/in (1.82 kN/cm)14.6 mph (35.1 km/hr) Velocidad de Traslado 1.56 mph (2.5 km/hr)16 pies (4.9 m) Max. Altura Excavación 36 pies (10.9 m)4” (0.098 m) Max. Profundidad Excavación 83” (2.10 m)20” (0.50 m) Distancia al suelo 35” (0.90 m)

La única ventaja del cargador sobre ruedas es la velocidad de desplazamiento.Todas las otras comparaciones son desfavorables

O&K RH 40 E

Costos

� COSTO CAPITAL

� COSTO OPERACION� Reparaciones� Neumáticos� Lubricantes� Filtros� Combustible

O&K RH 40 E

O&K RH 40 E

Menor Costo Excavadora: 13.13 %

Costos

Menor Costo Excavadora:44.85 %

Costo de propiedad y operación por hora

Costo de propiedad y operación por tonelada

CARGADOR SOBRE RUEDASBaja Producción a un Alto Costo

pero tieneGran Versatilidad

EXCAVADORA HIDRÁULICA

No es un auto de carrerapero tiene

Alta Productividada Bajos Costo

Verdad Simple

CostoTons

Distancia de Traslado

Producción (t/hr)Excavadora Hidráulica

Costo por tonCargador de Ruedas

Producción (t/hr)Cargador de Ruedas

Costo por tonExcavadora Hidráulica

Excavadora HidráulicaFavorable

Cargador de RuedasFavorable

Producción

A mayor distancia de traslado menor es la producción horaria. La productividad de lasexcavadoras hidráulicasdepende mucho mas de lasdistancias de traslado comparada con los cargadoresde ruedas.

Costos

El costo por toneladaaumentará si existen mayoresdistancia de traslado. Esto se refleja con mayor incidencia en una excavadora hidráulica queen un cargador sobre ruedasequivalente

Definición de cual es la verdad

Soluciones para Incrementar la Movilidad

SLEIPNER• Dos estructuras separadas con dos ruedas cada una y frenos de parqueo

• Menor desgaste en los componentes del rodado

• Velocidad de traslado 20 km/hr, pendientes de 15°

• Se requieren 3 minutos de preparación

OperaciónOperación

Llenado de BaldeLlenado de Balde Cargador de RuedasCargador de Ruedas Excavadora HidráulicaExcavadora Hidráulica

Generación de fuerza Generación de fuerza ataque dinámicoataque dinámico hidráulica por cilindros hidráulica por cilindros

de de penetraciónpenetración por manejo a la pilapor manejo a la pila

CinemáticaCinemática restringidarestringida avance (frentes altas)avance (frentes altas)

EstabilidadEstabilidad bajo (peso operaciónbajo (peso operación alto (peso operación)alto (peso operación)

(confort del operador)(confort del operador) y métodos de trabajo)y métodos de trabajo)

Minería SelectivaMinería Selectiva dificildificil fácil debido a configuraciónfácil debido a configuración

con con TripowerTripower

ExcavaciónExcavación no hay opciónno hay opción factible debido a las altasfactible debido a las altas

fuerzas de fuerzas de penetración penetración y y

desprendimientodesprendimiento


DescargaDescarga Cargador de RuedasCargador de Ruedas Excavadora HidráulicaExcavadora Hidráulica

Max. Altura descargaMax. Altura descarga suficientesuficiente app. 20 % mas altaapp. 20 % mas alta

Visión del OperadorVisión del Operador suficientesuficiente excelente excelente

Descarga segura yDescarga segura y dificil, por cercaníadificil, por cercanía controlling of bucket controlling of bucket controladacontrolada al camión y descargaal camión y descarga opening width via opening width via

adelantando solamenteadelantando solamente cylinders and highercylinders and higherel baldeel balde safety distancesafety distance

Carga a dos ladosCarga a dos lados necesita gran espacio necesita gran espacio proceso de carga normalproceso de carga normalpeligroso como equipopeligroso como equiporápido en movimientorápido en movimiento

Condiciones de PisoCondiciones de Piso se requieren pisos se requieren pisos no es necesario pisos planos, no es necesario pisos planos, suaves y planossuaves y planos recomendable para camionesrecomendable para camiones


ResumenResumen Cargador de RuedasCargador de Ruedas Excavadora HidráulicaExcavadora Hidráulica

Objetivos PrincipalesObjetivos Principales cargacarga excavación y cargaexcavación y carga

Aplicaciones Aplicaciones operaciones deoperaciones de Excava y suelta material Excava y suelta material

carga y traslado carga y traslado consolidadoconsolidado

excava en material excava en material carga rápidacarga rápida

sueltosuelto

DesgasteDesgaste tensión en la tensión en la menor tensión, debido a menor tensión, debido a

estructura yestructura y movimientos constantesmovimientos constantes

articulaciónarticulación

Aplicación Aplicación carga en material biencarga en material bien excavación y carga de excavación y carga de

RecomendadaRecomendada tronado con frecuentestronado con frecuentes material consolidadomaterial consolidado

cambios de fasecambios de fase

Match Pala Camión RH40

771 D771 D45 ton / 41 t

773 E60 ton / 55 t

777 D100 ton / 91 t

pases

775 E70 ton / 63 t

Calculos basados en densidad suelta de 1.8 t/m³ y 100 % factor de llenado

RH 40-E7.0 m³ / 9.2 yd³ SAE 1:1

RH 40-E7.0 m³ / 9.2 yd³SAE 2:1

Aplicación EstándarDensidad Suelta 1.8 t/m³

CAT 777D 91 - 96 t

100 - 106 tc

Match Pala Camión RH 90-C

CAT 775E 62 - 63 t 68 - 70 tc

Aplicación EstándarDensidad suelta 1.8 t/m³

CAT 777D 91 - 96 t

100 - 106 tc

3 - 4 Ciclos

Match Pala Camión RH 120-E

CAT 785 C 136 - 154 t 150 – 170 tc

5 - 6 Ciclos

RH 40-E Pala Frontal con TriPower

650 kN104 t

477 kW640 HP

7.0 m³(2:1)

500 kN

Pala Frontal y Tripower11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3 12 11 10 9 8 7 6 5 4 3 2 1 0 m

• 7.0 m³

• Fuerza de Penetración:Max. 650 kN

• Fuerza de desprendimientoMax. 500 kN

• ProductividadMax: 1400 t/hPromedio: 1000 t/h

Producción RH 40-E (Pala Frontal)Bucket size 7,0 m³ Number of cycles: 5 Material density: 1,8 t/m³

Fill factor

Load per bucket

Load per truck

Cycle time 21 sec 23 sec 25 sec 27 sec 21 sec 23 sec 25 sec 27 sec 21 sec 23 sec 25 sec 27 sec

Truck spotting 0,35 min 0,38 min 0,42 min 0,45 min 0,35 min 0,38 min 0,42 min 0,45 min 0,35 min 0,38 min 0,42 min 0,45 min

30 sec 0,50 min 1621 t/h 1524 t/h 1412 t/h 1338 t/h 1540 t/h 1448 t/h 1341 t/h 1271 t/h 1459 t/h 1372 t/h 1271 t/h 1204 t/h




















11,3 t

56,7 t

63%

12,6 t

63,0 t

12,0 t

59,9 t

Utili-zatiion

83%

78%

73%

68%

100% 95% 90%

RH 40-E Retro

400 kN

102 -106 t

477 kW640 HP

7.0 m³(1:1)

380 kN

Pala Retro14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-716 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 m

• 7.0 m³

• Fuerza Penetración Max. 400 kN

• Fuerza desprendimientoMax. 380 kN

• ProductividadMax. 1400 t/hPromedio 1000 t/h

Producción RH 40-E (Retro)Bucket size 7,0 m³ Number of cycles: 5 Material density: 1,8 t/m³

Fill factor

Load per bucket

Load per truck

Cycle time 21 sec 23 sec 25 sec 27 sec 21 sec 23 sec 25 sec 27 sec 21 sec 23 sec 25 sec 27 sec

Truck spotting 0,35 min 0,38 min 0,42 min 0,45 min 0,35 min 0,38 min 0,42 min 0,45 min 0,35 min 0,38 min 0,42 min 0,45 min





















11,3 t

56,7 t

63%

12,6 t

63,0 t

12,0 t

59,9 t

Utili-zatiion

83%

78%

73%

68%

100% 95% 90%

Cabina de Operación

–Excelente Visibilidad (nivel visual 7.6 m)

–Asiento con suspensión neumática con interruptor de seguridad.

–Asiento auxiliar para el instructor

–Sistema de Control a Bordo - BCS

Cabina de Operación

Sistema de Control BCS

– Pantalla transflectiva en colores.� Fácil de leer incluso con luz directa

del sol– Monitoreo de datos de operación

� App. 30 sensores análogos� App. 50 sensores digitales

– Comparación de los parámetros seteadosy sus desviaciones.

– Alarmas visuales y acústicas– Asistencia de detección de fallas.– Asistencia de servicio

� Programa de mantención y susintervalos.

� Memoria de fallas– Carácterísticas ajustable del Joystick de

acuerdo a las preferencia del operador.– Varios idiomas

� Español, Francés, Inglés, Alemán, Ruso

Ventajas Concepto de dos Motores

� La excavadora es totalmente operable con un solo motor (en el caso de falla de unode estos o en su defecto falla de alguna bomba, etc.):

– Por medidas de seguridad, el equipo puede ser movido fuera de algúna área de altapeligrosidad (bancos altos, etc.).

– El equipo puede ser movido para permitir tronadura.

– El equipo puede ser colocado en mejor posición para su reparación.

� Un 60% de la capacidad nominal de equipo se puede lograr con un solo motor, debidoa que:

– La máxima presión de trabajo se logra tambien con un solo motor. (las potencias de penetración y desprendimiento se mantienen intactas).

– Bajada de pluma y mango por gravedad.

– Circuito hidráulico cerrado de giro con recuperación de energía.

� Detección de falla en el módulo de potencia es mucho mas simple– Se puede determinar y detectar de manera fácil algúna falla o problema entre una

unidad de potencia y la otra.

� Dos unidades de potencia menores son de menor costo que una sola de grantamaño.

� Costo de inversión de componentes de respaldo es considerablemente mas bajo

PREGUNTAS

Loading on Truck_s Good Side Good side positioning occurs when the truck backs in for a load and the shovel or loader is on the same side of the truck as the operator_s cab. Full view of the shovel or loader is possible while backing. The key points are as follows: 1. Trucks advance clockwise. 2. If the loading area is not occupied and is clear of obstructions or spillage, the truck operator is to move directly into the loading area without being spotted, lining up the edge of the dump body with the banjo arm in the case of a shovel, or lining up the edge of the dump body with the bucket teeth in the case of a loader. (Refer to Figures 6.8.5.1 through 6.5.8.6.) Note: Bring the truck to a complete stop before moving the Transmission Selector control lever to the Reverse position. 3. If the loading area is occupied, the truck is to wait at Position B. Note: Occupied means that there is another haul truck, cleanup equipment, maintenance equipment, personnel, etc. in the area. The reason for waiting at Position B is to maintain total visibility of the loading area. 4. Maintain the distance between Position B and the loading area two truck-lengths apart. 5. When the truck in Position B does move, the truck must travel at least one truck-length forward before making a right turn into Position C. Note: The distance between the loading area and Position C should be one truck-length. The distance between Position A and Position B should be two truck-lengths apart. When the truck in Position A moves, the truck must travel at least one truck-length forward before making a right turn into Position B. 6. When pulling in under a shovel or loader, follow the signals of the spotter or the operator of the shovel or loader. (Refer to Spotting Procedures further on in this section.)

6.1.

When the shovel or loader operator is waiting with the bucket loaded and spotted, back up by lining up the edge of the dump body with the banjo arm in the case of a shovel, or lining up the edge of the dump body with the bucket teeth in the case of a loader. (Refer to Figures 6.5.8.1 through 6.5.8.6.)

6.2.

Continue backing slowly until the shovel or loader operator dumps the bucket or blows the horn to stop. Note: The shovel or loader operator should not dump the first load before the truck stops when the VIMS payload measurement system is being used. Dumping the first load before the truck has stopped and the transmission is in Neutral may affect the accuracy of the payload weight.

6.3.

Stage the truck as close to the digging face as possible while: Keeping the truck square to the shovel or loader. Avoiding tire damage from backing onto the digging face or spillage from previously loaded trucks. Keeping the truck on flat level ground, reducing torsional strain on the truck suspension.

CAUTION: Stop before the tires roll up on sloughing material at the digging face to avoid tire damage.

6.4.

When spotting, maintain a minimum of 1 meter to 1½ meters between the edge of the dump body and the rear of the shovel (counterweight) or radiator of the loader. When spotting a truck for loading by a loader, the best angle is at about 45° to the working face rather than at a right angle to it. In this position, the loader can swing some loads from the bank onto the truck with a minimal backward movement, thus increasing loading speed. It is always the loader operator_s responsibility to stage the trucks. (Refer to Figure 6.5.8.6.) 7. Do not back into the loading area if the shovel or loader is facing into the bank. Wait for the shovel or loader operator to turn the bucket away from the bank before backing. Note: Prompt and correct positioning of the trucks for loading cuts down on the loading cycle times and increases productivity. 8. While your truck is being loaded, stay in the truck cab. Place the Transmission Selector control lever in Neutral and engage the parking brake. Leave the engine running. Note: Staying in the truck cab is necessary because of the constant danger of material falling out of the bucket and injuring the operator. The exception to this rule is when the truck is being loaded with boulders. (Refer to Section 6.5, Operator Tasks: Loading Boulders.) WARNING: If the operator must leave the cab during loading, place the Transmission Selector control lever in Neutral and engage the parking brake. Leave the cab upon receiving positive communication from the shovel or loader operator. Dismount using the steps, grab irons, and three points of contact. Remain a safe distance from the truck during the loading cycle. 9. Do not drive over unprotected power cables. 10. When approaching or leaving the loading area, watch out for other vehicles and for personnel working in the area.

COMBINACIÓN DE MODELOS COMBINACIÓN DE MODELOS DE RUTAS DE VEHÍCULOS Y DE RUTAS DE VEHÍCULOS Y

SIMULACIÓN MICROSCÓPICA SIMULACIÓN MICROSCÓPICA DE TRÁFICO PARA EL DISEÑO DE TRÁFICO PARA EL DISEÑO

Y LA EVALUACIÓN DE Y LA EVALUACIÓN DE APLICACIONES DE LOGÍSTICA APLICACIONES DE LOGÍSTICA

URBANA URBANA (CITY LOGISTICS(CITY LOGISTICS-- GESTIÓN DE GESTIÓN DE

FLOTAS EN TIEMPO REAL)FLOTAS EN TIEMPO REAL)

J. Barceló(1), H. Grzybowska(1) J. Barceló(1), H. Grzybowska(1) and S. Pardo(2)and S. Pardo(2)

(1) (1) DepartamentDepartament d’Estadísticad’Estadística i i InvestigacióInvestigació OperativaOperativa

UnivesitatUnivesitat PolitècnicaPolitècnica de de [email protected]@upc.es, ,

[email protected]@upc.es(2)TSS(2)TSS--Transport Simulation SystemsTransport Simulation Systems

[email protected]@aimsun.com((http://www.aimsun.comhttp://www.aimsun.com))

16/06/05 I JORNADAS DEL TRANSPORTE (ZARAGOZA)

2

LOGÍSTICA Y LOGÍSTICA URBANA (I)LOGÍSTICA Y LOGÍSTICA URBANA (I)

• LOGISTICA (Según el “Council of Logistics Management”):“Aquella parte de la cadena de suministro que planea, implementa y controla el flujo y almacenamiento eficiente de bienes y servicios, y la información asociada, desde el punto de origen al de destino para satisfacer los requerimientos de los clientes”.


3

ESQUEMA CONCEPTUAL DE LA CADENA DE SUMINISTRO ESQUEMA CONCEPTUAL DE LA CADENA DE SUMINISTRO

Modelos de Rutas de Vehículos y de Gestión de Flotas

(ORIGEN A HUB)

Problema de Localización

ZAL

.

.

ORIGEN CARGA 1

ALMACENAMIENTO CONSOLIDACIÓNMANIPULACIÓN

TRANSPORTE: MARITIMO, AEREO,

FERROCARRIL,CARRETERA

ORIGEN CARGA 2

ORIGEN CARGA j

TRANSPORTE: MARITIMO, AEREO,

FERROCARRIL, CARRETERA

(ZAL A CENTROS

DISTRIBUCION O ALMACENES)

Logistic Centres

Warehouses

Logistic Centres

Warehouses

Logistic Centres

Warehouses

Logistic Centres

Warehouses

Logistic Centres

Warehouses

Client 1

Client 2

Client 3

Client 4

Client i

Client j

Client k

Client m

Client n

(ORIGEN A HUB)


4

LOGÍSTICA Y LOGÍSTICA URBANA (II)LOGÍSTICA Y LOGÍSTICA URBANA (II)• Las actividades logísticas en áreas urbanas

tienen características que las diferencian de las actividades logísticas generales:– su contribución a los flujos de tráfico (en

promedio del orden de un 10%), – las consecuencias que este tiene sobre ellas

(congestión, demoras en el proceso de suministro…) y

– el porcentaje que representan en la contribución a los costes de trasporte (hasta un 40%)


5

CITY LOGISTICS (Taniguchi et al.)CITY LOGISTICS (Taniguchi et al.)

• “Es el proceso de optimización total de las actividades de logística y transporte realizadas por medio de empresas privadas en áreas urbanas, teniendo en cuenta el ámbito en que se realizan, su interacción con el tráfico, la manera en que están afectadas por la congestión, su contribución a ella, las consumos energéticos y las contribuciones a la polución, todo ello en el marco de una economía de mercado”


6

PLANIFICACIPLANIFICACIÓÓN, DISEN, DISEÑÑO, EVALUACIO, EVALUACIÓÓN Y N Y MODELOSMODELOS

• Las decisiones sobre planificación y diseño, y la evaluación de las aplicaciones logísticas ha de tener una base cuantitativa, por medio de modelos adecuados a los objetivos

• Lo que implica disponer de un conjunto de modelos ad hoc para• La localización de los centros logísticos• La programación y determinación de las rutas

de los vehículos de las flotas• La gestión dinámica de las flotas


7

MODELOS DE RUTAS DE VEHÍCULOSMODELOS DE RUTAS DE VEHÍCULOS• Los modelos de Rutas de Vehículos (Vehicle Routing and

Scheduling) proporcionan las técnicas para modelar las aplicaciones de “City Logistics”, dos casos de especial interés son:• Cuando los clientes especifican la ventanas temporales dentro

de las cuales s han de realizar los servicios de entrega-recogida (pick-up and delivery) los vehículos de las flotas logísticas

• Cuando la programación y determinación de las rutas de servicio ha de ser dinámica, basada en información en tiempo real.

• Han de tener en cuenta que la información cambia mientras los vehículos prestan los servicios y debe procederse a una actualización secuencial de las rutas cuando se dispone de nueva información.

• Ejemplos de información en tiempo real son: • Sobre las condiciones de operación del sistema: Tiempos de

viaje, Tiempos de servicio, de espera, etc(afectados por congestiones, incidentes, averías…),.

• Sobre la demanda de los clientes: Localización, Ventanas temporales, cantidades, prioridades….,

• Sobre el vehículo: Localización, Estado de la carga…


8

UNA PROPUESTA METODOLÓGICA DESDE LA UNA PROPUESTA METODOLÓGICA DESDE LA PERSPECTIVA DE LA INVESTIGACIÓN OPERATIVAPERSPECTIVA DE LA INVESTIGACIÓN OPERATIVA

• MODELOS PARA TOMAR DECISIONES, SIGNIFICA– Que los modelos sean accesibles a los

responsables de la toma de decisiones – Asistiéndoles en

• El proceso de construcción del modelo• La selección y aplicación de los algoritmos

adecuados• El análisis e interpretación de los resultados• La evaluación de los resultados

• LO QUE IMPLICA QUE LOS MODELOS HAN DE SER COMPONENTES DE UN SISTEMA DE AYUDA A LA TOMA DE DECISIONES


9

IMPLEMENTACIÓN DE UN SISTEMA DE AYUDA A LA TOMA DE IMPLEMENTACIÓN DE UN SISTEMA DE AYUDA A LA TOMA DE DECISIONES PARA EL DISEÑO Y EVALUACIÓN DE APLICACIONES DE DECISIONES PARA EL DISEÑO Y EVALUACIÓN DE APLICACIONES DE

“CITY LOGISTICS” A PARTIR DE LA METODOLOGÍA DE TANIGUCHI“CITY LOGISTICS” A PARTIR DE LA METODOLOGÍA DE TANIGUCHI

ALTERNA TIVES

DATA COLLECTION

CONSTRAINTS

SENSITIVITY

SELECTION

REVIEW RESOURCES

EVALUATION

MODELS

IMPLEMENTATION

PROBLEM DEFINITION

OBJECTIVES CRITERIA DECISIÓN SUPPORT SYSTEM FOR

LOGISTIC ANALYSIS


10

ESQUEMA CONCEPTUAL DE LA ARQUITECTURA DE UN SISTEMA ESQUEMA CONCEPTUAL DE LA ARQUITECTURA DE UN SISTEMA DE AYUDA A LA TOMA DE DECISIONES CUANTITATIVAS DE AYUDA A LA TOMA DE DECISIONES CUANTITATIVAS

((SprageSprage, Turban), Turban)

BASE DE MODELOSBASE DE DATOS

SISTEMA DE GESTION DE

LA BASE DE DATOS

SISTEMA DE GESTION DE LA BASE DE MODELOS

INTERFAZ GRAFICA DE USUARIO

ACTUALIZACION DE DATOS

SIG-T


11

BASE DE MODELOSBASE DE MODELOS•• LOCALIZACIÓN DE PLANTASLOCALIZACIÓN DE PLANTAS

–– ContinuosContinuos–– DiscretosDiscretos–– En redesEn redes

•• DE RUTAS DE VEHÍCULOSDE RUTAS DE VEHÍCULOS–– Rutas de Vehículos con Limitaciones de CapacidadRutas de Vehículos con Limitaciones de Capacidad–– Rutas de Vehículos con Ventanas TemporalesRutas de Vehículos con Ventanas Temporales–– Rutas de Vehículos para problemas de Recogida y Rutas de Vehículos para problemas de Recogida y

Entrega (Entrega (PickupPickup and and DeliveryDelivery) con Ventanas Temporales) con Ventanas Temporales•• MODELOS DE TRÁFICOMODELOS DE TRÁFICO

–– Asignación de Tráfico (Equilibrio de Usuario) Asignación de Tráfico (Equilibrio de Usuario) –– Simulación Dinámica (Simulación Dinámica (p.ep.e. Simulación Microscópica con . Simulación Microscópica con

AIMSUN NG)AIMSUN NG)

GUIEdition, 2D and 3D animation

CAD

…

GIS

GETRAM

Traffic data

Internet

Transportplanning

Scenarioanalysis module

Validationtools

Demandanalysis

LogisticApplications

AIMSUNSimulator

Extensibleobjectmodel

ModelDB

Filters Kernel Traffic tools

Dataanalysis

LA ARQUITECTURA DEL AIMSUN NG (Entorno integrado para el análisis de sistemas de transporte)


13

AIMSUN NG Importing a .dwg


14

AIMSUN NG Importing a Shape File


15

Transport Planning: User Equlibrium Assignment


16

Transport Planning: Shortest Path Analysis


17

COMENTARIOS SOBRE LA AYUDA A LA COMENTARIOS SOBRE LA AYUDA A LA CONSTRUCCIÓN DE MODELOS CONSTRUCCIÓN DE MODELOS

Y LAS PECULIARIDADES DE LOS Y LAS PECULIARIDADES DE LOS MODELOS DE RUTAS DE VEHÍCULOS PARA MODELOS DE RUTAS DE VEHÍCULOS PARA

APLICACIONES CITY LOGISTICSAPLICACIONES CITY LOGISTICS


18

El modelo de la El modelo de la redred viariaviaria para las para las aplicacionesaplicaciones de Logística Urbanade Logística Urbana

• Modelada como un grafo G=(N,A) • Traducción de la red viaria urbana definida por un mapa (digital)• Cuyos nodos n∈N representan orígenes y destinos• Con centros logísticos y clientes localizados en nodos o arcos • Y arcos a∈A, que representan la infrastructura de transporte


19

DEL MAPA DIGITAL DEL MODELO DE MICROSIMULACION A LA DEL MAPA DIGITAL DEL MODELO DE MICROSIMULACION A LA REPRESENTACIÓN NODOSREPRESENTACIÓN NODOS--ARCOS ARCOS

(Detalle de la “traducción”: Inclusión explícita de los movimien(Detalle de la “traducción”: Inclusión explícita de los movimientos de giro)tos de giro)

1

6

4

3

2

7

8

5


20

EL “COSTE DE USAR UN ARCO” EN UNA RED URBANAEL “COSTE DE USAR UN ARCO” EN UNA RED URBANA

• Depósito: cuadrado rojo• Clientes: cuadrados

azules• Coste c0i: coste del

camino (en verde) desde el depósito (nodo 0) al cliente i (nodo i)

• Los Costes no son simétricos (c0i ≠ ci0)

• El grafo no es euclídeo• La propiedad triangular

no se satisface


21

EJEMPLO DE LA ASIMETREJEMPLO DE LA ASIMETRÍÍA DE LOS COSTES DE A DE LOS COSTES DE VIAJE EN UNA RED VIARIA URBANAVIAJE EN UNA RED VIARIA URBANA


22

DOS CASOS DE ESPECIAL INTERÉS EN LA DOS CASOS DE ESPECIAL INTERÉS EN LA LOGÍSTICA URBANA:LOGÍSTICA URBANA:

PROBLEMAS DE RUTAS DE VEHÍCULOS PROBLEMAS DE RUTAS DE VEHÍCULOS CON VENTANAS DE TIEMPOCON VENTANAS DE TIEMPO

PROBLEMAS DEPROBLEMAS DE ENTREGA Y RECOGIDA ENTREGA Y RECOGIDA (PICKUP AND DELIVERY) CON VENTANAS (PICKUP AND DELIVERY) CON VENTANAS

DE TIEMPODE TIEMPO


23

ProblemasProblemas dede Rutas deRutas de VehículosVehículos

MAGATZEMCENTRAL

2. Route sequencing 1. Assignment of clients to vehicles


24

PROBLEMAS DE RUTAS DE VEHICULOS CON VENTANAS DE PROBLEMAS DE RUTAS DE VEHICULOS CON VENTANAS DE TIEMPO (VRPTW)TIEMPO (VRPTW)

• El Problema de Rutas de Vehículos con Ventanas de Tiempo (VRPTW) es una extensión del CVRP en la que:

• Cada cliente i está asociado a una demanda no negativa di, una duración del servicio si no negativa y una ventana temporal [ei, li] que representa respectivamente los instantes más temprano y más tardío, en que se puede prestar el servicio.

•• El VRPTW consiste en asignar k rutas de vehículos en G

tales que:– i. Toda ruta empieza y acaba en el depósito– ii. Todo cliente pertenece exactamente a una ruta– iii. La carga total y duración de una ruta k no excede Ek y Lkrespectivamente– iv. El servicio al cliente i se realiza en el intervalo [ei, li], y todo

vehículo sale del depósito y regresa a él en en intervalo [e0, l0]; y– Minimiza tiempo total de viaje (o el coste) de operación de la

flota


25

• El VRPTW se define en un grafo G=(V,A) en el que el depósito está representado por los nodos 0, y n+1.

• Todas las rutas factibles corresponden a caminos en G que empiezan en el nodo 0 y terminan en el nodo n+1

• Los nodos 0 y n+1 tienen asociada una ventana temporal [e0,l0]=[en+1,ln+1]=[E,L] que representa, respectivamente, la salida más tempranan del depósito y el retorno al depósito más tardío posible.

• Existen soluciones posibles solo si :

• Un arco (i,j) ∈A, con un tiempo de viaje tij puede eliminarse debido a consideraciones temporales si

ei+si+tij>lj• O debido a limitaciones de capacidad di+dj>C• xijk, (i,j)∈A, k∈K, es igual a 1 si el arco (i,j) es utilizado por el

vehículo k, y a 0 en caso contrario.• N=V\{0,n+1} es el conjunto de clientes

{ }[ ]

{ }[ ]i0ii0Vi1n0ii0Vi0 tseMINLl and tlMINEe ++≥=−≤=

−∈+

−∈


26

FORMULACIÓN DEL (VRPTW) COMO UN MODELO DE REDES CON FLUJO MULTIARTÍCULO CON VENTANAS DE TIEMPO Y RESTRICCIONES DE

CAPACIDAD• Restricciones (2) ⇒ cada

cliente es asignado solo a la ruta de un vehículo

• Restricciones (3) a (5) caracterizan el flujo en la ruta del vehículo k

• Restricciones (6), (8) (9) aseguran la factibilidaden in términos de tiempoy capacidad

• Para un vehículo dado k las restricciones (7) fuerzan wik=0 cuando el cliente i no es visitadopor el vehículo k

• Las variables temporaleswik, i∈V, y k∈K especifican el principiodel servicio en el nodo i por el vehículo k

• Xijk = 1 si el arco (i,j) esutilizado por el vehículo k

( )

( )

( ) ( )

( )

( ) ( )

( ) ( )

{ }

( )

{ } ( ) (10) Aji,K,k ,0,1 x

(9) Kk C,xd (8) 10,niK,k L wE

(7) NiK,k xlwxe

(6) Aji,K,k 0, wtsw x

(5) Kk , 1x

(4) N,jK,k 0,xx

(3) Kk 1,x

(2) Ni 1,x s.t.

(1) xcMIN

ijk

i∆jijk

Nii

ik

i∆jijkiik

i∆jijki

jkijiikijk

1n∆ik1,ni,

j∆ijik

j∆iijk

0∆j0jk

Kk i∆jijk

Kk Aj)(i,ijkij

-

-

∈∈∀∈

∈∀≤

+∈∈∀≤≤

∈∈∀≤≤

∈∈∀≤−++

∈∀=

∈∈∀=−

∈∀=

∈∀=

∑∑

∑∑

∑

∑∑

∑

∑ ∑

∑ ∑

+

++

+

+

+

∈∈

∈∈

+∈+

∈∈

∈

∈ ∈

∈ ∈


27

A UNIFIED TABU SEARCH HEURISTIC FOR VRPTW A UNIFIED TABU SEARCH HEURISTIC FOR VRPTW ((CordeauCordeau, , LaporteLaporte and Mercier, JORS, Vol. 52, pp. 928and Mercier, JORS, Vol. 52, pp. 928--936, 2001)936, 2001)

• Tabu search, a local search meta-heuristic that explores the solution space by moving at each iteration from the current solution s to the best solution in its neighbourhood N(s).

• Anti-cycling rules to prevent deterioration of the solution

• Allow to explore infeasible solutions during the search

• Diversification mechanisms to help the search process to explore a broad portion of the solution space

• The heuristic has two main components:– A constructive phase that constructs at most K routes– An improvement phase


28

CONSTRUCTIVE PHASECONSTRUCTIVE PHASE• Constructs at most K routes as follows

1. Randomly choose a customer j∈{1,…,n}2. Set k:=13. Using the sequence of customers j,j+1,….,n,1,…,j-1, perform

the following steps for every customer i: I. If the insertion of customer i into route k would result in the

violation of load or duration constraints, set k:=MIN{k+1,K}II. Insert customer i into route k so as to minimize the increase in

the total travel time (cost) of route k• Taking into account that the insertion of customer i can

only be performed between successive customers j1 and j2 if ej1 ≤ ei ≤ ej2, otherwise customer i is inserted at the end of the route.

• At the end of the procedure routes 1,…,K-1 satisfy load and duration constraints, and route K may violate any of the three types of constraints.


29

Let S denote the set of solutions that satisfy constraints (i) and (ii)

• A solution s∈S is a set of K routes such that every customer belongs to exactly one route

• This solution may violate:– The maximum load and duration constraints– The time windows constraints associated with the

customers and the depot.• The time window constraint at customer i is

violated if the arrival time ai of the vehicle is larger than the time window upper bound li

• Arrival before ei is allowed and the vehicle then has to wait the time wi=ei-ai


30

IMPROVEMENT PHASEIMPROVEMENT PHASE• The tabu search starts from the solution of the construction phase and

chooses at each iteration the best non-tabu solution in N(s).• After each iteration the values of parameters α, β and γ are modified.• This process is repeated for η iterations and the best feasible solution s*

identified during the search is post-optimized by applying to each individual route a specialized heuristic for the Traveling Salesman with Time Windows 1. Set α:=1, β:=1 and γ:=1

If s is feasible set s*:=s and c(s*) = c(s) Otherwise set c(s*) = ∞

2. For κ = 1,…., η, do a. Choose a solution ( ) sNs ∈ that minimizes ( ) ( )spsf + and is

not tabu or satisfies its aspiration criteria b. If solution s is feasible, and ( ) ( )*scsc < , set s:s* = , and

( ) ( )sc : *sc = c. Compute ( ) ( ) ( )sw and sd,sq and update α, β and γ

accordingly d. Set s:s =

3. Appli post-optimization heuristic (Generalized Insertion Heuristic –GENI- for the TSPTW) to each route of s*


31

Generalized Insertion(GENI Construction)


32

Pickup and Delivery Problem with Time Windows (PDPTW)

• A generalization of the VRPTW • Consisting on determining a route and

the corresponding schedule for everyvehicle in a fleet that services a collectionof the transportation pickup and deliveryrequests, satisfying the time windows and the vehicle capacity constraints as well as the main objective function of minimizingthe total cost of a trip.


33

A Metaheuristic for PDPTW• Initialization. Construct the initial routes using a

Modified Solomon’s Insertion Algorithm.• Evaluation of the solutions. According to objective

function evaluate the initial solutions and choose the local optimal solution Sb.

• Configuration of the control parameters of the heuristics.

• Tabu Search procedure • Combines a Descent Local Search based on PD-

Shift and PD-Excahnge Operators• Followed by the application of PD-Exchange

Operator, with• Output: Sb.


34

METAHEURISTICS FOR PICKUP AND DELIVERY WITH TIME METAHEURISTICS FOR PICKUP AND DELIVERY WITH TIME WINDOWS (SHIFTING)WINDOWS (SHIFTING)

Route 1

P D

Route 2

Route 2

P D

Route 1

SHIFTING


35

METAHEURISTICS FOR PICKUP AND DELIVERY WITH TIME METAHEURISTICS FOR PICKUP AND DELIVERY WITH TIME WINDOWS (EXCHANGING)WINDOWS (EXCHANGING)

EXCHANGING

Route 1

P1 D1

Route 2P2 D2

D2

Route 1

P2Route 2

P1 D1


36

METAHEURISTICS FOR PICKUP AND DELIVERY WITH TIME METAHEURISTICS FOR PICKUP AND DELIVERY WITH TIME WINDOWS (REARANGING)WINDOWS (REARANGING)

Route

P D

REARANGING

Route

P D


37

UN ENFOQUE DINÁMICO INTEGRADO: UN ENFOQUE DINÁMICO INTEGRADO: ENRUTAMIENTO ENRUTAMIENTO ⇔⇔ SIMULACIONSIMULACION

MODELS FOR VEHICLE ROUTING AND SCHEDULING:

- Ordinary - Time windows - Pick up and delivery - Dial a ride - Others

OPTIMAL ROUTING

AND SCHEDULING

AVERAGE (Time depend.)

Link travel time

DYNAMIC TRAFFIC

SIMULATION MODEL


38

¿QUÉ TIPO DE SIMULACIÓN DINÁMICA DE ¿QUÉ TIPO DE SIMULACIÓN DINÁMICA DE TRÁFICO? TRÁFICO?

PROPUESTA: SIMULACIÓN MICROSCÓPICAPROPUESTA: SIMULACIÓN MICROSCÓPICA


39

El enfoque de la modelación microscópica de El enfoque de la modelación microscópica de la simulación de tráficola simulación de tráfico

•• Requiere una representación detallada de la geometría de la red Requiere una representación detallada de la geometría de la red viaria viaria

•• Se basa en la emulación del movimiento de los vehículos Se basa en la emulación del movimiento de los vehículos individualmente, vehículo a vehículo, teniendo en cuenta sus individualmente, vehículo a vehículo, teniendo en cuenta sus características particulares, y las múltiples clases.características particulares, y las múltiples clases.

•• La posiciones de los vehículos se actualizan mediante modelos La posiciones de los vehículos se actualizan mediante modelos de seguimiento, reglas de cambio de carril, etc., que incluyen de seguimiento, reglas de cambio de carril, etc., que incluyen componentes estocásticas. componentes estocásticas.

•• Se modela explícitamente la variabilidad de los Se modela explícitamente la variabilidad de los comportamientos de los conductores y las dinámicas de los comportamientos de los conductores y las dinámicas de los vehículos.vehículos.

•• Los vehículos viajan desde orígenes a destinos siguiendo rutas Los vehículos viajan desde orígenes a destinos siguiendo rutas variables con el tiempo, variables con el tiempo, elegidas según modelos estocásticos elegidas según modelos estocásticos de selección de rutasde selección de rutas..

•• Se utiliza una representación explícita de los planes de controlSe utiliza una representación explícita de los planes de control(fijo, actuado, (fijo, actuado, adaptativoadaptativo…) …) en las intersecciones semaforizadas en las intersecciones semaforizadas y reglas de cesión de paso, etc. en las no semaforizadasy reglas de cesión de paso, etc. en las no semaforizadas. .


40

Como trabaja la simulación microscópicaComo trabaja la simulación microscópica


41

Los Los modelosmodelos de de simulaciónsimulación comocomo laboratorioslaboratoriosvirtualesvirtuales parapara la la experimentaciónexperimentación

MODELO DE SIMULACION

INPUTS(Alternativas, políticas,

cuestiones ¿qué pasaría si?)OUTPUTS

(Respuestas)

EXPERIMENTACION

• El modelo de simulación puede considerarse como un laboratorio virtual en el ordenador para realizar experimentos que permitan extraer concusiones válidas sobre el sistema estudiado

• La Simulación deviene así un proceso experimental sobre el sistema real por medio de su modelo

• La fiabilidad de este proceso de toma de decisiones depende de la capacidad de producir un modelo de simulación que represente el comportamiento del sistema con suficiente validez


42

LA VALIDACIÓN DE LOS MODELOSLA VALIDACIÓN DE LOS MODELOS

• Análisis estadístico comparativo de los resultados de la simulación y las observaciones del sistema de tráfico

• Análisis e interpretación de las rutas utilizadas: estimación de tiempos de viaje

Simulated

Detector


43

INFORMACION PROPORCIONADA POR LA SIMULACION MICROSCOPICA: INFORMACION PROPORCIONADA POR LA SIMULACION MICROSCOPICA: Tiempos de viaje en los arcos dependientes del tiempoTiempos de viaje en los arcos dependientes del tiempo


44

Seguimiento de vehículos simulando AVL Seguimiento de vehículos simulando AVL de un vehículo equipado con GPSde un vehículo equipado con GPS


45

INFORMACION PROPORCIONADA POR LA SIMULACION MICROSCOPICA: INFORMACION PROPORCIONADA POR LA SIMULACION MICROSCOPICA: RutaRuta del del VehículoVehículo, , EmulaciónEmulación de la de la localizaciónlocalización automáticaautomática (GPS)(GPS)

Tracked Vehicle and

Vehicle’s data (FCD)


46

EmulaciEmulacióónn de la de la monitorizacimonitorizacióónn de un de un vehvehíículoculo equipadoequipadocon GPS en la con GPS en la simulacisimulacióónn microscmicroscóópicapica de de trtrááficofico

Vehicle information

Possibility to follow a vehicle during the simulation and to gather dynamic data while following the vehicle


47

DIVERSION ISSUES IN REALDIVERSION ISSUES IN REAL--TIME VEHICLE DISPATCHINGTIME VEHICLE DISPATCHING

• How to deal with thesituation when a newrequest appears?

• How to diverta vehicle from itspresent destination toserve the new client?

• Conceptual scheme of the diversion problem: Current movement

Planned movement

Optimization procedure

Current planned routes(including current destinations) New request

New planned routes(with the new request)

D D

D’ D’ A A

B B

C C


48

Ad Ad hochoc WaitingWaiting strategiesstrategies basedbased on realon real--time and short time and short termterm forecastedforecasted traveltravel times (times (AdaptedAdapted fromfrom MitrovicMitrovic--

MinicMinic and and LaporteLaporte))


49

EsquemaEsquema conceptual conceptual parapara la la evaluacionevaluacion de de sistemassistemas de de gestigestióónn de de flotasflotas en en tiempotiempo realreal

DEMANDA INICIAL Y ESPECIFICACIONES

DE LA FLOTA

MODULO DE CÁLCULO DE RUTAS Y PROGRAMACIÓN DE

SERVICIOS

PLAN INICIAL DE OPERACIONES

INFORMACIÓN EN TIEMPO REAL

•Nuevas demandas•Demandas insatisfechas•Condiciones de tráfico•Disponibilidad de la flota

MÓDULO DE REPROGRAMACIÓN Y CÁLCULO DE RUTAS

DINÁMICO

PLAN DINÁMICODE

OPERACIONES


50

Simulación de sistemas de gestión de flotas en tiempo real Simulación de sistemas de gestión de flotas en tiempo real • Calcular las rutas y programa

inicial de servicios– Costes de los arcos cij∼ tiempos

de viaje en los arcos tij• Ejecutar la simulación

– Seguir lo vehículos de la flota a lo largo de sus rutas

• Demanda de los clientes en tiempo real

– El nuevo cliente llama en el instante t

• Inputs al sistema de ayuda a la toma de decisiones

– Posiciones de cada vehículo en el instante t

– Identificación de los vehículos candidato

– Identificación de nuevas rutas dependientes del tiempo

• Tiempos de viaje en los arcos, en curso y previstos, proporcionados por la simulación

• Decisión– Considerar políticas de diversión

frente a no diversión– Asignar el nuevo cliente al

vehículo k– Calcular la nueva ruta

New route for vehicle 2

New customerCalls at time t

Position of vehicle 2 at

time t

Position of vehicle 1 at

time t

New route for vehicle 1


51

IMPLEMENTACIÓN DEL ESQUEMA IMPLEMENTACIÓN DEL ESQUEMA CONCEPTUAL CON EL AIMSUN NGCONCEPTUAL CON EL AIMSUN NG

DYNAMIC ROUTER AND SCHEDULER(External Application)

• Identifies the new demand • Reassigns vehicles • Changes stop points

AIMSUN MICROSCOPIC SIMULATION MODEL • Simulates traffic condition on the modelled network• Tracks fleet vehicles • Collects FCD

AIMSUN NG• Makes available

o The Link-node extended graph of the road network

o Stop points in the graph o Type of stop

• Provides access to o Current (and forecasted) link travel times o Fleet vehicles current routes and positions

DYNAMIC ROUTER AND SCHEDULER

• Initializes the process o Defines the initial schedule

• Provides o Stops changes, adding new stops o New routes for the fleet vehicles


52

TEST DEL PROTOTIPO DE SISTEMA TEST DEL PROTOTIPO DE SISTEMA DE AYUDA A LA TOMA DE DE AYUDA A LA TOMA DE

DECISIONES:DECISIONES:ESTUDIO DE DOS CASOS EN EL ESTUDIO DE DOS CASOS EN EL

PROYECTO MEROPE PROYECTO MEROPE (INTERREG III B MEDOC)(INTERREG III B MEDOC)

LUCCALUCCAPIACENZA PIACENZA


53

ModeloModelo AIMSUN de AIMSUN de LuccaLucca con con clientesclientes y y CentrosCentros LogísticosLogísticos


54

LuccaLucca: : ResultadosResultados parapara el el EscenarioEscenario 11

Route/Vehicle Route Cost (Distance)

1 6270,020 2 4366,700 3 4267,540 4 5264,860 5 3160,160 6 5188,260 7 4711,240 8 4734,820 9 4926,380 10 5186,280 11 5732,640 12 6118,840 13 6200,120 14 5801,100 15 5906,580 16 5976,620 17 6514,460

HUB 1

18 7426,120 Total 97752,74

Rutas de los tres primeros vehículos desde el

Centro Logístico 1


55

Rutas desde el Centro Logístico 2Rutas desde el Centro Logístico 2


56

PiacenzaPiacenza: : puntospuntos de de cargacarga--descargadescarga


57

ModeloModelo AIMSUN de AIMSUN de PiacenzaPiacenza: : detallesdetalles ((UbicacionesUbicacionesde de clientesclientes y y puntospuntos de de cargacarga--descargadescarga))


58

Resultados de Resultados de PiacenzaPiacenza: : Comparación de EscenariosComparación de Escenarios

(Por tipo de cliente, servicio directo/ Por (Por tipo de cliente, servicio directo/ Por puntos de cargapuntos de carga--descarga; distancia/tiempo)descarga; distancia/tiempo)

HUB by distance by time

HUB 1 elettrodomestici 105228,212 19436,123 HUB 2 elettrodomestici 302901,380 21636,601

HUB by distance by time

HUB 1 carico-scarico 28263,186 13972,171 HUB 2 carico-scarico 177938,200 11881,131


59

ReconocimientosReconocimientos y y conclusionesconclusiones

• AIMSUN es un simulador de tráfico desarrollado desde 1986 por el Laboratorio de Investigación Operativa y Simulación Del Departamento de Estadística e Investigación Operativa de la Universidad Politécnica de Cataluña, a través de la participación, entre otros, en más de 22 proyectos de los Programas de I+D de la Unión Europea.

• AIMSUN está comercializado desde 1998 por TSS-TransportSimulation Systems, una empresa spin-off de la UPC. Actualmente hay más de 350 licencias en uso en todo el mundo.

• Para información sobre AIMSUN visitar http://www.aimsun.com• Las ideas presentadas sobre Simulación y City Logistics fueron

desarrolladas inicialmente en el proyecto SADERYL de la DGICYT (TIC2000-1750-C06-03).

• El prototipo fue completado como parte del Programa Europeo INTERREG III B MEDOCC Project MEROPE Axe 3, Measure 4, Code 2002-02-3.4-I-091

• Los tests se realizaron en las ciudades de Piacenza y Lucca, que han probado la viabilidad de la combinación de simulación y modelos de Vehicle Routing para el diseño y evaluación de aplicaciones City Logistics.

• El desarrollo y verificación de los conceptos de gestión de flotas en tiempo real es objeto del proyecto SADERYL-2 de la DGICYT (TIC2003-05982-C05-04 ).


60

MUCHAS GRACIAS POR SU ATENCIÓN

?

Chapter 9.4CYCLES AND SYSTEMS

JON C. YINGLING

9.4.1 INTRODUCTION

Though mine production unit operations must be matchedto the characteristics of the site at hand–sufficient power mustbe available at the excavator’s cutterhead for effective fragmenta-tion, haulage vehicles must be matched to the physical character-istics of the roadways, bucket design must be matched to thehandling characteristics of the material being excavated, etc.—the process of design is not finished when equipment is identifiedthat satisfies these requirements. How the unit operations willwork together must be considered.

The integration of the unit operations discussed in previouschapters of this section into a system that can execute the produc-tion cycle efficiently requires great attention, both in initial de-sign of the system and in managing its day-to-day operations.Some of the important decision areas are as follows:

1. Scheduling and sequencing unit operations executed inparallel (i.e., simultaneously) so that any one operation seldomresults in excessive delay in execution of another.

2. Balancing production capacity of unit operations (e.g., siz-ing a truck fleet to match a loading shovel or a conveyor networkto match the output of multiple production sections). A goodsolution to this problem is often much more involved than simplymatching either the peak or the average material productioncapacities of the different unit operations.

3. Assessment of systems level design effects on availability.Overall, mine production systems tend to be highly interdepen-dent and serial in nature. Failure of one unit operation may causeproduction in a number of other dependent operations to cease.Buffer storage capacity in transportation systems and use of fleetoperations to perform a task (a number of smaller machinesinstead of one large one) are sometimes appropriate approachesto improving overall availability and, accordingly, the long-termrate of production output from these systems.

4. Assessment of working-section layout effects on the perform-ance of the production system. For instance, entry layout and cutsequence in room and pillar mines influence the total nonproduc-tive time spent moving equipment between the working places,the lengths of haulage runs, and tradeoffs between haulage dis-tances and downtime due to extension of the section belts.

5. Real-time operations control strategies, such as the rulesused to dispatch pooled truck fleets to service multiple loadingoperations at a surface mine.

Mine production systems engineering aims at evaluating themany alternative designs and operational strategies that can bedeveloped for a given application. It serves as a vehicle for identi-fying good, perhaps optimum, choices. It views the unit opera-tions collectively as integrated systems rather than independentoperations. The interfacing and interaction of the unit operationsis explicitly considered. It evaluates performance in terms withoverall relevance to mine management rather than in terms onlylocally relevant to the unit.

Though some general rules of “good practice” can be stated(see 9.0.1.4) and should always be considered, these rules are nothighly prescriptive of the detailed design and control of thesesystems. Production systems engineering is primarily a collectionof techniques, that, if properly applied, can give good answersto often rather complicated questions. The tremendous incen-

tives for efficiency of mine production systems are powerfulmotivations for routine application of these techniques. At themany operations where profit margins are low, these incentivesare often demands.

Consistent with the scope of Section 9, this chapter focuseson topics of mine production systems engineering relevant tosystems-level aspects of equipment selection and utilization. Spe-cifically, the following three technologies are treated in somedetail:

1. Simulation of mine production systems. This technologyhas taken a major role in detailed analysis of the performance ofthese systems. It uniquely can capture the stochastic (i.e., ran-dom) and dynamic character of these systems in models withlittle abstraction. Simulation models can be constructed to ad-dress any of the issues listed above.

2. Fleet dynamics and dispatch strategies. Addressed hereare approaches for real time control of mine production systemsinvolving fleet operations. These approaches are based on heuris-tic strategies, although the heuristics themselves sometimes em-ploy solutions to rather sophisticated mathematical models. (Theadjective “heuristic” is used in this chapter to refer to decisionrules that arise from one’s intuition regarding approaches thatappear appropriate for design or control of a system. The generalperformance of these rules cannot be characterized by deductivemathematical reasoning, and they lack complete theoreticalfoundation. However, they often provide a very useful and prac-tical basis for decision making.) In the case of truck dispatch,this technology has been proven to utilize equipment more effec-tively.

3. Stochastic process models of mine production systems.Though simulation techniques can be used to model the perform-ance of mining systems involving stochastic elements (e.g., truckqueues at a loader, material flows on a conveyor network), amore detailed mathematical analysis using the theory of stochas-tic processes can sometimes lead to a concise analytical model.Relative to simulation models of the same process, these modelscan greatly simplify comparisons of system design and controlalternatives and can thereby lead to stronger conclusions. Theycan be very useful in cases where the level of abstraction requiredto establish the model is not excessive.

Other aspects of production systems engineering that arebroader in scope and longer term in nature, such as mine devel-opment planning and production scheduling, are discussed fromthe perspective of mine exploitation in Chapters 8.3 and 8.4.Moreover, consistent with the theme of Section 9, the perspectiveof this chapter is general. Numerous other discussions of mineproduction systems engineering can be found throughout thisHandbook, addressing specific application areas, including theexamples listed.

9.4.2 GENERAL CONCEPTS AND TERMINOLOGY

A vocabulary that helps one to characterize these systemsand to understand the tools that may be used in predicting andanalyzing their performance follows.

A system is a collection of components on which processesoperate, causing the components to interact for some objective

783

784 MINING ENGINEERING HANDBOOKpurpose. Typically, the degree to which intended purposes of thesystem being met are assessed in terms of one or more perform-ance measures, e.g., “production rate,” “tons per employee-hour,” or “cost per cubic meter of material moved.” The optionsthat management have in design and control of the system areexpressed in terms of a set of decision variables. For example, indesigning a materials handling system, management may be ableto specify the number and size of trucks in its fleet or the widthand speed of its belt conveyors. The natural objective of manage-ment is to specify the decision variables so that system perform-ance in terms of the appropriate performance measures is good,preferably “optimum.”

Production systems engineering relies extensively on the useof mathematical/logical system models. System models are estab-lished using knowledge of the performance of individual unitoperations and the rules for interaction among these operations.The model should attempt to capture the essence of systemperformance and should adequately portray changes in perform-ance as values of the decision variables are changed.

An appropriate balance must always be sought with respectto the level of detail incorporated in the model. Too much detailunnecessarily consumes the analyst’s time. It may also hamperthe tractability of obtaining a solution to the model or realizingextended analytical objectives such as mathematical optimiza-tion. Conversely, too little detail may result in a model that isan abstraction of little relevance to the problem at hand.

The immediate utility of the model is that it enables examina-tion and evaluation of alternative values of the decision variables.One can readily discern good options from bad ones. This typi-cally is done at a fraction of the cost of experimenting with thereal world system. The model provides considerable opportunityfor both thoroughness and creativity on the part of the designeror analyst.

It is sometimes possible to explore by mathematical tech-niques all possible specifications of the decision variables and toselect the one that results in the best values for the performancemeasure(s). If one can accomplish this, optimization has beenachieved. However, one often must be content at considering alimited number of alternatives and, therefore, has little assurancethat the optimum solution has been found. The term optimiza-tion is frequently misused, referring to studies where the analystsimply selected the best from a few alternative designs that wereexamined rather than attempting comprehensive exploration ofthe range of the decision variables.

The scope of the models, that is, the extent of the real worldsystem that one attempts to represent explicitly in the systemmodels, is an issue of considerable importance. One should at-tempt to keep the scope as small as possible consistent with theobjectives in studying the system. For example, face operationsmight be the focus without special concern for outby transporta-tion or vice versa. One stands a much better chance in arrivingat a good, useful solution with small, focused problems.

Scope is delineated by system bounds, partitioning the systemunder study from its environment. The internal workings of thesystem, within the system bounds, are said to be endogenous(endogenous variables, endogenous events), whereas external im-pacts on the system are termed exogenous. Typically, manytransactions occur across the system bounds, both outputs fromthe system to the environment and exogenous inputs from theenvironment to the system. It is always assumed that the systemoutputs in no way determine the exogenous inputs.

To clarify the issue of scope and system bounds, consider abelt network in an underground coal mine where shuttle carsare used for face transportation. Assume that spillage problemshave been occurring at transfer points because of insufficient beltcapacity for handling situations where peak loads from several

Case 1: Fixed Feeder Speed

Case 2: Real Time Control of Feeder Speeds

Fig. 9.4.1. Contrast of minimum system bounds for two approachesto control belt spillage

production sections are superimposed. One wishes to adjustspeeds of the section feeders to reduce the incidence and extentof such problems. One approach might be just to reduce speedspermanently somewhat from current levels, spreading the dis-crete loads of material from the shuttle car into longer, thinnerlayers on the belt. Another might be to install belt load sensors,a data transmission network, and some type of intelligent controlsystem to reduce speeds only on an “as needed” basis to preventspills. Minimal system bounds (i.e., system bounds that keep theoverall scope of the model as small as possible) will be contrastedfor rigorous system models that one might construct to studythese two alternative approaches to control of the system.

In the first case, one could set the system bounds at thesection feeder, including the conveyor network in the model butexcluding face operations. One would need to input shuttle carinterarrival times and loads exogenously to the model, but theseinputs would in no way be influenced by outputs of the systemmodel for a given, fixed feeder speed.

For a rigorous model of the second case, however, one wouldhave to broaden the model’s boundaries relative to the first case,explicitly incorporating the face operations in some fashion. Thereason for this is that feeder speed would be varied with time bythe control system in response to circumstances on the beltnetwork. When feeder speed changes, the discharge time of anyshuttle car currently unloading is affected. This, in turn, influ-ences subsequent interarrival times. The face operations and thebelt network are intimately coupled here and, if rigor is desired,should not be modeled independently (Fig. 9.4.1).

The state of a system is defined in the model by the value of acollection of variables sufficient to characterize system operation

CYCLES AND SYSTEMS 785and performance. Static models are solved for a single value ofthe state variables. Dynamic models are solved to obtain a traceof how the state variables change over time or, perhaps, overspace or through a series of stages.

The first test for sufficiency of state variables is that oneshould be able to ascertain performance measures of interestwith respect to making comparisons among alternatives. Forexample, consider a surface mine haulage system where truckswait in line to be loaded by a shovel, travel to the dump site,dump (without having to wait in line), and return to the loadsite. One might be interested in analyzing the rate of productionof this system for a given size of truck fleet. For this purpose,state might be characterized at any point in time by the numberof trucks waiting to be loaded, the status of the loader (idle/busy), and the number of trucks in the process of dumping(ignoring equipment breakdowns). The stated performance vari-able as well as others that might also be of interest, such asaverage haul cycle times, average truck delay times, etc., canobviously be inferred from knowledge of how these variableschange through time.

For dynamic models, such as the example just noted, a sec-ond test of sufficiency is also required. One must be capable ofgenerating the subsequent state of the system given the currentvalue of the state variables, exogenous inputs, and the knownfunctional relationships among the system components. If onecan do this, such a system is referred to as possessing the Marko-vian property. Specifically, this property states that the subse-quent state of the system depends on the prior history of theprocess only through the present state. The next state may begenerated from the model input using known relations describingsingle-step transitions. This criterion, in conjunction with theability to infer performance variables of interest, provides a testto determine whether a given definition of state variables for thesystem is insufficient, sufficient, or superfluous.

With discrete-event dynamic models, the state variables onlychange at a countable number of points in time. A plot of thestate variables vs. time appears as a step function. Using the statevariables mentioned previously, the truck haulage system mightbe modeled as a discrete event system. Events are those occur-rences at discrete points of time that result in the state changes.For example, arrival of a truck to the loading site changes thenumber of trucks waiting to be loaded and may change the statusof the loader unit from idle to busy. Fig. 9.4.2 shows a plot ofthe state variables “queue length” and “loader status” vs. timefor this system.

With continuous dynamic models, the state variables changecontinuously with respect to time. An example where a continu-ous model might be used would be in sizing the capacity of amine drainage sump so that pumping can be shifted to off-peakperiods to reduce power costs. The level of the sump, a statevariable, would change continuously with respect to time as afunction of inflow and outflow rates. As will be noted in thefollowing with respect to a discussion of conveyor network mod-eling, sometimes one can convert from a continuous to a discretemodel by making an appropriate selection of state variables. Ingeneral, discrete-event systems are easier to model than continu-ous systems. Some real world systems may require that a mixeddiscrete/continuous representation be used.

Stochastic models are used where the exogenous input to themodel is random in nature. Note that this input is characterizedin the form of some appropriate type of probability distribution(e.g., a distribution fitted to dump cycle times obtained in a timestudy of haulage operations). The input distributions are known,both their form (e.g., normal, exponential, gamma) and appro-priate parameters. The modeling effort is to see, for a givenspecification of the decision variables, how the system responds

Fig. 9.4.2. Plot of state variables vs. time for a discrete-eventdynamic model.

Fig. 9.4.3. Output from a stochastic modelperformance.

of production system

to this input. Such response will also be stochastic in nature(Fig. 9.4.3). By modeling, one attempts to infer or deduce thedistribution of the response, or important properties of this distri-bution, such as mean levels of the performance variables.

If, on the other hand, the input is not stochastic, the modelis deterministic. In general, deterministic situations are easier tomodel and analyze.

Many times, mean levels of input variables are inserted intoa mathematical expression that represents performance of thesystem such as the equations given for cycle calculations forhaulage systems in Chapter 9.3. For example, one might insertmean trip times, mean spotting times, mean loading cycle times,mean dipper fill ratio, truck volume, and long-term averageunit availability into a mathematical equation representing theproduction rate of a truck/loader system. Note, however, thatprobability theory provides no guarantee that the resulting an-swer would represent the mean level of the performance variable.Such approaches, when randomness is significant, only provideapproximations. It is an expressed role of the techniques discussedin this chapter to eliminate the errors inherent in such approaches

786

Elapsed timesince previousarrival atthe feeder

Fig. 9.4.4. Nonstationary input distribution required to describe shut-tle car arrivals to the feeder.

and establish more accurate and meaningful performance predic-tions.

A model where the exogenous input and internal relation-ships do not vary systematically over time may yield what iscalled a steady-state solution. All static models are steady state.Such a solution represents an equilibrium behavior reflectinglong-term performance of the system. A requirement for a sto-chastic model to provide a steady-state solution is that the pa-rameters of the input distributions are held constant.

Note that if the the foregoing condition is not true, the inputis said to be nonstationary and the transient behavior of thesystem must be studied. Although one might think that study oftransient behavior is more difficult than steady state, often thereverse is true. In simulation of production systems, particularshort periods of interest in analysis of transient behavior canoften be defined. For instance, performance of a rail transportsystem might be studied only during the hour around shiftchanges when demands on the system are at their peak (assumingboth men and ore are being transported simultaneously). Themodel might appropriately focus on transient behavior for thisinterval of time.

Input distributions to many mining models are nonstation-ary. For instance, the input to the belt network model discussedpreviously would systematically change as the mining machineproceeds through its cut sequence. The time between consecutiveshuttle car arrivals should reflect this underlying cycle. Whencuts are close to the feeder, interarrival times will be small. Whencuts are far from the feeder, they will be large. If rigor is desired,interarrivals should not be taken as independent draws from aprobability distribution since the influence of cut sequence onthe sequence of interarrivals will be lost (Fig. 9.4.4).

The concepts previously discussed are useful in characteriz-ing a system, selecting an appropriate modeling technique, de-termining the proper structure of the model, and in assessing theoutput or results produced by the model. The chapter continueswith an overview of techniques that may be employed for detailedperformance analysis of integrated systems of mine unit opera-tions.

9.4.3 SIMULATION OF MINE PRODUCTIONSYSTEMS

Discrete-event and continuous simulation are the modelingtechniques that have been most widely applied in mine produc-tion systems engineering for the detailed analysis of equipmentinteraction. There are several good reasons for this. Most impor-tantly, these approaches can readily accommodate the strongdynamic and stochastic character of these systems. Further,great levels of detail can readily be incorporated in simulationmodels. If properly carried out, such detail can insure validrepresentations of the real system without undesirable abstrac-tions.

The technique is also one of the easiest to learn. The mainprerequisites are a modest degree of computer literacy and areasonably strong background in probability and statistics. Con-structing the models is usually a conceptually easy process(though perhaps time consuming in some cases). Analysis of theoutput in proper scientific fashion is the more technically diffi-cult issue.

9.4.3.1 Nature of Simulation Models

Simulation models are distinguished from other systemsmodels in that the basis for model construction and solution isthe run. A run is used to generate an artificial history of theprocess, specifying how state variables change either throughtime or through a sequence of stages. These histories, in wholeor in part, provide information useful to the analysis of systemperformance.

To understand what is meant by a run and why the idea isso useful in constructing many types of process models, thefollowing example will be considered. A number of boxes ofdifferent sizes, shapes, and weights are to be loaded on a cargoplane. The center of gravity of the boxes is of concern and someloading pattern that locates the center of gravity in a positionacceptable for stable flying needs to be identified.

Generating a candidate loading pattern in a single step is amentally forbidding task. However, if the task is broken into asequence of stages, it becomes much less intimidating. For in-stance, a candidate loading pattern might be generated step bystep using a three-dimensional graphics package, putting onebox alongside or on top of others as one would if the boxes werebeing physically stacked. This is an example of using a run toconstruct a candidate solution to the model. In this example,only the terminal state of the run is of interest; but in many casesthe entire history of the process evolution is of value.

The advantage of this approach to systems modeling is thatit is often quite easy to specify the mechanics of the run. Onecan readily express rules for stacking boxes one atop the others.Given these rules, one can arrive at a candidate loading patternby building up the pattern sequentially. However, given a collec-tion of boxes of assorted weights, sizes, and shapes, a feasibleloading pattern could not be deduced in a single step. In short,the mechanism of a run can generate information useful to thesolution of a problem when attempts to summarize system be-havior, via deductive mathematical analysis, cannot be madefruitful. However, as will be seen later in this chapter, the infor-mation provided by a run is often of weaker nature than thatwhich might be obtained if analytical techniques can be appliedto the problem.

Note that many models called simulations are misnamed.For example, one often says that a chemical process, a coalpreparation flowsheet, or a mine ventilation network has beensimulated. However, if steady state flows through the system are

CYCLES AND SYSTEMS 787

Fig. 9.4.5. System structure for truck haulage example.

being computed, one is really solving a model expressed as asystem of equations in each of these cases. A run has not beenexecuted, generating an artificial history of system behavior. Thismisnomer arises from the fact that many of the equation-solvingtechniques used for these models are similar to the run mech-anism.

9.4.3.2 How Simulation Models Are Structured

Discrete-event Models: In the next few paragraphs a simpleexample is introduced to help the reader gain some appreciationfor discrete-event simulation. Consider a situation where twoloading shovels are serviced by a pooled fleet of four identicaltrucks (Fig. 9.4.5). Trucks wait in line at a shovel, first-come,first-served, if they arrive and find the shovel busy loading an-other truck. The material from each loading shovel is dumpedat a distinct site, but trucks need not wait for trucks ahead ofthem to dump.

A dispatcher continuously keeps track of the trucks, andwhen a truck has finished dumping, it is assigned to returnto one of the two shovels depending on the current situation.Specifically, assume the dispatcher keeps track of the number oftrucks waiting in line at each shovel and the number in transitto that shovel from the dump site (previously dispatched). Hecalls this number “assigned transport capacity.” He sends anytruck that has just completed dumping to the shovel with thelower value of assigned transport capacity.

In evaluating system performance, assume one is interestedin the production capacity of the system, that is, the amount ofmaterial dumped per unit time at each of the two dump sites,the utilization of each of the two shovels, and the amount oftime the trucks spend waiting at the shovels.

In constructing a simulation model for this system, the fol-lowing input data for the model might be established:

1. Combined time to spot and load a truck at the shovel.2. Time to transport the loaded truck between each shovel

and its respective dump site.3. Time to transport the empty truck from each dump site

to either loading shovel.These data might come from time studies or from other

sources (e.g., determination of haul cycle times using rimpullcurves and data descriptive of haul road characteristics). Any orall of the input variables might be described as distributionsrather than constant values. Depending on the detailed objectivesof the study and needs for accuracy, it might be more appropriateto break the aggregate truck spotting/loading time into spottingand a sequence of swing cycles. But things will be kept simplehere.

Fig. 9.4.6. Mechanism of a simulation model.

A set of state variables for the system might include:1. Each shovel’s operating status (idle or busy).2. Assigned transport capacity (ATC) for each shovel.3. The number of trucks waiting in line at each shovel.The state variables for a given simulation are not unique;

alternatives often exist. Moreover, the state variables employeddepend on the objectives of the study. Progressing through thesection, it should become clear to the reader that the shoveloperating status is necessary as a state variable here only becauseof the interest in utilization of the shovels.

In constructing the model, the objective is to generate a run,that is, an artificial history of the behavior of the loading/haulagesystem as it progresses forward in time.

In general terms, the overall operation of a simulation modelis described in Fig. 9.4.6. The initial conditions provide the start-ing point. They include, among other items, a specification ofthe initial state of the system. In the example, one might specifythat one truck is waiting in line at each loader, loading by theshovel has just started for the second truck, ATC is two, andboth shovels are busy. Time is subsequently advanced and stateis updated as appropriate. Next, a check is made to see if it istime to stop the run. This might be ascertained by checking thecurrent state with some terminating condition or by checking tosee if the simulated time exceeds some predetermined stoppingtime specified by the analyst. If not, time is advanced and stateis updated again as shown in the figure.

The key issue is time advance. Changes in the values of thestate variables for the example only occur at discrete points intime. In such a situation, it is clear that one knows the behaviorof the system completely if a sequence of “snapshots” of thesystem at those points in time where state changes can be gener-ated. For generating a run efficiently, time should advance fromthe time of occurrence of one event to the time of occurrence ofthe next event.

Note, however, that some simulation models for mining sys-tems advance time in fixed increments of short duration. Eventsand state changes may or may not occur at the end of theseincrements. Though appropriate for systems where continuousstate variables are required for the analysis, for most discrete-event simulations, this technique loses not only in speed of execu-tionas it

but also in accuracy since state is notwould in the real world, at arbitrary

permitted to change,points in time.

788 MINING ENGINEERING HANDBOOK

L: Load Truck TF: Tram Full TE: Tram Empty

Fig. 9.4.7. Possible run for truck/shovel example.

In discrete-event simulation, those input variables that spec-ify a time duration are called activities. For the example, all threeinputs—spotting/loading time, transport empty time, transportfull time—are activities. Fig. 9.4.7 shows how the state variablesmight change with time for an example run of the truck haulagesystem. Referring to this figure, one sees that:

1. All events (an event corresponds to any change in thevalue of any of the state variables) occur upon the terminationof activities. For instance, whenever a “transport empty” activityis terminated, an event occurs where the queue length increasesby one and, if not already in the busy mode, shovel status changesto busy.

2. Upon termination of an activity, one might, using theexternal input to the model, be able to forecast the terminationof some future activity. If this can be done, a point in time whensome future event will occur has been identified. For instance,when the truck loading activity is finished, one can forecast,using the model input, when that particular truck will finishdumping. If “transport loaded” times are random, a typical time

Fig. 9.4.8. Flowchart for the event scheduling approach to discrete-event simulation and corresponding program structure.

that follows the input distribution of these times would have tobe “drawn” from this distribution. Nonetheless, the forecast canbe made just using the input to the model.

Note that a future event cannot always be predicted upontermination of an activity. For instance, if a truck arrives andfinds the shovel busy loading another truck, no activities areinitiated, and no future events can be forecast. If the truck arrivesand finds the shovel idle, a truck loading activity begins and themodel input can be used to forecast when it will end. Thisillustrates that whether or not some future event can be forecastwhen the current event occurs is a function of the current stateof the system.

The names for events are usually derived from the activitiesused to predict their occurrence. In the example, there are threeevents: (1) truck arrival at a shovel, (2) completion of truckloading at a shovel, and (3) completion of truck dumping at adump site.

Now a position has been reached where it is possible to seehow a computer might be programmed to execute a simulationrun via what is known as the event scheduling approach. This isone of two major general purpose approaches for constructingdiscrete-event simulation models; the other is discussed later.Fig. 9.4.8 shows an overall flowchart for this approach. As notedpreviously, the initial conditions define the initial state of thesystem. In addition, they also give a few events for priming themodel. For the example, if the initial state described above wereto be used, a “completion of truck loading” event would have to

CYCLES AND SYSTEMS 789Table 9.4.1. Event Logic Tables for the Shovel Truck

Problem

be specified for each shovel. In general, one priming event shouldbe specified for each ongoing activity as the simulation runbegins.

The priming events, both their identity and time of occur-rence, are stored on the future event list (FEL). The events onthis list are kept in order from earliest to latest. The computerthen removes the most imminent event from the list, advancessimulated time to the time of occurrence of that event and exe-cutes an event subroutine (there is one for each type of event).The event subroutine does two things:

1. It updates state.2. It forecasts any new events due to activities initiated at

the time of the current event and puts these new events on theFEL.

The results of both of these operations are determined strictlyby the event type and the current value of the state variablesusing known functional relationships regarding the behavior ofthe system. No other information is required. Table 9.4.1 givesevent logic tables for the three events of the example. These tableseffectively describe the action of the event subroutines that onewould incorporate with the event scheduling algorithm shownpreviously in Fig. 9.4.8 when coding the model.

Note that at any point in time, the content of the FEL isdetermined by the ongoing activities. A new event placed on theFEL would not necessarily go at the bottom of the list. Forexample, when truck 3 finished loading at shovel 1, its dumpcompletion event would be placed on the FEL. While it is travel-ing loaded to the dump site, truck 4 may have begun loading atshovel 2. Its load completion event would then be placed on theFEL, and it may be placed ahead of the dump completion eventfor truck 3. Further, in general, events may be removed fromthe FEL before they occur. This would happen if activities existthat preempt ongoing activities.

Two new concepts, entities and attributes, useful for codingsimulation models, are now introduced. Entities correspond tothose dynamic objects in the physical system that require explicitrepresentation in the model. In the example, entities might beused to represent the trucks and the shovels. Attributes areproperties of a given entity, for example the operational statusof the shovel, the size of the material load in a truck.

In the computer program, entities are often represented asrecords and order is maintained using files. For example, a sortedfirst-in, first-out (FIFO) file of records representing truck entitiesmight be used for the waiting lines at each of the shovels. Whenan end of loading event occurs, the top record of this list isremoved to identify the next truck to be loaded by the shovel.Discrete-event simulation programs have much in common withstandard data processing routines. Good codes (i.e., codes thatare efficient in their use of computer memory and in speed ofexecution) written from scratch in a general purpose languagesuch as FORTRAN or Pascal require the use of list processingtechniques and search algorithms to handle properly dynamicrepresentations of the system using entities and attributes.

The event scheduling approach, discussed previously, is pri-marily an approach for organizing the simulation program. Aquite different organization of simulation programs called theprocess interaction approach will now be discussed. Here codingis based on what are called process routines. One process routineis written for each type of entity in the system. In the example,two process routines would exist, one for truck entities and onefor shovel entities.

The process routine describes everything that can happen tothe entity as it passes sequentially through the system. Fig. 9.4.9gives a process routine for the truck entities in the example. Tounderstand how a process interaction simulation program works,it is useful to imagine that each entity is given, as it enters thesystem, a copy of the process routine that corresponds to thetype of entity it happens to be. The entity then executes theroutine sequentially in a fashion described below until it exitsthe system or the run otherwise is terminated.

The entity’s process routine is activated. It starts at somepoint in the routine and executes as many steps in the routine aspossible with zero time advance. These steps might change thevalue of global state variables, change the value of attributes ofthe entity, or schedule future events and put them on the FEL.Note that the FEL is common to both the event scheduling andprocess interaction approaches. Both are variable time incrementtechniques that advance the clock from the time of one event tothe next.

Execution of the routine is temporarily suspended once timeadvance is required for the entity to take an additional step.These stop points correspond to the blocks before the dashedconnection lines in the flowchart of Fig. 9.4.9. Note that someof the suspensions correspond to the beginning of activities. Herea future event will be placed on the FEL. Initiation of truckloading, block 6, is an example of this. Other stops correspondto indefinite delays, for example, wait in the queue at the shoveluntil removed, block 4.


Once the process interaction routine stops, the process rou-tines for other entities may be activated to see if they can alsobe advanced with zero time delay. In the example, a shovelentity’s process routine would at some point in time remove aparticular truck entity from the queue and subsequently stopexecution. Before time advances, execution of that truck’s pro-cess routine would resume from block 5 in Fig. 9.4.9.

Once all of the process routines have been advanced as faras possible with zero time advance, the most imminent event isremoved from the FEL and time is advanced to the time ofoccurrence of that event. This corresponds to conclusion of anactivity, and it reactivates the process routine of the entity thatscheduled the event. The process routine of that entity is thenexecuted sequentially starting from the block following the previ-ous stop point.

If one writes a simulation model in a general programminglanguage such as FORTRAN, the event scheduling approachshould be used rather than process interaction. If the programwriter must take care of all details, process interaction routinesbecome very complex and the organization of the code is notnatural. However, most of the special purpose simulation lan-guages, including all of the more recent languages, are based onthe process interaction approach.

When writing a program in these languages, one effectivelydefines a process interaction routine for the system entities. How-ever, the statements available are at a macro level; a single state-ment may take care of many detailed operations automatically.These statements are geared to common situations that ariseagain and again in simulation models, and they are very power-ful. Also some complete process interaction routines for commonsituations are built into these languages. In the example problem,one probably would not have to write any code for the shovel’sprocess routine, just one for the trucks.

With these macro statements, writing a process interactionroutine is often quite natural and is typically much less involvedthan writing an event routine for the event scheduling approach.Table 9.4.2 gives a process interaction routine for the example

Fig. 9.4.9. Process routine for truck entity.

problem written in the SIMAN simulation language. Note thatonly 18 lines of code were required for this model, and one neednot explicitly write such a routine for the shovel. The use ofsimulation languages in mine systems simulation is discussed inmore detail in a later section.

Continuous Simulation Models: Continuous simulation dif-fers from discrete-event simulation in that the state variables donot change strictly at discrete points in time. Rather, they changecontinuously with respect to time. Simulation is not required ifa closed-form relation that gives the value of the state variable forany time and any specification of initial state can be established.However, often one can only specify the rate of change of thestate variable with respect to time as a function of the currentstate.

For instance, from basic mechanics, one can specify a differ-ential equation relating the state variable x, position of the vehi-cle, to equipment performance data that describe acceleration av

of the vehicle:

(9.4.1)

If av were a constant, it would be simple to establish a closed-form expression of x as a function of time and initial position.However, av is determined by the the rimpull characteristic (ameasure of available force for acceleration) and the motion resist-ance of the vehicle, both of which, for a given vehicle and op-erating conditions, change as a function of the vehicle’s velocity(see 9.4.2.4).

If the rate of change of the state variable is described as afirst-order ordinary differential equation (i.e., the highest-orderderivative is one, and all derivatives are taken with respect tothe same variable, e.g., time), then a first-order Taylor’s seriesexpansion of x about t yields:

(9.4.2)

Ignoring higher order terms, this expansion suggests a simple

CYCLES AND SYSTEMS

Table 9.4.2. SIMAN Code for Truck/Shovel Simulation

791

792 MINING ENGINEERING HANDBOOKnumerical approach to computing x(t). Start with x(t0), the initialstate at time t0, then, ignoring the higher-order terms, use theexpression and the expression for dx/dt as a function of the statevariables to estimate x(t0 + ∆t) for some small increment ∆t.Repeat this procedure to estimate x(t0 + 2∆ t), x(t0 + 3∆ t), etc.The magnitude of ∆t is called the step size. The error in comput-ing x for a single step is given by the unknown term O( ∆ t 2),which can be made small by selecting a small step size.

This approach is seldom used directly because, relative toother available approaches, errors are large and computationalefficiency is poor. However, this illustrates the basic idea behinda class of algorithms called Runge-Kutta methods that are rou-tinely applied for this type of application. With minor extensions,these techniques can be applied to higher-order ordinary differen-tial equations like the second-order one given previously to de-scribe vehicle motion.

9.4.3.3 Coding Options for Mine SimulationModels

One has three options for establishing a model for use in mineproduction systems analysis: (1) write the code from scratch ina general purpose programming language, (2) select an appro-priate and existing, often commercial, mining simulation soft-ware package, or (3) write the code from scratch in a simulationlanguage. The issues one should consider in selecting fromamong these alternatives are now briefly discussed.

The first option is probably one that should only be consid-ered by research institutions or engineering firms. The justifica-tion for considering this option is that a general purpose languageoffers complete flexibility in constructing the model. In contrast,the other two options might be constrained in the type of processthey can model and/or in the efficiency with which they canexecute a particular type of simulation run. These constraints donot exist for a general purpose language.

However, this option is often a time-consuming one. Thesemodels typically involve thousands of line of code and have, inthe past, taken months, even years, to code. One should becomevery familiar with list-processing techniques and data structuresprior to attempting such programming. Note that executionspeed for models written in a general purpose language should,if proper data processing routines are employed, at least equalthat achieved by the simulation languages. Often these speedscan be exceeded because the situation being modeled may allowuse of more specialized routines than those implemented by thesimulation language.

If one elects to code in FORTRAN, one might consider useof the GASP language. Though often referred to as a simulationlanguage, GASP is a collection of FORTRAN subroutines thatcan be used to organize filing structure for the program, handlefiling operations, handle input and output, and provide a clock-advance mechanism. The program would be coded using eventscheduling. Several other simulation language packages also of-fer such utility routines for user-written FORTRAN codes.

However, writing simulation models in general languagesother than FORTRAN that have better data structures anddynamic storage allocation (e.g., Pascal or C) is often morenatural. FORTRAN is only prominent in simulation because oftradition, not because of any special suitability of the languageitself.

Numerous simulation software packages exist for mine pro-duction systems, such as conveyor network models, truck/shovelmodels, surface mine simulators, continuous mining section sim-ulators, longwall simulators, etc. Some of the more prominent ofthese packages are discussed in the next segment of this chapter.

These packages provide the core routines necessary for simu-lating these types of operations, and they accept alternative userspecifications on system structure. The main advantage of suchpackages is that the user need not generate the code. Further,some of these packages have an impressive range of capability.For example, the General Purpose Surface Mining Simulator(GPSMS) package incorporates detailed ore body and spatialdescription of the mine along with capability to simulate a widerange of production operations and their interaction on thisproperty (Albert, 1989).

There are some limitations of these packages, however, thatshould also be kept in mind. Input requirements can be extensiveand learning these requirements can be quite time consuming.The better packages have given considerable attention to simpli-fying the user interface. For packages with broad scope, one maynot be interested in using all this capability, but the packagemay, regardless, require extensive input description. Many of theexisting packages use discrete increment time advance. Thoughnecessary for simulating systems with continuous state variables,this approach leads to very slow execution times and inaccuracyfor discrete-event simulations, and is inappropriate for some ofthe systems modeled.

Perhaps the most serious limitation of this class of softwareis that it is nearly impossible for the package developer to foreseeall the systems alternatives that users might like to model. Thescope of available options may not meet user needs. Moreover,since the software is written in general purpose languages withthousands of lines of code, major modifications of the packageto accommodate user needs, other than by the original developer,is often a forbidding task.

The third option is the use of simulation languages. Here theuser must write his own code. However, because of the powerfulnature of the statements of these languages, the amount of coderequired to write the model is typically dramatically reducedrelative to that required when writing the model in a generalpurpose language. This is especially true when the process inter-action approach is employed.

For instance, a simulation model was developed by the au-thor of a surface mine where a truck fleet serves as an intermedi-ate transport link between a pair of loading shovels and twoskip hoists. Features addressed in the model included a detaileddescription of the truck loading cycle, haul road segmentationwith different operating conditions, pooled use of the truck fleetwith special dispatch rules, modeling of truck failures, use ofstandby trucks that are activated when breakdowns occur, in-terfacing with a fixed capacity bunker at the hoist stations withspecial control logic for skip loading, and shift start-up andshutdown routines. Using a simulation language, a model forthis system was written with fewer than 130 lines of code. Thisis substantially less than 5% of the amount of code that wouldbe required to construct the same model using a general purposeprogramming language.

The proficient programmer in these languages can writereasonably complex models in a matter of hours or days, notmonths. In the course of developing the code, the programmerbecomes intimately familiar with how the process is being mod-eled. The level of model validity can be judged better relative tojudgments made when using a package developed by others.Most importantly, the programmer has considerable flexibilityin customizing the model and the output it provides to suit needsand analytical objectives.

Simulation languages possess what is called a world view.This reflects the scope of the macro-statements used in the modeland the type of real-world processes to which they are oriented.This is an important factor to consider since it influences theease with which one might model a given situation or the ability

CYCLES AND SYSTEMS 793to model it at all using the language. Many simulation languagesare oriented toward modeling queueing systems. The SIMANlanguage, developed for manufacturing applications, has a num-ber of features useful for mine systems modeling. These includematerial handling modules for discrete vehicle and conveyortransport and special features for accommodating spatial aspectsof the system. Other languages have recently started to introducesuch features.

It is not likely that one will find the world view of mostsimulation languages too restrictive or awkward for mining ap-plications; most situations can be modeled using these languages.General constructs in the language can usually be combined tomodel specialized processes when the specialized constructs areabsent. Differences may exist in the facility with which varioussituations can be modeled. Moreover, to overcome restrictionsin scope, most of the modern simulation languages allow theuser to interface routines written in a general purpose languagewith the routines written in the simulation language. One canthereby accomplish operations that the language cannot performitself directly. At least in principle, one is not constrained in thescope of processes that may be modeled if user-defined routinescan be integrated with the code.

If possible, it is suggested that someone interested in model-ing a particular process contact users of the various simulationlanguages to see if example codes they have developed for variousmining applications are available. Because of their brevity, thesecodes can be readily “digested” by individuals familiar with thesimulation language. These examples can aid the learning pro-cess and greatly speed development of a custom model for aparticular application.

The major simulation languages currently available includeGPSS (GPSS/PC, GPSS/H), SLAM, SIMAN, and SIM-SCRIPT II. Since these languages and their supporting softwarepackages have been undergoing extensive updating and improve-ments in recent years and these trends are likely to continue forthe foreseeable future, detailed comparisons of features will notbe undertaken here. The following issues, however, should beconsidered when purchasing a license for a simulation language.

1. Availability of the package in a PC version. The computingpower of today’s personal computers is adequate for many (butcertainly not all) applications. OS/2 packages that are now be-coming available will increase the size of model that can beinvestigated using a microcomputer.

2. Available modeling orientations supported by the language.Preferably the language should support process interaction,event scheduling, and continuous simulation. Process interactionis typically the main approach employed for discrete-event simu-lation using the language. User-written event routines may oftenbe interfaced with the process routines to increase flexibility andscope of the language; the package will typically have utilitysubroutines available to the user for creating these programs. Ifmodeling of systems with continuous state variables is supported,mixed continuous/discrete systems can be represented. Detailedexamination of the approach used for interfacing user-writtenroutines and for mixing discrete/continuous representationsshould be undertaken if one believes there will be need to usethese capabilities.

3. Special application orientations for the language. Somelanguages are directed especially toward queuing systems simula-tions, which is a major aspect of many real-world simulations,including mining systems (see 9.4.5). Some packages have builtin features to make the simulation of materials handling systemseasy.

4. Output analysis software. Custom reporting capabilityshould be provided, and it should be easy to gather a wide rangeof system performance statistics. Many packages enable one to

create files with detailed performance data generated duringa run and include rather sophisticated statistical software foranalyses using these data.

5. Capability of animation of the simulation run. This in-cludes a graphics interface to the simulation package that pro-vides a dynamic display of the system state using symbolic repre-sentations that the user designs. Effectively, it provides anopportunity to obtain a dynamic, global view of system operationat a faster or slower pace than could be observed in the realworld. The importance of this capability depends on user needs.It may provide a means for gaining insights into system operationand can be an effective communication tool when presentingresults to management or clients. At present, costs for animationcapability can be high.

6. Availability of good documentation with example programsto illustrate modeling approaches. A well-written manual withillustrative examples can greatly speed the process of learningthe code.

7. Quality of debugging facilities. The language packageshould have convenient facilities for debugging with abilities togenerate program traces, set break points, etc. Debugging effortfor programs in a simulation language is, relative to typicalcomputer programming applications, slightly disproportionateto the size of the programs because of the powerful nature of thestatements. Animation capability can also aid the debuggingprocess.

9.4.3.4 Using the Models in Systems Analysis

The capability of simulation models to accommodate inputsthat are described as random variables is most useful. Miningengineers are well aware of the ramifications such randomnesshas on the performance of real-world mine production systems.One might attempt to answer questions such as

1. How do truck breakdown rates and repair team perform-ance influence the preferred size of a truck fleet?

2. How do different belt sizes and speeds influence theamount of spilled material at a transfer point, given the stochasticpatterns of loaded material on the intersecting belts?

3. How much increased production can be expected if abunker of a particular size is installed in the belt network toprovide a storage buffer when outby belts fail?

4. What are the implications of the randomness in truckloading and haulage cycle times on the way a dispatcher shouldcontrol the truck fleet so that production rate is maximized andblend qualities are maintained?

In answering questions such as these, there is a key issueto recognize (an issue that, unfortunately, is often ignored bypractitioners). If the input variables are random variables, theperformance variable(s) also is a random variable. The propergoal, therefore, is to know the probability distribution for theperformance variable as a function of the input variables andspecification of the decision variables.

However, the simulation model, because it is based on a runmechanism, does not give us this distribution directly. Rather,a single run gives one possible realization of this process. Forexample, it describes the way production might go for a particu-lar shift. One must use multiple and/or extended runs and statis-tical inference to infer properties of the distribution of the per-formance variable (e.g., the mean level of the variable). Drawingconclusions on performance of a system from a single, shortsimulation run can be as misleading as management using, say,one shift’s production figures for evaluating a field-implementedsystem.

The first issue of output analysis is to establish a clear defini-tion of the performance variable(s) of interest. There is usually

794 MINING ENGINEERING HANDBOOKopportunity to collect observations on a large number of vari-ables of interest during the simulation run. In the truck haulagemodel of 9.4.3.2, one might be interested in utilization of eachloader, the average waiting time of the truck in the loader queue,the average production rate from each loader, the average totalcycle time for the trucks, and perhaps others. Although any orall of these data are readily obtained from a simulation run ofthis system model, one is strongly discouraged from consideringmore than one or two variables in formal comparisons betweenalternative specifications of the decision variables.

There are two reasons for this statement. First, as will be-come more clear in the discussion that follows, there is uncer-tainty involved in any estimate of performance from a stochasticsimulation run. If one wants to ascertain the value of severalperformance variables with high accuracy, often an extremeamount of computer time will be required.

Second, one is faced with difficulties in comparing alterna-tive systems when multiple performance criteria are involved. Inthe example, if system A has higher loader utilization but higheraverage total truck cycle time than system B, how does one tradeoff a unit of loader utilization vs. a unit of total truck cycletime to decide which system is preferred? Multi-criteria decisionmaking, that is, ranking alternatives while considering multipleperformance variables of distinctly different natures, is an areaof active research interest. However, most results from this fieldare not yet considered very practical.

It should be noted that one can often aggregate many per-formance variables in terms of their contribution to cost or profitfrom the operation. In the truck haulage example, a revenuemight be associated with each ton of ore produced, a cost mightbe imposed for each hour the vehicle is operated and for eachfailure incident. In turn, a single criterion such as net profitbecomes the performance variable of interest in comparing alter-native system design or control options.

Other criteria might become performance constraints thatall system designs must satisfy if they are to be considered truecandidates for implementation. For instance, one might wish toselect the production system alternative that produces at thelowest cost per ton subject to the constraint that the alternativeproduces at an minimum average rate of X tons per month. Herethe performance variable “production rate” is not used directlyin comparing alternatives. One just ensures that all candidatesproduce at the minimum acceptable level.

Though it is strongly encouraged that the analyst establisha single performance criterion for formally comparing systemalternatives, this is not to say that one should ignore the othercriteria. Ad hoc, intuitive experiments with a simulation modelcan often provide considerable insight into system operation andoften suggests useful design and control options. Within reason,such experimentation is strongly encouraged. Indeed, it is herewhere the animation of the simulation run can often serve auseful role in the analysis. Nonetheless, the study should con-clude with formal, scientific comparisons.

A final point must be emphasized regarding selection ofperformance criteria. Most of the literature discusses basing sys-tem comparisons on the value of the mean or average level ofthe performance variable (e.g., mean rate of production, meanavailability). The mean is often, but not always, an appropriatebasis for comparisons. The mean is so useful because it “boilsdown” the entire distribution to a single value. This value canbe directly used in making comparisons in cases where totalrewards or costs are proportional to the accumulated value ofthe performance variable over repeated or extended runs of thesystem. For example, total production revenues are likely pro-portional to the sum of individual tonnages produced during

Fig. 9.4.10. Performance variable of interest for conveyorspillage example.

future shifts. Here the mean is a reasonable basis for comparingtwo or more system designs.

However, often other properties of the distribution of theperformance variable, such as its variance, are also of interest.Consider the following example.

In simulating material flows in a conveyor network, flowrate (cubic yards or cubic meters per hour) at each of the transferpoints might be included among the system state variables. Beltwidth effects on flow rate at some critical intersection in themodel might not be explicitly incorporated in the model (a fixedconveyor width would simply truncate the flow rate when itexceeds some fixed level). Rather, one might attempt to size thebelt, ex post facto, once the model output has been obtained.Here one is using what some might call a functional model—amodel where unit sizing or capacity effects on its operation areignored. Such models are often appropriate when designing asystem since unit size is typically a decision variable.

What kind of performance variable would be of interest here?One that comes to mind is that time-persistent statistics mightbe gathered on the flow rate variable for the critical intersection.These data could be used, for instance, to generate a histogram(Fig. 9.4.10), where the magnitude of the vertical bars is equalto the proportion of time the flow rate is at any particular ob-served value. This histogram, assuming it accurately portrayslong-run performance, could be used to provide information onexpected spillage for any particular belt width. One would simplytruncate the distribution at some fixed capacity level correspond-ing to a particular belt size; spillage rate would be proportionalto the area above the point of truncation.

Here it is clear that one would like to know the entire distri-bution of the performance variable. The information providedby the mean flow rate is insufficient for and, in fact, has littlerelevance to the needs of this analysis.

As noted previously, simulation output does not give thedistribution of the performance variable directly. Rather, thisdistribution, or properties of the distribution, must be inferredfrom data generated during a run using statistical techniques.

There are some interesting complications that arise whenapplying statistical methods to simulation output. Consideragain the truck haulage example. Assume that truck delay timein the loader queue is the primary performance variable of inter-est. It is quite clear that the delay times of individual trucks willbe related to one another. If the delay time of one truck is long,it is very likely that the delay of the next truck will also be long.Similarly, if the delay for one truck is short, the delay of the nexttruck is also likely to be short. This illustrates a key feature ofsimulation output. Individual observations of output variablesare likely to be correlated (positive correlation in this case).Classical methods of statistical inference that are based on as-sumptions that successive observations are independent and fol-low the same distribution, that is, they are independent and

CYCLES AND SYSTEMS 795identically distributed random variables (IIDRV), do not applyto simulation output.

Two distinct cases can be identified for analysis of output:terminating simulations and steady-state simulations. Such dis-tinction arises not from the nature of the simulated process itselfbut from the nature of the performance variable of interest tothe analyst when evaluating that process. With terminating simu-lations, the desired measure of performance is defined relativeto a specific interval of simulated time. With steady state simula-tion, the desired measure of performance is defined relative tothe limiting distribution of the variable as simulated time goesto infinity.

As an example of a terminating simulation, one might beinterested in the volume of material moved for a production shiftin the truck haulage example. A terminating simulation musthave well-defined start-up conditions and terminating condi-tions. In the example, one might start as previously described in9.4.3.2. One might terminate using a rule such that if a truckdumps its material within 10 min of quitting time, it returns tothe service area.

Often one might be interested in system performance onlyduring periods of “peak demands” on the system. For example,for some performance variable, one might simulate a track haul-age system only during the period around shift changes, say,from 3 pm to 5 pm. Such simulations are also terminating;however, definition of initial conditions may be more difficultthan in the previous example since activities of the system thatare in progress when the simulation run begins may not beknown and might be random.

As an example of a steady-state simulation, one might study,using a simulation model that accommodates unit failures, theavailability of the furthest inby face conveyors as influenced bythe size and location of surge storage bins in the belt network.If contemplating incorporating such buffer capacity in the net-work, one would certainly want to know implications on mineproduction over an extended time horizon. However, there areno natural starting or terminating conditions for consideringperformance of this system. Steady-state simulations are fre-quently employed where performance measures are long-term innature and where there are no natural events to terminate therun.

An inherent characteristic of steady-state simulation is thatthe initial state of the system influences the early observationsof the performance variable. For instance, in the truck haulageexample, assume that for some reason one is interested in thesteady state value of the mean delay of the trucks at the loaderqueue. The simulation might be started with all trucks queuedup at the two loaders. Under such circumstances, the early delayswill be longer than they typically would be. If data from theearly portion of the run are used in estimating the mean steady-state delay, the estimate will be biased high because of these longdelays. Any other starting condition is also arbitrary and willintroduce some type of bias. This is called initialization bias, andit should be dealt with carefully.

The distributions for the exogenous input variables forsteady-state simulations must remain constant throughout thesimulation run. In contrast, terminating simulations are by na-ture transient. These distributions may change over simulatedtime. Moreover, no effort is made to eliminate the effect of initialstate on the performance observations. In fact, one wants toexplicitly capture the effects of initial state on performance. It isconsidered a fundamental aspect of the process under study.

Terminating simulations are much easier to analyze thansteady-state simulations. Assume interest is focused on the meanvalue of some performance variable. The analytical procedure isto make multiple runs of the simulation model, each spanning

the performance period of interest. Each of these runs, or replica-tions, would use a different sequence of random numbers. Thenthe mean value of performance variable, observed for eachindividual replication ii = 1,2, . . . , r, where r is the total numberof replications, is calculated. Though the individual observationsof the performance variable within a replication are not statisti-cally independent, the i = 1,2, . . . , r, since they are generatedusing independent random number streams, clearly may betreated as IIDRV, and classical statistical techniques may beapplied. Since the are averages, they will tend to be normallydistributed in many applications. (There are central limit theo-rems for correlated random variables.) The data can be used tocompute a confidence interval for the performance interval asfollows. Let

(9.4.3)

(9.4.4)

Then compute a (100 – a)% confidence interval for the meanvalue of the performance variable as

(9.4.5)

What has been discussed is a procedure that has high proba-bility, specifically 100 – a, of constructing an interval thatcontains the unknown value of Preferably, the interval willbe small in width, but this depends on the innate variability ofX. One can overcome wide intervals by increasing the r, as isevident from the previous formulas. In using this approach tocompute a confidence interval, one does not say that is con-tained in the interval with probability 1 – a. The probabilitystatement is about the procedure. A probability statement about

is inappropriate since it is a constant (though unknown), nota random variable.

Fig. 9.4.11 illustrates two major approaches for characteriz-ing the mean value of a performance variable in a steady-statesimulation. The first illustrated approach is similar to that usedin terminating simulations. One makes several replications ofthe model using different random number sequences. Like theterminating case, the mean level for each replication will beIIDRV. However, since interest is in steady-state performance,observations from the early part of each run are eliminated toprevent these observations from biasing the estimator.

The second approach is called the batch approach. Ratherthan making several replications, a single long run is made. Thislong run is divided into a number of batches. For example, if4000 truck delays are observed in the simulation run, the runmight be divided into 40 batches of 100 observations each. (Thereis little incentive to ever create more than 40 batches.) Althoughconsecutive individual observations of the performance variablesare correlated, intuition suggests that if the batches are bigenough, the means for each batch will tend to be uncorrelated.This is frequently observed to be true. These means will alsotend to be normally distributed. The batch observations mightthereby be treated as IIDRV.


batch 1 batch 2 batch 3 batch r

Fig. 9.4.11. Two approaches to estimating a performancefor a steady-state simulation.

variable

The batch approach has the advantage over the replicationapproach in more efficient use of data since one only throws dataaway for the initial transient period once, not r times. Moreover,it is difficult to ascertain how many data should be eliminatedto eliminate initialization bias. This differs from one system tothe next. In the batch approach, initialization bias becomes lessand less significant as more data are collected by extending thelength of the run. However, with the replication approach, onemight collect more data by adding replications. If the lengthof the initialization period has been underestimated, a narrowconfidence interval might be constructed around a biased estima-tor of performance and such an interval can be very misleading.Both the batch and the replication approach would use the sameformulas given previously for terminating simulations in thenumerical computation of the confidence interval.

Room exists here only to highlight some of the major pointsin analysis of output from simulation models. Hopefully, it isclear to the reader that simulation models with stochastic inputvariables do not directly describe performance of the system.Rather, they give data from which performance can be inferredwith appropriate use of statistical techniques. Failure to considerformally these techniques is a weak point of many applicationsof simulation to mining problems. The reader is referred to thetexts Law and Kelton (1982), Banks and Carson (1984), andFishman (1978) for more detailed discussions of output dataanalysis. These texts address additional topics as follows:

1. How to determine how many replications of a terminatingsimulation are necessary to characterize a performance variablewith a level of precision specified by the analyst.

2. Procedures to determine how long the initialization periodlasts for a steady-state simulation. However, these procedurescan only be viewed as giving approximate answers to this difficultquestion.

3. Procedures for determining the batch size and run lengthnecessary for determining the mean level of a steady-state per-formance variable with a certain level of precision using thebatch approach.

4. Procedures for comparing system alternatives. These in-clude techniques for computing confidence intervals on the dif-ference between the mean levels of performance in two systems,for selecting the best of a number of distinct system alternatives,and the use of formal experimental design in characterizing sys-tem response to the adjustments of the decision variables.

5. Procedures for reducing the variance of the response vari-ables by manipulations of the input data to the model. Withthese procedures, response variables can often be estimated withgreater precision, and comparisons between alternatives can of-ten be more easily made.

9.4.3.5 Discussion of Specific Applications

The objective of this segment is to identify typical applica-tions of simulation modeling in mine production systems engi-neering, to discuss some of the key technical issues in structuringthese models, and to identify software packages that might beapplied to these problems. Major differences in structure existbetween models involving continuous material handling systemsand discrete vehicle transportation systems, and this forms thebasis for organizing this section.

Continuous Material Handling Systems: The major continu-ous material handling application involves conveyor networkmodeling. Some of the problems that might be addressed usingsimulation models of these systems are as follows.

1. Design of systems for throughput capacity. When a belthandles the output from several production sections, designingcapacity to meet the combined peak loads from all of the sectionscan lead to unneedful expense in terms of capital and operatingcosts. Simulators can describe the distribution of material flowrates into any belt transfer point. This in turn can be used toevaluate a particular system configuration—specified in termsof network structure, belt speeds, use of surge bins to trim peakflow rates, use of limit switches and other operating controls,etc.—for its ability to handle material flows without excessivespillage or curtailments of availability of the network to theproduction sections.

2. Assessment of network configuration impacts on availabilityof the transportation system to the production systems. In manyapplications the production section and belt system form anextensive serial chain of operations. Belt system failures fre-quently provide a major constraint on production output. Thesimulators provide a means for testing alternative configurationoptions to assess their impact on network availability. This in-cludes assessing the impact of buffer storage capacity (e.g., bun-kers), appropriately sized and inserted at strategic locations,which are a means to temporarily breaking the serial dependenceof one portion of the network on other portions.

3. Testing control strategies for belt monitoring and controlsystems. The potential for computer-based monitoring and con-trol in underground mines is now just becoming evident, withthe belt system a major focus of attention. A variety of meansfor real-time control of the dynamic material flows potentiallyexist, such as variable speed belts and feeders and feedback to

CYCLES AND SYSTEMS 797the production operations. Simulation will no doubt play animportant role in development of these strategies.

Turning the discussion to highlight some of the key technicalaspects of modeling these systems, there are two major ap-proaches used to represent material flows. In the first approach,a conveyor is viewed as a collection of small adjacent cells, whichis represented in the computer as an array. Attributes associatedwith each cell can denote properties of the material, for example,thickness on the belt or type of material. Time is advanced insmall discrete time increments and, effectively, the attributes areshifted ahead a single register, representing material flow in theoutby direction. At junctions or transfer points, cell attributes arecombined in an appropriate fashion to represent superposition ofmaterial flows. For example, if the outby belt travels at the samespeed as the inby belts, thickness attributes are simply added.This is, effectively, a simple form of continuous simulation.These models execute slowly relative to the approach discussedin the following, especially if one physically shifts records in thearray to model material movement. It is much more efficient toshift a pointer to the array location that corresponds to the cellat the head of the belt, as done in some packages, than it is tomove all of the records for each time advance.

The second approach employs discrete-event simulation. Formany analytical purposes, one obtains adequate information ifthe flow rates are known at each transfer point, into and out ofeach bin or feeder, and out of each discharge point. For example,spillage and throughflows can be ascertained directly using theserates. Though knowledge of position of material along the con-veyor at any point in time requires continuous representation asdiscussed previously, flow rates may be modeled as variablesthat only undergo changes at discrete points in time. If a changein flow rate occurs at one transfer point, one simply uses beltspeed to forecast the time when a resulting change in flow ratewill occur at the next outby transfer point. The magnitude ofthis future rate change is determined by multiplying the ratio ofthe speed of the incoming belt to the outgoing belt times thecurrent rate change. A change of flow rate into a feeder/bin canbe used to schedule a feeder bin overflow event if the new inputflow rate exceeds the maximum discharge rate of the feeder, anevent that may be preempted if rates decrease in the future beforethe scheduled event occurs. It may also schedule an increase indischarge rate if the current outflow rate is not currently atmaximum. Further, such a change in flow rate can be used toschedule a future decrease in the outflow rate of the feeder if theinput rate is less than the current outflow rate. Models usingthis representation may be coded using the event-schedulingalgorithm mentioned previously. Since a variable time incrementapproach is used, they operate much faster than the other classof models. The BELTSIM program uses an approach similar tothis (Bucklen et al., 1969).

Perhaps the most critical aspect of conveyor network model-ing is obtaining a realistic representation of material arrival tothe system. Exceeding the throughput capacity of units in areasonably designed conveyor network will typically be a “rareevent .” Predicting accurately, with a reasonable amount of runtime, the incidence of rare events via stochastic simulation canbe difficult. For this reason, it is important that the descriptionof material arrivals accurately portray the real-world situation.

For example, one might represent material arrivals from acontinuous miner section in a coal mine using a sequence ofdiscrete arrivals to the system. Shuttle car interarrivals wouldbe random, but the parameters of the interarrival distributionwould not be held constant through the simulation run. Rather,these parameters would be changed in a cyclic fashion to reflectthe underlying cut sequence. A random place-change delaywould also be allowed between each cut. The entire sequence of

interarrivals may be preempted from time to time with delaysrepresenting major equipment failures. If additional realism isdesired, interarrival times might alternate between high and lowvalues for the two cars for those cuts where the tram paths differsubstantially in length. One might also provide for shuttle carfailure, changing the interarrival pattern when this event occurs.For a longwall unit, material arrivals would be continuous, butrates would vary for different portions of the cut. The overallarrival pattern would be cyclic and interruptions might be al-lowed to represent equipment failures. Available conveyor simu-lation packages vary in their ability to accommodate such detail.Some are quite flexible.

A number of packages for simulation of conveyor networksexist. These include BELTSIM (Bucklen et al., 1969), Continu-ous Material Handling Simulator (CMHS) (Tan and Ramani,1988), Coal Mine Belt Capacity Simulator (CMBCS) (Thompsonand Adler, 1988), BETHBELT- (Newhart, 1977), and Under-Ground Materials Handling Simulator (UGMHS), (Manula,1974). The recent paper by Sturgul (1989), discusses the use ofa simulation language to construct a belt simulator.

Discrete Vehicle Transportation Systems: Simulation alsoprovides a basis for analysis of many detailed aspects of miningsystems employing discrete vehicle haulage in combination withexcavation/loading equipment. Some of the issues one mightattempt to address follow.

1. Design of haul road profiles. For example, should requiredclimbs be achieved through use of short steep road segments orextended segments of lesser grade?

2. Fleet makeup of transporters. This addresses the determi-nation of the best structure of a fleet of haulage vehicles at amine, including the number of vehicles, their size, the numberof units kept on standby in the event of breakdowns, and staticallocation of the transport units among multiple loaders in orderto maintain desired production ratios among the loaders.

3. Analysis of real-time fleet control strategies. Modern com-puter-based dispatching and fleet management systems oftenemploy sophisticated computational schemes for improving theeffectiveness of equipment utilization and maintaining controlof quality of the mined product. However, the schemes are basedon heuristic approaches (see 9.4.4). Simulation provides a techni-cal basis for testing the quality of these heuristics and comparingalternative tactics.

4. Detailed analysis of equipment interactions on overall sys-tem performance. For example, one might consider modificationsof the loading site to change maneuvering required for truckspotting or to allow double-sided loading at a shovel.

5. Analysis of working section and pit layout options. Exam-ples of such analyses include where should an in-pit crusherbe located to best serve multiple load sites and what are theramifications of alternative cut sequences for a room and pillarsection?

The detailed description of vehicle motion may require useof continuous simulation. A basic differential equation (9.4.1)can be used to describe the spatial position of a vehicle. Whenthe vehicle is increasing in speed, av is typically determined fromthe expression,

(9.4.6)

In this relation, Fr is the rimpull force at the current velocity,which may be taken directly from the rimpull chart for thevehicle. Fm is the resistance force offered by the vehicle, whichdepends on rolling resistance, air resistance, and grade resistance.Corrections for rolling and air resistance are usually incorpo-

798 MINING ENGINEERING HANDBOOKrated as a function of current velocity of the vehicle when makingsuch simulations. Mc is the corrected mass that accounts notonly for the actual mass of the vehicle, but incorporates a correc-tive term, which is also a function of current velocity, to accountfor losses in the drive system of the vehicle. It is seen that av canbe known given a collection of state variables that includes thecurrent velocity of the vehicle, grade, and rolling resistance ofthe haul road. Given av, Eq. 9.4.6 can be integrated to forecastthe velocity and position of the vehicle at the end of a subsequenttime increment.

Other factors taken into account in such simulations arespeed limits for the road segment, which restrict maximum at-tainable speed, braking/retardation, and losses for the “deadtime” when shifting gears (depending on the nature of the drivesystem). The VEHSIM package (Anon., 1984) is widely usedfor such simulations. It incorporates performance parameters ofmany Caterpillar vehicles and allows users to input parametersfor other vehicles.

Recall that the selection of state variables, in part, dependson the the objectives of the simulation study and is not directlydefined by the physical nature of the system. In simulationsof material excavation and handling systems, performance istypically addressed in terms such as material production orthroughput rates, equipment utilization, average cycle or delaytimes, etc. Performance measures such as these may be reliablyobtained from simulation runs that do not provide knowledge ofvehicle position at each instant of time. If one is in a situationwhere travel times are not available for various hauls (e.g., fromtime study data), it is often a good practice to use a vehiclemotion simulator to provide data descriptive of haulage timesfor various segments of the haulage cycle. Subsequently, one usesthese data as a basis for the input to a discrete event simulationmodel of the mining operation. The discrete-event model willoperate much more efficiently, will not be repetitively computingdeterministic haulage times, will readily accommodate stochasticaspects of the process, and can flexibly handle detailed aspectsof the process relevant to the performance variables of interest.

A number of software packages have been developed formodeling these systems for both surface and underground min-ing. They include:

1. GPSMS, General Purpose Surface Mine Simulator (Al-bert, 1989), couples ore body modeling with operations simula-tion. Block models may be constructed to describe local geologyand mine property boundaries. Operations descriptions are inputto the package via a two-level structure. The first, “EquipmentFace Activity Description,” details excavation operations. Thesecond, “Equipment Deployment Description” describes equip-ment operations and activities spatially and sequentially (i.e., theoverall mining plan) and ties extraction with materials handling.Support modules are incorporated for simulating dragline opera-tion, truck haulage (continuous simulation using rimpull curves),and conveyor haulage. This package extends the capability of itspredecessors, the Total System Surface Mine Simulator (Albert,1979) and Open Pit Materials Handling Simulator (O’Neil,1966), although these packages have unique modules that maybe of value and are not supported in GPSMS.

2. FACESIM (Prelaz, et al., 1968; Suboleski and Lucas,1969) and UnderGround Material Handling Simulator(UGMHS) (Manula, 1979) can be used to simulate room andpillar mining operations, including ancillary operations. The in-put structure for UGMHS is similar to that for GPSMS. Motionof haulage vehicles may be established using continuous simula-tion in UGMHS, whereas distributions or constant values areinput using FACESIM. The paper by Bise and Albert (1984)compares these packages and the use of simpler deterministicmodels of the mining cycle.

3. LHDSIM (Beckett et al., 1979) is a package for simulatinga load-haul-dump system for room and pillar mining operations.

4. SCSMLT (Peng et al., 1988), simulates haulage in openpit mines and has features for interfacing discrete vehicle haulagesystems to a crusher/continuous haulage system.

Examples of applications where the modeling was executedusing a simulation language include Sturgul (1987), where alter-native locations for an in-pit crusher were investigated; Mutman-sky and Mwasinga (1988), who examined the general applicabil-ity of SIMAN to modeling mine production systems and appliedthe language to model a truck/loader system; Weyher (1976)who modeled room and pillar operations using GPSS; and Har-rison and Sturgul (1988), who examined the main haulage systemfor a large underground mine and modeled several alternativetransportation systems mixing both truck and train transport.

9.4.3.6 Simulation Case Study

A case study will illustrate the process of conducting a simu-lation study. The study has been “manufactured” by the author,but it is intended to portray major aspects of the execution of asimulation study in a realistic fashion.

Statement of Problem: A multi-mine coal operator has re-cently experienced some difficulty in meeting sulfur specifica-tions for one of its major clients. Although construction workwill begin shortly for new operations in a low-sulfur reserveowned by the company, in the interim, a greater quantity oflow-sulfur coal is being obtained through the addition of twocontinuous miner sections at one of its existing operations work-ing a low-sulfur seam. The addition of the two units brings thetotal number of working sections at the mine to four. A problemhas been experienced because of the inadequate size of mainlinebelts to handle the peak production capacity of the four units.Several overload-related spills have occurred in the past fewweeks since the new units have come on-line, and action needsto be taken so that this situation does not continue.

Decision Alternatives: The mine is nearing the end of its life,and since the belt line carrying the combined flow from the fourunits is quite long, the capital expenditure for modifying theexisting conveyors so that they have higher capacity cannot bejustified.

However, one option that is easy to implement and is be-lieved to have potential for alleviating this problem is fine tuningthe feeder discharge rates at the production sections. By slowingthe feeders from their current levels, the discharge of an individ-ual shuttle car is spread on longer, thinner layers on the conveyorbelt. This, in turn, directly reduces the magnitude of the loadobserved at the transfer point where flows from the four unitsconverge. Such a modification is expected to reduce the incidenceand severity of spills. Note that it may not be desirable, from theperspective of overall production output from the mine, to set allof the feeders at the same speed. Hence the decision alternativesconsidered in this case study may be expressed in terms of foursetpoint values, one for each of the four section feeders.

Of course, there are other control options that probablyshould be considered. With minor modifications, the model pre-sented in the following is flexible enough to consider many otherdecision alternatives that one might conceive such as, for exam-ple, staggering start-up times of the production units so that theduration of the periods when all four units are active is mini-mized. However, for the purpose of this study, only feeder dis-charge rates will be considered.

Structure of the Simulation Model: The simulation modelwill incorporate (1) face operations for the four production units,(2) the feeders, and (3) the belt network to the transfer point

CYCLES AND SYSTEMS 799Table 9.4.3. Event Logic Table for Event – Shuttle Car

Arrival at Feederwhere the material flow from the four units converges. The thirdcomponent of the model is actually quite trivial for this study.

A fairly detailed model of face operations is necessary fortwo reasons. First, for the units where feeder speed will be re-duced from current values, there is no direct way of predictingwhat the shuttle car interarrival times will be after the changeis implemented. Certainly, there is a chance that on some cycles,the car dumping time will be increased from its current value ifthe material from the previous car has not cleared the feeder,but there is no direct way of knowing how often this will occurand what the net effect will be on total shuttle car cycle time.

Second, for this particular problem, there is a coupling be-tween the belt network and face operations that should be consid-ered. Changing feeder speeds has potential for both positive andnegative impact on overall economics at the mine. By increasingshuttle car dump times on occasion, the short-term rate of pro-duction output from the mine will be negatively affected. On theother hand, if a major spill is avoided, one prevents shuttingdown the face units while the spill is cleaned up and productionis increased through the increase in available operating time. Asdiscussed in more detail in the following, the average rate ofproduction output is employed to compare decision alternatives.To accurately reflect the coal output, the serial dependency ofthe face units on the operation of the belt should be incorporatedin the model. It is interesting to note that the coupling exists inthis case due to the nature of the performance criterion that isused in making the comparisons.

An issue that is believed to be important for the study is theeffect of cut sequence. The variable distance between the cut andthe feeder might have a pronounced influence on the effect ofchanging feeder speeds. If the cuts are close to the feeder, shuttlecar interarrivals will be short and the feeder is likely to havemore surge when the arrival occurs. Short hauls also have moredead time, and a delay in dumping is not as likely to turn intoan overall delay in cycle time. For this reason, the model wasconstructed to incorporate the cut sequence followed by eachsection.

The model was coded in the SIMAN simulation language.Process interaction routines (in SIMAN, these are called “blockmodels”) were written to describe operation of the face units andthe belts. Coal flow through the feeders and belts were modeledusing flow rates as state variables since this approach has consid-erable advantages when modeling bulk material flows on contin-uous haulage systems (see 9.4.3.4). The SIMAN language doesnot readily accommodate such a representation for a surge stor-age device like a feeder, and for this reason the following eventroutines were written: (1) shuttle car arrival at feeder event, (2)feeder full event, (3) shuttle car empty event, and (4) feeder surgedepletion event. Table 9.4.3 gives, as an example, the event logictable for event 1.

There are several interesting features of the block model.First, as one might expect, a separate process routine is notrequired for each face unit. The sequence of operations under-taken by a continuous miner, a shuttle car, and a roof bolter isvery similar among the four units. The SIMAN macro concept(similar mechanisms are available in other simulation languages)allows entities from each of the four units to share the sameprocess routines that describe the overall sequence of operations.Moreover, details necessary for describing spatial aspects of theprocess are readily decoupled from the process routine. In themodel that has been developed, the shuttle car routine is roughlydefined as follows:

1. Wait at the miner change point if the other shuttle car hasnot cleared the change point.

2. Once access to the miner is possible, seize a resource toblock entry of the other shuttle car and tram to miner.

First compute the current surge level in the feeder, E, as

where D is the current discharge rate of the feeder, t is the currenttime, and Te is the time that the next surge depletion event (event4) has been scheduled. (If D > 0 such an event is always scheduled.)

Condition

Always

Action

Set feeder input rate I to theshuttle car discharge rate R.Schedule a shuttle car emptyevent (event 3) at timet + L/I

If D < I (feeder filling)

where L is the payload of theshuttle car.Schedule a feeder full event(event 2) at timet + (K – E)/(l – D)where K is feeder surgecapacity. Also, delete anypreviously scheduled surgedepletion event (event 4).

If D > I (emptying) and E > 0 Schedule a surge depletionevent (event 4) at timet + E/(D – I )

3. Wait while loaded.4. Tram to miner change point and release the resource that

allows the other shuttle car to enter.5. Tram along a sequence of stations until arriving at the

feeder change point.6. Seize a feeder access resource and tram to feeder.7. Activate a shuttle car arrival event (user-written event

routine 1) and wait.8. Release the shuttle car from the wait state when shuttle

car empty event (user-written event routine 3) has occurred.9. Return to the feeder change point and release the feeder

access resource.10. Tram along a sequence of stations until returning to the

current miner change point.Externally defined input data to the model define stations

that correspond to physical locations of the crosscuts and entries.In addition, sequences of these stations are defined that controlvehicle movements. Equipment moves along the cut sequenceare handled in similar fashion. Only a few statements were re-quired to model the four continuous miner units and movementof material along the belts.

Input data to the program, in addition to the station layoutsand tram sequences noted above, are as follows:

1. Feeder discharge rates and surge capacity.2. Belt transit times from the section feeder to the point of

convergence.3. Tonnage per cut.4. Distribution of shuttle car, miner, and bolter tram rates.5. Distribution of shuttle car payload size.6. Distribution of time to load a shuttle car.7. Distribution of time to bolt a cut.8. Distribution of downtime when an overload spill occurs.9. Distribution of time between unscheduled delays in the

face production cycle and duration of such delays.

800 MINING ENGINEERING HANDBOOKAs can be seen, the amount of field work to obtain the

various input distributions required by the model is not excessive.Simulation can usually proceed with a rather small investmentin time studies. Moreover, these studies typically should focuson the various elemental times of the production operation,spending perhaps a few hours observing each of the major partsof the operation. Simulation is a means of synthesizing timestudy data and drawing meaningful conclusions from this datathat otherwise cannot be obtained. In this case, perhaps themost difficult data to obtain would be the distributions involvingunscheduled delays in the face production cycles. For the pur-pose of relative comparisons among the decision alternatives thathave been studied, it might be reasonable to ignore such delays.Ignoring such delays would, however, be inappropriate if onehoped to obtain accurate cost figures from the simulation study.

Application of the Model: From examination of the capacityof the belts handling the combined flow from the four units, itis clear that the overload incidents occur at this mine only whenpeak loads from all four units meet simultaneously. In such asituation, reducing the frequency of overloading incidents canonly be accomplished by reducing the sum of the discharge ratesof the feeders to the minimum capacity of the belts handling thecombined flow of the four units. Moreover, there is clearly noincentive to reduce the discharge rates below this level since thiswill only reduce the rate of production from the working faces.These questions remain:

1. Will the reduction in feeder discharge rates cause an exces-sive decrease in the rate of production that cannot be offset bythe gains in operating time?

2. How should one best go about allocating the dischargerate reductions among the four units?

To help answer these questions, four alternative strategieshave been investigated. Alternative 1 represents the status quo.Alternatives 2, 3, and 4 all specify the same combined feederdischarge capacities equal to the capacity of the belts handlingthe combined flows. With alternative 2, the rate reduction is splitequally among the four units; with 3, it is split equally amongthree units; and with 4, it is split among just two units. Allocatingall of the reduction to one unit was not considered since thiswould clearly be an excessive choke on output from that unit.

Though there is some cost associated with cleaning up aspill, the costs are an order of magnitude less than the lostproduction costs associated with any belt shutdowns that mightoccur. These shutdowns are reflected directly in the simulationmodel. Ignoring cleanup costs, the alternatives have been com-pared in terms of the time average flow rate on the mainlinebelts, a measure of total production output from the mine.

Simulation runs were made for a single production shift sincethis represents a natural termination point for the run, and theoutput is analyzed as realizations from a terminating simulation.To deal with the potentially significant influence of cut locationsand the cut sequence, the starting cuts were randomized for eachrun. (One could perhaps find better ways to handle the influenceof the cut sequence, which introduces a long cycle into theoperations, than through randomization; this appears to be arather complex issue from a technical perspective.) A total of 20runs was made for each alternative and the results are given inTable 9.4.4. As the histogram for the performance variable foralternative 1 in Fig. 9.4.12 shows, there is considerable variabilityof the output response. The sample mean production rate foreach alternative is shown in the table along with a 95% confidenceinterval for the mean.

The results appear to imply that a reduction in feeder speedis desirable and that it is best to allocate the reduction equallyamong the four units (alternative 2). An equal allocation in thiscase is not surprising, but such a result probably would not

Table 9.4.4. Output for the Four AlternativesConsidered in the Case Study

Fig. 9.4.12. Production rate distribution for alternative 1, current feeder setpoints.

hold if there were significant differences in the production cycleamong the four units. Though a comparison of sample means isthe device for selecting the best alternative, such a selectioncannot be made with certainty. The sample means only representestimates of the true, but unknown, mean. The fact that theconfidence intervals of several alternatives overlap provides anindication that one might expect some difficulty when comingto a decision about the best alternative.

CYCLES AND SYSTEMS 801In this problem, one might apply a procedure where the

results of the first 20 runs are used as a basis for determininghow many more runs to make before making a final decision onwhich alternative is best. These initial runs give considerableinformation in the inherent variability of system performancefor each alternative. Using these measures of variability, thenumber of additional runs might be established on the basis of(1) the level of probability of a wrong decision that one is willingto accept, and (2) the minimum difference in performance amongalternatives that one considers to be of significance. Once theseadditional runs are made, a final decision could be made bycomparing the means, and one would have assurance that thetwo stated conditions on uncertainty are satisfied when makingthe decision. Further discussion of the nature of such proceduresare beyond the scope of this presentation; interested readers arereferred to the texts cited at the end of 9.4.3.4.

9.4.4 FLEET DYNAMICS AND DISPATCH

The stochastic aspects of mine operations—an equipmentfailure incident, variation in tram times or loading rates, etc.,—preclude development and field implementation of a fully pre-scriptive plan for operations. Rather than attempt to follow arigid sequence of operations, often much can be gained from on-going, real-time analysis of the current status and recent historyof the operations. This analysis might then be used as a basis fortaking control actions to improve subsequent performance of thesystem. This is perhaps most evident, and the technology ismost fully developed and accepted, for real-time management(dispatch) of pooled truck fleets serving multiple loading units.Ideas similar to these might be applied to any type of mineproduction system employing discrete vehicles, although a largesize of operations and the ability to allocate flexibly the transportvehicles among multiple excavators/loaders enhances the poten-tial utility of such approaches.

The field is one with little theory; the basis for control actionsinvolves application of heuristic approaches. Though innatelyheuristic, some procedures prescribe control actions on the basisof solutions to quite sophisticated mathematical models. Theproof of the pudding is in the eating, and though heuristic, thesetechniques have been reported to be quite effective in increasingthe rate of production from these mines for a given level ofloading and transport equipment (Clevenger, 1983). Some ap-proaches have also helped in simultaneously meeting a numberof additional operational objectives such as better control of ore-grade targets.

An opportunity one has in certain discrete vehicle materialtransport systems involves the fact that the vehicle may be flexi-bly routed. Rather than running the vehicle in a locked cyclebetween a particular loader and dump site, one may use thevehicle to service multiple loaders and dump sites. Moreover,rather than following a predetermined, rigid sequence of move-ments, routing can be dynamically controlled, switching thesequence that loader and dump sites are visited by the truckfrom one cycle to the next.

The underlying reasons why advantages in system perform-ance can be gained by such dynamic control include:

1. One can respond to information on the current state ofthe system that reflects the realization of particular randomvariables (e.g., the observed cycle time to load a particular truck)that could not have been predicted exactly ahead of time;

2. One can appropriately respond to deviations from theexpected levels of performance that were used to develop theoperational plan (e.g., one shovel is having an easy time diggingand is completing its load cycle more quickly than expected and

this provides opportunity for increased production over whatwas expected if levels of truck capacity allocated to the shovelare increased).

In examining truck dispatch strategies that have been em-ployed, distinctions among them can be made with respect totwo major factors as follows.

1. The extent a forecast of future states of the system isemployed to make the current dispatch decision. Some approachesconsider only the current truck (e.g., immediately upon comple-tion of dumping) when making the dispatch decision prescribingwhere the truck should next be routed. Others attempt to forecastthe state of the system for a number of future dispatches andmake the current dispatch while cognizant of this forecast. Forinstance, one might send the current truck to its “best” shovel(e.g., the one that will be ready to load the truck at the earliestfuture point in time), but there is a good second choice for thistruck. The next truck that will complete dumping also has thesame “best” shovel but no second choice that is very good.Considering performance of the two trucks together, it would bebetter to send the current truck to its second-best choice.

2. The scope of the operational objectives that drive the selec-tion of dispatch assignment. Some strategies base dispatch deci-sions on narrow criteria (e.g., send the truck to the shovel whereit is expected to be loaded first). Other strategies base dispatchdecisions in accordance with how well the decision contributesto conformance with a production plan. The plan is developedto enhance specific performance criteria such as overall mineproduction rate. It may also recognize various operational con-straints such as achievement of grade targets with the ore blendfrom the multiple loading sites and desirable ore/gangue pro-duction ratios. These production plans are typically short termin nature, are routinely updated, and are frequently based onsolution to math programming models for short-term productionscheduling and equipment allocations.

Two examples of some simple “one truck at a time” dispatchheuristics are as follows:

1. As mentioned before, “send the current truck to be dis-patched to the loader where it is expected to be loaded first.”One would use figures on average load times and tram rates andcurrent positions of previously dispatched trucks headed to theloader in question to forecast when the loader will have servicedall of these previously assigned trucks. Then travel time to thisloader for the truck to be dispatched is compared to the forecasttime when the loader will be free to estimate the future point intime that truck loading for the dispatch vehicle would begin.This is done for all loaders and the truck is sent on the shortestpath to the one that is expected to load it at the earliest point intime.

2. “Send the current truck to be dispatched to the loaderthat is next expected to become idle (after servicing all previoustrucks assigned to that loader).” One would forecast the timeeach loader is expected to become idle as discussed in the firstexample, and without consideration of the distance to thatloader, the current truck is sent to the loader expected to becomeidle at the earliest point in time.

These rules are very simple and have some intuitive appeal.Note that one may use recent history on load time and tramrates to obtain better forecasts as operating conditions change atthe mine. The first rule is noted to cause loader utilizations tobecome unbalanced (Lizotte and Bonate, 1987), since trucks tendfrequently to be sent to the closest shovels, ignoring the remoteones. In the second case, production ratios will be more con-trolled but are primarily influenced by allocation of the shovel tothe available loading sites. Both rules may result in shortsighteddecisions because the current decision may be unfavorableconsidered in conjunction with dispatches that might be

whenmade

802 MINING ENGINEERING HANDBOOKin the near future. Further, the objective criteria for both rulesare very narrow and may not conform to overall operating objec-tives for the operations.

To see how one might approach overcoming the shortcom-ings of these simple rules, the operation of one of the moresophisticated dispatching systems, DISPATCH, which has beendeveloped recently and is described by White and Olson (1986),is now discussed.

The DISPATCH system first solves a sequence of two linearprogramming problems to establish a short-term productionplan. This plan is updated routinely as will be discussed in thefollowing. When the plan is established, it is based on the currentstatus of mine operations, reflecting siting and current availabil-ity of the loading shovels, estimates of quality characteristics ofore at working faces and stockpiles, and operational status of theprocess plant.

The first linear programming (LP) model defines “opti-mum” production rates for the various shovels, including thoseoperating from stockpiles. The objective function of this optimi-zation accounts for penalties associated with failure to meetprocess-plant input demands and violations of blend-quality con-straints, and weights established by management reflecting thecurrent relative desirability that plant feed originate from stock-piles or from active faces.

Given these overall flows from the material sources (stock-piles and working faces), a second LP is solved to determine theallocation of truck resources to move material flows efficientlyalong available haulageways. The model prescribes how manycubic yards (cubic meters) of haulage capacity should be allo-cated to all “paths” in the system. The second model is set upto maximize production rate from the system. It is loosely cou-pled to the first model in that the first model prescribes minimumproduction from working faces and stockpiles for the secondmodel. Any excess production from working faces that can beachieved would be stockpiled.

The use of the output of the second model is to provide acriterion for truck assignments in real-time dispatch. Roughlyspeaking, the objective of the dispatch will be to implement andmaintain the “optimum” haulage allocation determined by thesecond model, which is given in terms of the volume of haulagecapacity that should be allocated to each path. Contrast this tothe objectives of dispatch decisions for the two simple heuristicscited.

As mentioned previously, the two LP models form a short-term production plan. Whenever a major upset such as a shovelbreakdown or process plant outage occurs, the models are solvedagain to establish a new short-term plan. Moreover, blend con-straints in the first-level model are structured to allow someslack in conformance to rigid bounds on ore grade. An estimateof the moving average quality of the ore feed to the process plantis continuously maintained. There is a bound imposed on themaximum period of time that can pass without replanning sothat excessive and sustained deviations from target grades donot occur. The more slack permitted in complying with graderequirements when solving the first-level model, the more fre-quently operating plans must be updated.

The actual dispatching procedure uses the deviation betweenactual current assignment of trucks to a path and the optimumassignment levels determined by the second stage LP as a basisfor evaluating dispatch decision alternatives. All trucks that arein transit from a loader to a dumpsite are considered collectivelywith the current truck to be dispatched when making assign-ments. At the time of a dispatch, the time each loader will “need”a truck assignment (typically in the future) is forecast. “Need”is determined by the LP haulage capacity prescription. Theloader with the earliest need is considered first. The truck closest

to this shovel is nominally assigned to it. Eliminating this loaderand truck from consideration, the shovel with the second earliestneed is considered in the same fashion, etc., until all loaders havebeen considered. This will typically result in an assignment forthe current truck to be dispatched.

The point of this discussion is to illustrate a way that dy-namic dispatch systems can be used to (1) help achieve a goal-oriented production plan that, because of its short-term nature,is itself responsive to changing conditions at the mine, and (2)make decisions using updated forecasts of expected future statesof the system rather than making each truck assignment indepen-dent of such forecasts.

The overall logical structure of most of the more recentlydeveloped dispatch systems will resemble the one discussed here.However, they will vary considerably in details. Although themathematical models are described rather than explicitly re-ported, the system at the Mount Wright mine (Soumis et al.,1989) apparently differs from DISPATCH in a number of re-spects. Some of these include (1) consideration of alternativeloader site locations when making preliminary equipment assign-ments, (2) use of a nonlinear objective function in determiningoptimum haulage allocation, which results in a more balanceddistribution of truck capacity assignments, (3) use of a simpleprocess-plant model for estimating the actual costs of deviationsfrom blend targets (in the previous procedure these were, moreor less, guesses), and (4) solution of a classical assignment modelfor dispatch decisions where the objective function minimizesthe squared difference between current forecast waiting timesfor the shovels and trucks and average waiting times expectedfor implementing the operational plan.

This segment is concluded with two additional notes. First,the dispatch algorithm (but not the planning models) for thesesystems must be able to execute in a very short period of time(a matter a few seconds). With careful consideration of the math-ematical techniques employed, one can use rather extensive mod-els, as evidenced by the Mount Wright system, for making dis-patch decisions. Second is a reminder that the procedures areheuristics, and many modifications are conceivable. Simulation,as discussed in the previous section, can serve to evaluate alterna-tive dispatch heuristics and tactics for a given mining operation.

9.4.5 STOCHASTIC PROCESS MODELS OF MINEPRODUCTION SYSTEMS

The weakness of simulation as a tool for systems analysisshould be evident from the discussion of 9.4.3. One wants toknow the distribution of performance variables, perhaps, evenhow these distributions change as a function of time, but simula-tion only gives data from which one may infer some of the majorproperties of these distributions. It does not give the distributionsdirectly. Moreover, it is typically quite cumbersome to makegeneralizations regarding system performance and its responseto the decision variables on the basis of simulation output.

On the other hand, the theory of stochastic processes providesa basis for analytical modeling of these processes. The field iscomprised of a number of basic topics including Poisson pro-cesses, Markov chains, renewal theory, continuous-time Markovprocesses, semi-Markov processes, Brownian motion, etc. These,in turn, service many applications including results in queuingtheory, inventory theory, reliability theory, sampling plans forquality control, and inference-based measurements using signalsgathered by sensing instruments, among many others.

The analytical results may, in some cases, give the distribu-tions of the performance variables directly. They may also facili-tate comparisons among alternative values of the decision vari-

CYCLES AND SYSTEMS 803ables, perhaps permitting mathematical optimization. Often theygive valuable insights in to the nature of system operation thatwould not have otherwise been obtained. An example of this fora mining application is given in the following.

Typically, more assumptions are required in order to prog-ress with this approach to systems analysis than are requiredwhen using simulation. If one is not careful, the result of themodeling effort may be an abstraction of little relevance to thereal-world system. One is cautioned against “pulling a formulafrom a book” without understanding the assumptions and natureof the result. Nonetheless, the results that can be obtained byusing these approaches often justify the efforts.

Subsequently, some examples of the more recent work inmining-related applications of stochastic process models thathave resulted in—or with more work may lead to—practicalachievements are discussed. These applications are in the area ofmodeling of continuous material handling systems and queueingtheory applications. Space exists here only to present a descrip-tive discussion. Readers interested in learning about fundamentalaspects of these techniques are referred to the well-known textsby Ross (1983), Cinlar (1975), and Karlin and Taylor (1975).

9.4.5.1 Stochastic Process Models of ContinuousMaterial Handling Systems

As examples of the type of issues that can be addressedin applying this technology to analysis of continuous materialhandling systems, the work of Baral et al. (1987) and Sevim(1987) are discussed.

Baral et al. Model: This work addresses the implications ofinstalling a bunker as a storage buffer in a serial arrangementof conveyors to increase the availability of that system to theproduction section it services. The role of such bunkers is to holdproduction for intervals of time when outby conveyors havefailed, temporarily isolating the production section from its de-pendence on the outby transport network. They must be largerthan bins used to reduce surge loading on an outby belt to controlspillage. The service of the system depends on the availability ofthe conveyors between the face and the bunker and between thebunker and the end of the conveyor line. For the bunker toincrease production, the inby belts must be available to haulmaterial to the bunker when the outby belts fail. Moreover, theoutby belts must be capable of clearing a substantial portion ofthe stored material between successive failures of the outby belts,else the effective capacity of the bunker might be reduced to thepoint where it provides little isolation. The availabilities of thebunker inflow and outflow belts are a function of where thebunker is located in the sequence of belts. Thus both the size ofthe bin and its location in the network are decision variableswith important ramifications on performance of such a system.

It was assumed by the authors that the time between failuresand time to repair the belts are exponentially distributed randomvariables. This permits the system to be modeled as a continuous-time Markov process. For a simple two-conveyor system with abunker between the first and second conveyor, state is describedby the triplet (up/down status of the inby conveyor, up/downstatus of the outby conveyor, and proportion of bin volumecurrently filled). It is clear that one can assess the availabilityof the system to the production section given the value of thesevariables. For larger networks, it was shown that the belts inbythe bunker and the belts outby the bunker may be considered inaggregate analogous to the two-belt system to reduce the statespace and simplify computations. Expressions were derived forsteady-state availability of the conveyor/bunker system to theproduction system as a function of the bunker volume, and

the time to failure and the time to repair distributions for theindividual conveyors.

Analysis of these expressions suggested the following strat-egy for optimal specification of bunker storage. The bunkershould be located at the location where the differential betweenthe availability of the inby belts and the outby belts is the small-est, that is, at the location where these availabilities are closestto being equal. (Simple expressions can be used to compute theavailability for an arbitrary serial chain of belts.) It is shownthat the rate of increase of availability decreases and reaches anasymptote as bunker volume increases. Volume should be setprior to reaching the asymptote. Plots can be constructed to aidthis decision.

Perhaps the most serious criticism of this work might be theassumption of constant flow on the belt when the system is up.The ramifications of this assumption are not known. It appearsthat additional work might also be done on how one combinesmultiple production sections serviced by the same network, al-though this was addressed by the authors to a limited extent.

Sevim Model: The work of Sevim (1987) focused on a differ-ent aspect of performance: the use of a bin to smooth outflowfrom multiple production sections that operate in a discontinu-ous fashion. Here, in contrast to the work just discussed, greaterattention was given to modeling the production sections. Outputfrom the face was modeled as a semi-Markov process, whichallows for an arbitrary form of distribution of the times betweenup and down states as well as different classes of up and downstates. It was assumed that the rate of production was constantduring the up periods. Transient distributions of the probabilityof coal flow from a section were established for the first half-shift (from arrival at the section until the lunch break). It wasalso shown how these could be combined for multiple sectionsserviced by the same belt network. One thereby has knowledgeof the probabilities (as a function of time of day) associated withthe various aggregate levels of material flow on a belt. Thesedistributions were then used to describe the inflow into a bininstalled for the purpose of smoothing flow. A heuristic approachwas established for sizing this bin. Both constant and controlledoutflow rates from the bin were considered. Similar work appliedto control of flow in slurry transport systems is presented inSevim and Yegulalp (1984).

9.4.5.2 Queuing Models of Mine ProductionSystems

The basic structure of queuing systems is as follows. A call-ing population provides a source of customers who request serviceat some service station. One should take a broad interpretationof the term customers; in a mining context it might refer toshuttle cars waiting to be filled, belts needing repair, or even, aswill be seen in an example that follows, working faces requestingan operation in the cut, drill, blast, load, roof-bolt sequence ofcoal mining operations. The calling population may either befinite or infinite. The latter is most common in queuing modelsand is simpler analytically. It typically refers to a large sourceof customers external to the system such as the body of potentialcustomers for a fast food restaurant. In each of the three miningcases discussed before, and probably in most queuing systems ofinterest in mining, the calling population is finite and fixed.

The service station referred to previously contains one ormore parallel service channels; each such channel is called aserver. If the number of channels is finite, there is a limit inthe number of customers that can be serviced simultaneously.Arriving customers finding all channels filled must wait for ser-vice in a queue. The queue may or may not correspond to awaiting line in the real-world system being modeled. For in-

804 MINING ENGINEERING HANDBOOKstance, broken machines (customers) may have to wait for therepair crew (servers) to finish a number of jobs before beingserviced. But the machines are never “lined up” physically.

The queue itself provides an opportunity for controlling thesystem. It may be desirable to service some waiting customersahead of others independent of their order of arrival to the queue.For example, one might load 80-ton (72-t) trucks ahead of 50-ton (45-t) trucks regardless of which truck arrived first. Thesecontrols are specified in terms of a queue discipline, which givesrules for determining the priority for removing customers fromthe queue when a service channel becomes available.

The queue may have limited capacity, and customers arriv-ing when the queue is full may be balked from the system or sentto another service station. Each server is typically assumed ableto service only one customer at a time. This customer is retainedand occupies the server for a period of time called the servicetime. For example, an empty, spotted truck ties up the loadingshovel until it is filled. Once service is completed, the server isnow available to service another customer and the customer isreleased.

The system may consist of multiple service stations. A singlecustomer may progress from one service station to the next in afixed or a flexible sequence. This arrangement is frequently calleda queuing network. In many mining systems, the customer iscycled among a number of service stations. For example, thetruck goes from a loader to a dump site and back again. Whenmultiple services stations are involved, state is often describedin terms of the number of customers at each station.

Overall, the structure of queuing models is quite broad andflexible. Hopefully this brief discussion of structure has left thereader with the impression that a number of mining processesmight potentially be modeled in this framework.

Two assumptions are frequently made to make queuing mod-els more tractable analytically. First is that one is interested inequilibrium probabilities at steady state as opposed to transientperformance of the system. As explained in 9.4.3.4, the accept-ability of this assumption depends on the objectives of the study,not the system itself. Second is that the temporal variables ofthe system—customer interarrival times, customer service times,interstation transfer times—are exponentially distributed. Thisallows the theory of continuous-time Markov processes to beapplied to compute the steady-state probabilities.

The latter assumption is a restrictive one. Though the expo-nential distribution is an excellent model for many situationssuch as time between failures of certain types of components,time between arrivals to a system from a large external callingpopulation where customers act independently, it is not a goodmodel for service times (e.g., time to load a truck) and intersta-tion transit times (e.g., time to travel from the loader site to thedump-site) in many mining applications.

An approach that may be used to overcome this limitationis to employ what are called generalized Erlangian distributionsor phase-type distributions. The general idea is to view a temporalvariable with an arbitrary distribution, such as a service time, asbeing executed in a sequence of phases. The order of the phasesis defined by either series or parallel structures or a combinationof both. A serial structure implies that one phase is executedsequentially after another until the required number of phases inthe series is completed. A parallel structure implies that multipleserial structures are available and one of these is selected with aspecified probability then executed as just described. Time foreach phase in the sequence is exponentially distributed. Thephase structure and parameters of these exponential distributionsmay be determined so that as customers pass through the se-quence of phases, the distribution of total elapsed time closelymatches the arbitrary distribution that the modeler wants. Since

all times are now exponentially distributed, the result is that acontinuous-time Markov process model can be employed, withaccompanying advantages in tractability. This, however, comesat the expense of an expansion of the state space relative to theinitial problem. The theory of stochastic networks (Kelly, 1979)provides means for computing the steady state probabilities forthe various states of the system.

Recently, this approach has been applied to mining systemsin the work by Kappas and Yegulalp (1987). In their model ofa room and pillar coal mining operation, working faces areviewed as customers that transit through a fixed series of servicestations corresponding to the undercutting, drilling, blasting,loading, and roof-bolting operations of the conventional miningcycle. Distributions of general form were fitted to field data onthe time required to complete each of these operations. A phasestructure was fitted for each service station that resulted in adistribution of total elapsed time that matched the first twomoments of the general distribution exactly (mean and variance)and was close to the third moment (skewness). They used special-ized versions of computational algorithms for computing steady-state probabilities of the various states, which were given interms of the number of faces undergoing each operation of themining cycle. From these probabilities, various aspects of per-formance, such as steady-state production rate, could be ob-tained. They compared the effect of various numbers of workingfaces on production rates. Though a number of shortcomingswere noted by the authors, including the uncertain utility ofsteady-state measures and inadequacies in accommodating spa-tial aspects of entry layouts when comparing system alternatives,the work certainly shows promise in bridging the major gapsin applying queuing theory to mining systems over previousapplications where exponential times for activities were assumed.

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Transaction

Paper

Introduction

Shovel-truck systems are a prevalent loadingand hauling system in surface miningoperations. The loading units are typicallywheel loaders (WL), hydraulic excavators(HEX) or rope excavators. The trucks can beoff-highway trucks (OHT), articulated dumptrucks or coal haulers as in coal mining.Generally truck fleet sizes increase withprogressive mining or when expansionprojects are envisaged. Haulage distancesinvariably increase with increasing pit depth asmining progresses, consequently reducingindividual truck productivity and demandingmore trucks to maintain the same level ofproduction. Expansion projects require higher

production rates, and with same level of truckproductivity, it means more trucks will berequired to meet the increased production rate.

The stochastic-dynamic nature of shovel-truck production cycle variables rendersdeterministic calculations inadequate toestimate the required shovel-truck fleet sizes.Consequently, simulation models are used toestimate the additional truck requirements.Several simulation models or softwarepackages are available for this purpose.However, these models yield different fleetsizes for the same input parameters. The mainreason why these different models each yieldunique results is based on the assumedprobability distributions fitted to the maincycle variables and the correspondingcalculation of waiting time for both trucks andloaders.

Of-the-shelf simulation software packagescan be very expensive for once-off use andmines would need to be able to analyse theirnew truck requirements using affordable andreliable models. Consequently, most mineshave to rely on the original equipmentmanufacturers’ (OEM) fleet size recommen-dations. Mines can increase their confidence inthe OEM estimations by using simple modelsto substantiate the estimations. The modifiedMachine Repair Model based on Markovchains and running on an MS Excel platform,can used for this purpose because mines havecomputers that run MS Excel. The MachineRepair Model can therefore be used as anaffordable model for checking OEM recommen-dations.

The shovel-truck sizing problem is a two-stage problem even for a shift start-up (Ta etal., 2005). The first stage is truck resource

Modelling open pit shovel-truck systemsusing the Machine Repair Modelby A. Krause* and C. Musingwini†

Synopsis

Shovel-truck systems for loading and hauling material in open pitmines are now routinely analysed using simulation models or off-the-shelf simulation software packages, which can be veryexpensive for once-off or occasional use. The simulation modelsinvariably produce different estimations of fleet sizes due to theirdiffering estimations of cycle time. No single model or package canaccurately estimate the required fleet size because the fleetoperating parameters are characteristically random and dynamic. Inorder to improve confidence in sizing the fleet for a mining project,at least two estimation models should be used. This paperdemonstrates that the Machine Repair Model can be modified andused as a model for estimating truck fleet size in an open pit shovel-truck system.

The modified Machine Repair Model is first applied to a virtualopen pit mine case study. The results compare favourably to outputfrom other estimation models using the same input parameters forthe virtual mine. The modified Machine Repair Model is furtherapplied to an existing open pit coal operation, the Kwagga Sectionof Optimum Colliery as a case study. Again the results confirm thoseobtained from the virtual mine case study. It is concluded that theMachine Repair Model can be an affordable model compared to off-the-shelf generic software because it is easily modelled in MicrosoftExcel, a software platform that most mines already use. This paperreports part of the work of a MSc research study submitted to theUniversity of Witwatersrand, Johannesburg, South Africa.

Keywords: simulation, bunching, probability distributions, cycletime, queuing, matching, shovel-truck, OEM.

* Endeavor Mine, CBH Resources Ltd, NorthSydney, Australia.

† School of Mining Engineering, University ofWitwatersrand, Johannesburg, South Africa.

© The Southern African Institute of Mining andMetallurgy, 2007. SA ISSN 0038–223X/3.00 +0.00. Paper received Mar. 2007; revised paperreceived Aug. 2007.

469The Journal of The Southern African Institute of Mining and Metallurgy VOLUME 107 REFEREED PAPER AUGUST 2007 ▲

Modelling open pit shovel-truck systems using the Machine Repair Model

allocation or fleet size estimation. The second stage, which isa truck dispatching stage, is a real-time implementation ofthe estimated truck resource and is done either manually orusing computerized truck dispatch systems such asDispatch®. Truck allocation is critical because if it isincorrectly done then the dispatch stage inherently carriesover errors made in the first stage, resulting in sub-optimaltruck dispatching decisions. This is the reason why at projectinception the fleet size has to be estimated as accurately aspossible. Two extreme undesirable trucking conditions canexist if truck allocation is done incorrectly. These are an‘over-equipped’ condition where there are more trucks thanare required or an ‘under-equipped’ condition when there arefewer trucks than required. There are consequencesassociated with these conditions. For example over-estimating truck fleet size by one extra CAT 777D truckimplies about R10 million (in 2006 monetary terms)unnecessary extra capital expenditure, while under-estimating truck fleet size carries the risk of loss of potentialrevenue due to production shortfalls.

Central to the estimation of shovel-truck fleet size is thedetermination of the load-and-haul cycle time. The number ofcycles a haulage unit can complete per hour are thendetermined. Subsequently, the system’s productivity in tonsper hour is determined as the aggregate of the productivity ofall haulage units, hence sizing the shovel-truck fleet system.However, in any load-and-haul system there exist variationsin the cycle variables such as loader bucket payload, truckpayload, haul road distances, haul road conditions, operatorproficiency, truck waiting times and truck loading time, toname but a few. Variations in these variables and theirsubsequent interaction contribute to the complication in theestimation of real-time waiting time, hence the estimation ofthe cycle time in real-time. Waiting time is an inherent butundesirable part of any load-and-haul system because itrepresents real-time equipment mismatch and ultimatelyproduction loss from idling equipment. Any shovel-truckanalysis must therefore include estimation of waiting time.Accordingly, optimization of shovel-truck systems must aimto minimize or eliminate the total waiting time for bothshovels and trucks (Temeng, Francis and Frendewey, 1997).

Models for analysing shovel-truck systems

To date, a number of off-the-shelf commercial simulationsoftware packages have been developed to estimate shovel-truck fleet size requirements for given mining productionrates and conditions. The various models associated withthese packages and considered in this study can be broadlyclassified as:

➤ Iterative models that fit discrete empirical values tocycle variables. Examples are the Elbrond (1990) modeland Machine Repair Model (Winston, 2004). In thispaper, the Machine Repair Model is also alternativelyreferred to as the Winston model

➤ Regressive models that treat waiting time as a functionof fleet matching and bunching correction factors.These models are based on static simulation algorithmsthat are driven by prescribed processing flow that is notdependent on time or interaction of resources. Anexample is the Fleet Production and Cost model (FPC®)

developed by Caterpillar Inc. and discussed in detail byMorgan (1994)

➤ Stochastic Monte Carlo type models which fitprobability distributions to cycle variables. An exampleis the Talpac® model developed by Runge Software Ltd

➤ Stochastic graphic simulation methods in which trucksand shovels (or loaders) are represented by physicalentities (icons) within a virtual environment followingprobability distributions within a Monte Carlosimulation environment. The simulation progress canbe viewed as an animation. An example is the Arena®

model developed by Rockwell Software Inc.

The reasons for the choice of the above models are firstly,that the Elbrond (1990) and Winston (2004) models areiterative models, which can easily be programmed in MSExcel. The Talpac and FPC models were chosen because theyare commonly used in the mining industry for shovel-truckanalysis although they are limited to fitting probability distri-butions to a maximum of five major shovel-truck cyclevariables. Lastly, Arena was chosen because it can beprogrammed with any number of probability distributionmodels fitted to an unlimited number of cycle variables and istherefore a very flexible model for use in analysing severalvariables in shovel-truck analysis. This characteristic ofArena gives it the potential to closely imitate real systemsand was therefore chosen as the benchmark model in thisstudy to compare the output from other simulation models.

Other useful models that were not considered in thisstudy, due to reasons of non-availability and financialconstraints, include Shovel Truck Analysis Package(STRAPAC®), General Purpose Simulation System (GPSS/H®)developed by the Wolverine Software Corporation, andVehicle Simulation (VEHSIM®). Panagiotou andMichalakopoulos (1994) discussed the STRAPAC frameworkand its application to a shovel-truck system in a bauxite openpit mine. Today the STRAPAC® name is associated withplastic holding ties produced by Sublett Co. The GPSS/H®

program, which has been used for both surface andunderground mine simulations, is discussed in detail both interms of architecture and application by Sturgul (2000).Dowborn and Taylor (2000) successfully used GPSS/H® tosimulate a production system for an underground narrow reefplatinum mine on the Bushveld Complex in South Africa.Other mining applications of GPSS/H® are reported bySturgul, Jacobsen and Tecsa (1996), Sturgul and Jacobsen(1994), and Sturgul and Tecsa (1996). VEHSIM® wasdeveloped by Caterpillar Inc. in the late 1960s primarily forsales and technical support of the CAT 779 (85 ton) electricdrive OHT truck, but was discontinued due to the decline inthe truck’s use. FPC® has essentially the same program setupand functionality as VEHSIM®.

Review of the machine repair model

In queuing theory, models in which arrivals (or customers)are drawn from a small population are called finite sourcemodels (Winston, 2004). The Machine Repair Model is anexample of a finite source model. The model or systemconsists of K machines and R repair bays. The length of timethat a machine spends away from the repair bays beforecoming back for repair follows an exponential distribution

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470 AUGUST 2007 VOLUME 107 REFEREED PAPER The Journal of The Southern African Institute of Mining and Metallurgy

with rate λ and the time to repair a broken down machine ata repair bay follows an exponential distribution with rate μ.In other words, λ is the inter-arrival rate and μ is the servicerate. Using the Kendall-Lee notation (Winston, 2004), theMachine Repair Model can be described as an M/M/R/GD/K/Kmodel, where the first M is the inter-arrival rate, the secondM is the service rate, R represents the number of repair bays,GD states that the machines are serviced following somegeneral queue discipline, the first K is the number ofmachines being serviced in the system, and the last K statesthat the machines are drawn from a population of size K.

Typical queue disciplines include first-come, first-served(FCFS), last-come, first-served (LCFS), service in randomorder (SIRO) and priority queuing disciplines. In FCFScustomers are serviced in the order of their arrival, in LCFSthe most recent arrivals are serviced first, and in SIRO theorder in which customers arrive has no effect on the order inwhich they are served. In priority queue discipline, eacharrival is classified into one of several categories, eachcategory is allocated a priority level, and within each prioritylevel, customers are serviced on an FCFS basis. For mostshovel-truck systems, trucks are serviced on an FCFS basis.

When arrivals to a system are drawn from a smallpopulation, the arrival rate may depend on the state of thesystem. For example, if the Machine Repair Model is in astate where j ≤ R machines are broken down, then a machinethat has just broken down will be assigned for repairimmediately, and if in a state where j > R machines arebroken down, then j - R machines will have to queue in a linewaiting for the next available repair bay. The state of asystem can be described as stable or unstable. Winston(2004) describes the conditions under which a system will bestable or unstable, as explained below.

Let ρ represent the traffic intensity for an M/M/1/GD/∞/∞system with exponential inter-arrival and service rates.

[1]

where λ is the number of machines arriving for repair perunit time and μ is the number of machines successfullyrepaired per unit time. Further, an M/M/1/GD/∞/∞ can bemodelled as a birth-death process with parameters asdescribed in Equations [2] to [4].

[2]

[3]

[4]

These equations describe the flow balance of a birth-death process where: expected no. of departures from state jper unit time = expected no. of entrances to state j per unittime

The steady state probabilities that j machines will bepresent are given in Equation [5].

[5]

where π is described as the probability that at a futureinstant, j machines will be present or may be perceived as thefraction of time that the j machines are present in the distant

future. The sum of the probabilities should be equal to unityas indicated in Equation [6], since at any given time thesystem must be in some state.

[6]

This infinite sum will diverge to infinity should ρ ≥1 andno steady state will exist, resulting in an unstable system.

Adapting machine repair model to shovel-trucksystem analysis

In this study the Machine Repair Model was modified tomodel shovel-truck systems and the modelling resultsobtained compared to output from other simulationmodels/packages. The Machine Repair Model equivalents areshown in parenthesis. A truck is sent for loading (repair)every cycle with the number of shovels or shovel loadingsides or number of tipping bins (repair bays) being equal toR and the inter-arrival and service times both assumed tohave an exponential distribution. Therefore, a shovel-trucksystem can be described as M/M/R/GD/K/K, where the first Mis truck arrival rate, the second M is loader service rate, R isthe number of shovels or shovel loading sides that areloading K trucks drawn from a population of size K, wherebythe loading follows some general queue discipline, GD.

As with the Machine Repair Model, trucks are drawnfrom a finite population and their arrival pattern willtherefore depend on the state of the system. For example,should all the trucks within a particular circuit be present atthe loading unit, such as when a loading unit is experiencingan unexpected breakdown, then the truck arrival rate will bezero. At any other instant when there is less than themaximum number of trucks at the loading unit, the arrivalrate will be positive. Under steady state conditions, the lengthof time that a truck spends away from the shovel follows anexponential distribution with rate λ, and the length of timethat a shovel takes to load a truck follows an exponential rate μ.

If we define ρ = μλ as in Equation [1], the steady-state

probability distribution will be given by Equations [7] and [8].

[7]

[8]

For any queuing system under steady-state conditions,Little’s queuing formulae can be applied to the system(Winston, 2004). Under steady-state conditions, an analogyof the shovel-truck system and the Machine Repair Model(Winston model) is illustrated in Table I.

By applying Little’s queuing formulae, the modelparameters are obtained from the calculations in Equations[9] to [12].

[9]

Modelling open pit shovel-truck systems using the Machine Repair ModelTransaction

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471The Journal of The Southern African Institute of Mining and Metallurgy VOLUME 107 REFEREED PAPER AUGUST 2007 ▲


[10]

[11]

[12]

The average number of arrivals per unit time is given byλ—

, where:

[13]

If Equation [11] is applied to trucks being loaded ortrucks tipping at a bin, then the trucks that are waiting forservice, W, are given by Equation [14].

[14]

If Equation [12] is applied to trucks waiting to be loaded,Wq, we obtain the relationship shown in Equation [15].

[15]

The inter arrival time λ1 at the loading unit is thus a

function of the truck’s waiting time at the dumpingdestination, Wq (and vice versa for trucks at the dumpingdestination). This system of equations defining the MachineRepair Model was then programmed into MS Excel.

Application of Machine Repair Model to virtual mine

The virtual mine has 10 m benches that extend from surfaceto a depth of 135 m (Figure 1). The ramp is constructed at8% up-grade (GR) with a 4% rolling resistance (RR) keptconstant throughout the haul route. A wheel loader loadsOHT trucks that dump material at either a plant tipping bin orwaste dump. For the virtual mine three loader cycle timeswere simulated, these being 3 minutes (for Caterpillar 777OHT), 4 minutes (for CAT 777 OHT) and 5 minutes (for CAT793 OHT). The dump and manoeuvre time was kept constantat 2.5 minutes, assuming a consistent operator proficiency.

Simulations were performed using the five modelsdescribed earlier on. The Arena model was used as thebenchmark model for the reason stated in Section 2.0 of thispaper. The shovel-truck model created in Arena for this studyis illustrated by the screen snapshot in Figure 2. By usingdifferent loader service times of three minutes, four minutesand five minutes, the five estimation models were run toproduce estimates of attainable loads per shift. A comparisonof the Winston (Machine Repair Model), FPC, Elbrond andTalpac to Arena in terms of the loads per shift is shown inFigure 3.

Several observations and accompanying explanations canbe made in relation to Figure 3. Generally, the loads per shiftobtained from the models are quite close to those obtainedusing Arena, with estimates from the other models rangingbetween 97% and 99.7% of the Arena estimates. The Talpacmodel with predominantly lognormal distributions fitted tocycle variables (standard distribution spreads embedded inprogram) produced estimates that were very close to thoseobtained from the Machine Repair Model, which has predomi-nantly exponential distributions. Although FPC does notspecify its embedded distributions, its estimates were closerto the estimates produced from lognormal and exponentialdistribution based models and appears to produceintermediate estimates compared to estimates from the othertwo models. The Elbrond (1990) model produced estimatesthat had the lowest percentage in comparison to Arenaestimates compared to the rest of the models. This isprimarily due to underestimation of waiting time by the FPCmodel when compared to the other models. By increasing thestandard deviation of service time to return time ratios by 0.2to 0.5, the difference of the Elbrond from with other modelsdecreases, improving its percentage estimation compared tothe other models. With an increase in service time theestimates of loads per shift deviate further away from Arena

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Table I

An analogy of shovel-truck system and Machine Repair Model

Notation Machine Repair Model Repair model adjusted for load and haulDescription

L Expected number of broken trucks Expected number of trucks at the loading unit or destination server (plant or dump)

Lq Expected number of trucks waiting for service Expected number of trucks waiting for serviceat the workshop repair bays at the loading unit or dumping distination

W Average time a machine spends broken (down time) Average time a truck spends at the loading unit or dump destination

Wq Average time a truck spends waiting for service Average time a truck queues at the loading unit or the plant/dump

Figure 1—Layout of the virtual mine

550 m to dump/plantflat/haul

550 m to loading areaflat/haul

Bench height: 10 m (depth: 10–135 m)Ramp length: 168–2828 mHalf cycle distance: 1268 m–2932 mRolling resistance: 4% constant

estimates. Arena reported slightly higher loads per shift witha possible explanation that the other models are more conser-vative, which could be a benefit to the user because the riskof potential loss of planned production is reduced. The slightimprovement in the estimates from the Winston, FPC andTalpac models compared to those from the Arena model withthe increase in service time from four minutes to five minutescan partly be explained by the difference in machine charac-teristics between the CAT 777D and CAT 793D OHT trucks.The reason why Talpac does not show this improvement canpartly be explained by the tendency of the Talpac program tounderestimate the performance of Caterpillar trucks. Overall,the results show that the Winston (Machine Repair) modelproduces productivity estimates in terms of loads per shiftthat closely match those of the other models.

Application of machine repair model to OptimumColliery’s Kwagga section

Optimum Colliery is a surface coal mine owned by Ingwe CoalCorporation and BHP Billiton. Kwagga section is part ofOptimum Colliery. Coal from Kwagga section is mined fromthree areas namely the North (or Rail), Central and Southsections. The haulage routes for all three areas wereconsidered in the study. Figures 4 depicts the haulage routesfor the North (or Rail) section to show a typical haul routelayout for the mine. The general geology of the North sectionis illustrated by a geological section (Figure 5). The strataconsist mainly of a relatively thick, white, coarse grainedmassive sandstone layer followed by a thick shale layerbelow. Thinner alternating shale and sandstone bands occur


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The Journal of The Southern African Institute of Mining and Metallurgy VOLUME 107 REFEREED PAPER AUGUST 2007 473 ▲

Figure 2—Screen snapshot of shovel-truck simulation process in Arena

Figure 3—Comparison of loads per shift of other models with arena for virtual mine

Co

rrel

atio

n %

Loader service time (min.)

Model correlation with Arena: across service time

shovel

count entrance

arrive no.

arrive 2

Arrive at shovel

Plant Arrive

Dispatch to Plant

Spot at plant

Back to shovel

in places. The top 8 metres consist of soft unconsolidatedmaterial. The geology illustrated in Figure 5 dictates that thegeneral mining direction should be up-dip so that thegradient can be used to drain water away from the loadingoperations. Consequently, in-face haulage roads on the mineare developed with a slight dip. Major segments constitutingthe haulage profiles and their associated haulage resistances,for the three sections are presented in Table II.

Prior to the study, the haulage equipment fleetcomplement for Kwagga section was constituted as follows:

➤ 4 x Caterpillar 776D coal haulers (CAT 776D)➤ 7 x Caterpillar 777D OHT (CAT 777D)➤ 2 x Caterpillar 992G Wheel Loader (WL) with a high lift

(HL) design (CAT 992 G WL HL)➤ 1 x Caterpillar 992D WL HL (CAT 992D WL HL).

At the North section one CAT 992D WL and fourCaterpillar 776D coal haulers are used. At the Central andSouth sections seven Caterpillar 777D OHT and twoCaterpillar 992G WL are used. The travel distances aremoderate for the Central and South sections while the North(or Rail) section has longer haul routes. It is for this reasonthat the CAT 776D coal haulers are predominantly confinedto the North (Rail) section since they are more suited forlonger hauls. Three Marion draglines are used for overburdenstripping. Front end wheel loaders load blasted coal into theOHT trucks and coal haulers. The trucks haul the coal to two

tips situated at the Central and South sections from wheretwo main conveyors feed the washing plant that delivers coalto the Hendrina Power Station.

The above equipment suite hauls about 10.5 million tonsof run-of-mine (ROM) coal per annum with the distributionby section as shown in Table III for a planned 8 322 site-scheduled hours per year. As can be derived fromTable III, the fleet has a scheduled production rate of about 1 260 t per site-scheduled hour. It was required to estimatethe additional trucks required to raise the production rate to 3 022 t per scheduled site hour. Simulation runs wereperformed using five different models including the MachineRepair Model. The simulated truck fleet requirements for aproduction rate of 3 022 t per site-scheduled hour arepresented in Table IV.

From Table IV it can be seen that the Arena and Winstonmodels, which are both modelled on exponential cycle timevariable distributions, yield the same truck requirement. TheElbrond model also yields the same truck requirement as theArena and Winston models. Although the Elbrond modelyields the same result as the Arena and Winston models, thedifference between its estimation of tons per hour (THP) andthe required TPH is double the difference between estimatedTPH and required TPH for other models. This can be directlyattributed to the Elbrond model reporting zero waiting timefor the coal haulers at the loaders. The FPC and Talpac


▲


Figure 5—Section through North (Rail) section

Figure 4—Aerial photograph showing haulage routes for the North (Rail) section

KGM-B12

North

K0261

K4344

KWN76

NO. 2

NO. 2A

KWN57KWN78

KWN99


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Table II

Distances, grade and rolling resistance of the haulage profiles

Section Face to ramp Ramp to haulage Haulage to tip Total

Distance Grade % RR% Distance Grade % RR% Distance Grade % RR% distance

NorthRamp 1 1 050 5% 4% 800 9.5% 4% 4 100 0% 3% 5 950Ramp 2 400 5% 4% 500 9.5% 4% 8 715 0% 3% 9 615Ramp 3 Load from stockpile 6 800 9.5% 4% 10 000 0% 3% 10 600

26 165

CentralRamp 1 200 5% 4% 400 9.5% 4% 2 000 0% 3% 2 600Ramp 2 350 5% 4% 450 9.5% 4% 1 300 0% 3% 2 100Ramp 3 400 5% 4% 400 9.5% 4% 700 0% 3% 1 500Ramp 4 650 5% 4% 5 800 9.5% 4% 400 0% 3% 1 500

7 750

SouthRamp 2 500 5% 4% 1 000 9.5% 4% 1 000 0% 3% 2 500Ramp 3 450 5% 4% 700 9.5% 4% 400 0% 3% 1 550Ramp 4 350 5% 4% 700 9.5% 4% 400 0% 3% 1 450Ramp 5 300 5% 4% 400 9.5% 4% 1 100 0% 3% 1 800Ramp 6 250 5% 4% 600 9.5% 4% 1 500 0% 3% 2 350Ramp 7 350 5% 4% 700 9.5% 4% 1 900 0% 3% 2 950

12 600Distance = travel in metres (one way)Grade % = grade resistance %RR% = rolling resistance %

models estimate one additional truck requirement comparedto the other models for the Central section. The Talpac modelestimates an additional coal hauler for the North sectioncompared to the other models. This can be attributed toTalpac reporting higher truck travel times, which result inhigher waiting times at both loader and dumping tips.Consequently, individual truck total cycle times are higher

compared to other models. Ultimately, in order to meet therequired TPH, more trucks are required compared to othermodels. Overall, it can be seen again that the Winston(Machine Repair) model produces truck fleet size estimatesthat closely match those from other models.

Subsequent to this study the mine decided to purchasetwo extra CAT 777D OHT trucks to bring the total CAT 777Dfleet size to six. They also decided not to supplement the coalhauler fleet due to a change in the North section mining

Table III

Planned production distribution by section

Section Site schedule hours Tons per annum planned

NorthRamp 1 3 177 1 046 093Ramp 2 2 951 971 373Ramp 3 2 194 722 303Sub-total 8 322 2 739 769

CentralRamp 1 1 040 598 357Ramp 2 1 820 1 047 125Ramp 3 2 081 1 196 714Ramp 4 3 381 1 944 661Sub-total 8 322 4 786 857

SouthRamp 2 1 891 663 278Ramp 3 1 702 596 951Ramp 4 1 324 464 295Ramp 5 1 135 397 967Ramp 6 946 331 639Ramp 7 1 324 464 295Sub-total 8 322 2 918 425Total 8 322 10 445 051

Table IV

Simulated truck fleet size estimates from the fivemodels

Model Section Truck type Total truck no.776D 777D 776D 777D

North 6 -Elbrond Central - 5 6 9

South - 4

North 6 -FPC Central - 6 6 10

South - 4

North 6 -Winston Central - 5 6 9

South - 4

North 6 -Arena Central - 5 6 9

South - 4

North 7 -Talpac Central - 6 7 10

South - 4


strategy. This decision was supported by a road improvementstrategy using mobile crushers to provide sound underfootconditions. This improvement will result in a reduction ofrolling resistance and travel time and thus total cycle timeand the number of coal haulers required.

Concluding remarks

Each of the five truck fleet size estimation models produceddifferent estimates for the same project input parameters. Theunderlying reason for the differences, as was observed fromthe two case studies, derives from the way the models assignprobability distributions to the individual cycle timecomponents. The simulations showed that the Arena modelwith exponential distributions fitted to the cycle timecomponents yielded similar results to the Winston model. TheElbrond and FPC programs, which do not have a specifiedunderlying distribution model and can be described as fieldmodels, yielded similar results compared to that of Arena andWinston (Machine Repair) models. The case studiesdemonstrate that the Winston (Machine Repair) modelproduces truck fleet size estimates that closely match theestimates produced by other models. The Winston (MachineRepair) model is an affordable model, even for once-off use,for mines needing to estimate project truck requirementsbecause it can be programmed on an MS Excel platform, asoftware package that most mines already use.

Acknowledgements

The authors wish to acknowledge Coaltech 2020 for fundingthe research and granting permission to publish this paper.Optimum Colliery is also acknowledged for allowing access totheir mine and providing data used in the second case study.

References1. DOWBORN, M. and TAYLOR, W. Simulation modelling of platinum operations

using GPSS/HTM, Proceedings of the 30th Application of Computers andOperational Research in the Mineral Industry, 2000. pp. 365–382.

2. ELBROND, J. Queuing Theory, Surface Mining, 2nd Edition, Society forMining and Metallurgy and Exploration (SME), Littleton, Colorado, 1990.pp. 743–748.

3. MORGAN, B. Optimizing truck-loader matching, Proceedings of the ThirdInternational Symposium on Mine Planning and Equipment Selection,Istanbul, Turkey, 18–20 October 1994, pp. 313–320.

4. PANAGIOTOU, G.N. and MICHALAKOPOULOS, T.N. Analysis of shovel-truckoperations using STRAPAC, Proceedings of the Third InternationalSymposium on Mine Planning and Equipment Selection, Istanbul, Turkey,1994. pp. 295-300.

5. STRUGUL, J.R. and JACOBSEN, W.L. (1994). A simulation model for testing aproposed mining operation: Phase 1, in Proceedings of the ThirdInternational Symposium on Mine Planning and Equipment Selection,Istanbul, Turkey, 1994. pp. 281–287.

6. STURGUL, J.R. and TECSA, T.L. Simulation and animation of a surface ironore mine, Proceedings of the Fifth International Symposium on MinePlanning and Equipment Selection, Sao Paulo, Brazil, 22–25 October1996, pp. 81–86.

7. STRUGUL, J.R., JACOBSEN, W.L., and TECSA, T.L. Modeling two-way traffic inan underground one-way decline, Proceedings of the Fifth InternationalSymposium on Mine Planning and Equipment Selection, Sao Paulo, Brazil,22–25 October 1996, pp. 87–90.

8. STURGUL, J.R. Mine Design: Examples Using Simulation, ISBN 0-87335-181-9, Society for Mining, Metallurgy, and Exploration, Inc. (SME),Littleton, Colorado. 2000.

9. TA, C.H., KRESTA, J.V., FORBES, F., and MARQUEZ, H.J. A stochasticoptimization approach to mine truck allocation, International Journal ofSurface Mining, Reclamation and Environment, vol. 19, no. 3, September2005, pp. 162–175.

10. TEMENG, V.A., FRANCIS, O.O., and FRENDEWEY, JR., J.O. Real-time truckdispatching using a transportation algorithm,International Journal ofSurface Mining, Reclamation and Environment, 1997, vol. 11, 1997. pp.203–207.

11. WINSTON, W.L. Operations Research: Applications and Algorithms (4thEdition), pp. 1104–1165, ISBN 0-534-38058-1. Indiana University,Brooks Cole. 2004. ◆

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A pesquisa Operacional e o Meio Ambiente6 a 9 de novembro de 2001 - Campos do Jordão - SP

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MODELOS DE PROGRAMAÇÃO MATEMÁTICA PARA RESOLUÇÃO DEPROBLEMAS DE MISTURA DE MINÉRIOS E ALOCAÇÃO DE

EQUIPAMENTOS EM MINAS A CÉU ABERTO

Luiz Henrique de Campos MerschmannCOPPE / UFRJ

Rio de Janeiro –[email protected]

Luiz Ricardo PintoEscola de Minas / UFOP

Ouro Preto – [email protected]

Resumo

O trabalho apresenta modelos matemáticos para resolução de problemas operacionaisrelacionados com o planejamento de lavra de minas a céu aberto. Os modelos se prestam àdeterminação do ritmo de lavra a ser implementado em cada frente de lavra, levando-se emconsideração a qualidade do minério em cada frente, a relação estéril/minério desejada, a produçãorequerida, as características dos equipamentos de carga e transporte e as características operacionais damina. Os modelos também consideram a possibilidade de alocação estática e dinâmica doscaminhões. No caso de alocação dinâmica, o modelo determina qual deve ser a produção de cadafrente e aloca os equipamentos de carga às frentes escolhidas. No caso da alocação estática, além daalocação dos equipamentos de carga, o modelo também faz alocação dos caminhões às frentes.Palavras-chave: programação matemática, mineração, mistura de minérios

Abstract

This paper presents mathematical models to solve operational problems in open pit miningdesign such as ore blending and equipment assignment. The models determine the productivity of eachworking bench in one mine. They also consider the ore quality in order to make the blending,production goals, truck and shovel characteristics and availability, and support both static and dynamicallocation. The dynamic allocation model provides productivity and haulage equipment assignment.The static allocation model also provides truck assignment.Keywords: Mathematical programming, mining, ore blending1) Introdução

A lavra de uma mina geralmente é feita em diversas frentes de modo que, realizando a misturados minérios retirados das frentes, seja possível fornecer para a usina de tratamento um minério queesteja de acordo com as especificações de qualidade necessárias. Deste modo, precisa-se conhecer qualo ritmo de lavra a ser implementado em cada frente, que atende as especificações quantitativas equalitativas da usina. Entende-se por ritmo de lavra a produção horária da frente.

Uma mina possui equipamentos como caminhões, carregadeiras e escavadeiras que viabilizama lavra nas diversas frentes. Mesmo mantendo uma frota com um número fixo de equipamentos, aquantidade disponível em condições de operar pode variar ao longo do tempo. Isso pode acontecer pormotivo de quebra desses equipamentos, manutenção preventiva, atrasos operacionais, etc. Sendoassim, o cumprimento do ritmo de lavra com objetivo de atender as especificações da usina dependeda disponibilidade dos equipamentos na mina.

Diante deste cenário diversas questões podem surgir, tais como:

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Com quais frentes deve-se trabalhar para atender as especificações de qualidade da usina detratamento?

Com a frota de equipamentos disponíveis será possível atender um ritmo de lavra que possibilita oatendimento das especificações da usina?

A partir de uma determinada frota de equipamentos e das especificações impostas pela usina, qualé a máxima produção que pode ser obtida? E qual é o ritmo de lavra de cada frente?

Cada uma das questões apresentadas anteriormente pode ser respondida mediante a construçãode modelos distintos de programação matemática. Pinto (1995) fez uma abordagem sobre o temarelacionado à mistura de minérios. Naquele trabalho, no entanto, não foram consideradas diversasquestões relacionadas às características dos equipamentos, nem à relação estéril/minério.

A seguir, dois modelos serão apresentados. Ambos têm como objetivo determinar o ritmo delavra de cada frente disponível e alocar os equipamentos existentes às mesmas, de forma a maximizara produção. Os modelos se diferem pela forma de alocação dos caminhões. Um trabalha com alocaçãoestática, ou seja, cada caminhão trabalha fixado a um único par de pontos de carga e descarga. Destaforma, cada caminhão atenderá uma única frente e descarregará sempre no mesmo ponto. O outromodelo trabalha com alocação dinâmica, onde a definição da frente a ser atendida por cada caminhão eseu ponto de descarga, acontece ao término de cada viagem, sendo o controle desta alocação realizadopor um sistema de despacho automático.

No modelo de alocação dinâmica, a alocação de equipamentos fica restrita a carregadeirase/ou escavadeiras. Já o segundo modelo considera um sistema de alocação estática e, deste modo, omodelo contempla também a alocação de caminhões.

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2) Modelo matemático - alocação dinâmica de caminhões

Seja uma mina a céu aberto onde, durante a lavra, exista um controle dos teores das diversasvariáveis envolvidas. Neste trabalho, considerou-se o controle dos teores das variáveis químicas, maso mesmo poderia ser feito para o controle das variáveis físicas, como a granulometria, por exemplo.

A cada plano de lavra de curto prazo elaborado, existem n frentes disponíveis, onde a lavrapode acontecer simultaneamente em m (m ≤ n) dessas frentes, dependendo da disponibilidade deequipamentos de carga (carregadeiras e/ou escavadeiras).

Caso entre em operação, por razões técnicas e econômicas, cada equipamento de carga devetrabalhar entre limites preestabelecidos de produção. Além disso, uma relação estéril/minério mínimapreestabelecida deve ser cumprida.

O modelo matemático para o problema descrito anteriormente é o seguinte:Seja:M o conjunto das frentes de minérioE o conjunto das frentes de estérilPi o ritmo de lavra da frente i (t/h)

0, se o equipamento de carga j não trabalhar na frente ixji =

1, se o equipamento de carga j trabalhar na frente i

t v i o teor da variável v na frente i (%)linf v o teor mínimo admissível para a variável v (%)lsup v o teor máximo admissível para a variável v (%)Pmin j a produção mínima admissível para o equipamento de carga j (t/h)Pmax j a produção máxima admissível para o equipamento de carga j (t/h)R a relação estéril minério mínima requeridaPreq a produção mínima requerida (t/h)

Função Objetivo:

Maximizar ∑∈Mi

iP

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Restrições de Qualidade:

(1) sup

inf vlP

tP

l v

Mii

Mivii

v ∀≤≤∑

∑

∈

∈

Restrições de Alocação:

)2( , 1 EiMixj

ji ∈∈∀≤∑

)3( 1 jx

EiMi

ji ∀≤∑∈∈

Restrições de Produção:

)4( , maxmin EiMixPPxP jij

jijij

j ∈∈∀≤≤ ∑∑

)5( Pr eqPMi

i ≥∑∈

)6( RP

P

Mii

Eii

≥∑∑

∈

∈

)7( , 0 EiMiPi ∈∈∀≥

As restrições de qualidade (1) garantem que o produto resultante da mistura dos minérios dasdiversas frentes esteja com a qualidade exigida pela usina de tratamento.

As restrições de alocação (2) e (3) fazem com que cada frente possua somente umequipamento de carga – restrições de alocação (2) – e que cada equipamento de carga atenda somenteuma frente – restrições de alocação (3).

Já as restrições de produção estão divididas em quatro grupos: (4) essas restrições garantemque os equipamentos de carga trabalhem entre os limites de produção preestabelecidos; (5) restriçãoopcional, caso se deseje impor uma produção mínima; (6) restrição que garante a relaçãoestéril/minério preestabelecida e (7) é a restrição que garante produção em nível positivo em todas asfrentes de lavra.

3) Modelo matemático - alocação estática de caminhões

Inicialmente, será considerada a mesma situação apresentada no caso do modelo anterior. Adiferença é que no caso de alocação estática tem-se também que realizar a alocação de caminhões àsfrentes de lavra. Para isso, deve-se levar em consideração dois fatos:

Cada caminhão deve atender uma única frente de lavra, sendo que, uma frente pode ter mais deum caminhão alocado a ela.

Um caminhão somente poderá trabalhar numa determinada frente se o seu modelo for compatívelcom o modelo do equipamento de carga que foi alocado àquela frente.

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Sendo assim, o modelo matemático é o seguinte:Seja:M o conjunto das frentes de minérioE o conjunto das frentes de estérilPi o ritmo de lavra da frente i (t/h)

0, se o equipamento de carga j não trabalhar na frente ixj i =

1, se o equipamento de carga j trabalhar na frente i

0, se o se o caminhão k não trabalhar na frente idk i =

1, se o se o caminhão k trabalhar na frente i

0, se o equipamento de carga j não trabalhar com o caminhão kyj k =

1, se o equipamento de carga j trabalhar com o caminhão k

t v i o teor da variável v na frente i (%)linf v o teor mínimo admissível para a variável v (%)lsup v o teor máximo admissível para a variável v (%)C k i a produtividade do caminhão k quando ele trabalha na frente i (t/h)Pmin j a produção mínima admissível para o equipamento de carga j (t/h)Pmax j a produção máxima admissível para o equipamento de carga j (t/h)R a relação estéril/minério mínima requeridaPreq a produção mínima requerida (t/h)

Função Objetivo:

Maximizar ∑∈Mi

iP

Restrições de Qualidade:

(1) supinf vlP

tP

l v

Mii

Mivii

v ∀≤≤∑

∑

∈

∈

Restrições de Alocação:

)2( , 1 EiMixj

ji ∈∈∀≤∑

)3( 1 jx

EiMi

ji ∀≤∑∈∈

)4( 1 kd

EiMi

ki ∀≤∑∈∈

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)5( ,,, 12 kjEiMiydx jkkiji ∈∈∀≤−+

Restrições de Produção:

)6( , maxmin EiMixPPxP jij

jijij

j ∈∈∀≤≤ ∑∑

)7( , EiMidCP kik

kii ∈∈∀≤ ∑

)8( Pr eqPMi

i ≥∑∈

)9( RP

P

Mii

Eii

≥∑

∑

∈

∈

)10( , 0 EiMiPi ∈∈∀≥

Com relação ao primeiro modelo (alocação dinâmica) três grupos de restrições foramacrescentados, cujas funções são:

Restrições de alocação (4): garantem que cada caminhão atenderá somente uma frente. Restrições de alocação (5): permitem que somente modelos compatíveis de equipamentos de carga

e de caminhões trabalhem numa mesma frente. Restrições de produção (7): garantem que a produção de cada frente fique limitada a produtividade

dos caminhões que a ela estão alocados. A produtividade dos caminhões é calculada dividindo-sea sua capacidade de carga pelo tempo de ciclo total. Entende-se por tempo de ciclo total osomatório dos tempos de carga, deslocamento carregado, descarga e deslocamento vazio.

4) Implementação computacional

Os modelos propostos devem ser resolvidos com a utilização de software específico, já quesua resolução manual é inviável devido ao grande número de restrições. Existem no mercado, diversosdestes softwares, tais como o LINDO e “What’s Best” da Lindo Systems Inc ou CPLEX da CplexOptimization Inc. Para geração do modelo matemático que servirá como entrada destes softwares,aconselha-se o uso de um programa construído especificamente para este fim, pois isso evita erros naconstrução do modelo. Estes programas podem ser desenvolvidos a partir de linguagens genéricascomo C++, Pascal, Fortran, Delphi, Visual Basic, etc.

5) Exemplo de aplicação

Seja uma mineradora de ferro que disponibiliza em seu plano de curto prazo 6 frentes deminério e 2 de estéril. Todo minério lavrado é descarregado no britador primário que alimenta a usinade tratamento de minério e todo estéril é depositado em uma única pilha. As variáveis controladasnesta mina correspondem aos teores de ferro, fósforo, alumina e sílica e para o plano de lavra emquestão seus valores são mostrados na tabela 1. Os limites requeridos pela usina para cada uma dasvariáveis são mostrados na tabela 2.

Tabela 1 – Teores das frentes de lavraFrente/Tipo Ferro (Fe) - % Fósforo (P) - % Alumina (Al2O3) - % Sílica (SiO2) - %

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F1 / Minério 45,34 0,038 1,21 3,56F2 / Minério 48,87 0,059 1,35 4,94F3 / Minério 53,76 0,038 0,87 3,05F4 / Minério 52,56 0,041 0,91 4,74F5 / Minério 47,00 0,032 1,10 4,57F6 / Minério 50,12 0,039 1,31 4,58F7 / Estéril 34,00 0,058 0,97 6,65F8 / Estéril 41,00 0,055 1,89 5,95

Tabela 2 – Limites admissíveis para usinaVariável Limite Inferior (%) Limite Superior (%)

Ferro (Fe) 48,50 58,00Fósforo (P) 0,030 0,043

Alumina (Al2O3) 0,50 1,15Sílica (SiO2) 4,00 4,50

A empresa dispõe de 4 equipamentos de carga (carregadeira e/ou escavadeira) e 15 caminhõesfora-de-estrada. Por razões operacionais cada equipamento de carga deve trabalhar com umaprodutividade entre 450 e 900 t/h. Os caminhões têm capacidade média de 120 t. Os tempos de ciclomédios para cada uma das frentes estão mostrados na tabela 3. A usina requer no mínimo 2500 t/h deR.O.M. (run of mine) e a relação estéril / minério mínima deve ser de 0,3.

Tabela 3 – Tempos de ciclosFrente T Carga (min) T Desl Car (min) T Desc (min) T Desl Vaz (min) T Total (min)

F1 2,3 5,33 0,8 4,16 12,59F2 2,3 6,24 0,8 4,42 13,76F3 2,3 7,28 0,8 5,85 16,23F4 2,3 4,81 0,8 3,9 11,81F5 2,3 5,2 0,8 4,16 12,46F6 2,3 9,75 0,8 8,06 20,91F7 2,3 8,45 0,8 7,15 18,70F8 2,3 10,92 0,8 8,97 22,99

T Carga: tempo de carga, T Desl Car: tempo de deslocamento carregado, T Desc: tempo de descarga, T Desl Vaz: tempo de deslocamentovazio, T Total: tempo de ciclo total

O problema proposto foi resolvido utilizando-se os dois modelos apresentados anteriormente,sendo sua implementação computacional feita com o uso do sistema LINDO da LINDO Systems Inc.A geração do modelo de entrada foi feita por meio de programa desenvolvido em Borland Delphi 5.0.Os resultados de produtividade e alocação de equipamentos obtidos para cada um dos modelos sãoapresentados a seguir nas tabelas 4 e 5.

Tabela 4 – Resultados para alocação dinâmicaFrente F1 F2 F3 F4 F5 F6 F7 F8

Ritmo(t/h) 0 900 900 0 900 0 900 0Eqpto carga -- nº 3 nº 1 -- nº 4 -- nº 2 --

Eqpto carga: equipamento de carga

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Tabela 5 – Resultados para alocação estáticaFrente F1 F2 F3 F4 F5 F6 F7 F8

Ritmo(t/h) 0 0 900 900 0 900 810 0Eqpto carga -- -- nº 2 nº 1 -- nº 4 nº 3 --

Quant. Caminhões -- -- 3 2 -- 3 3 --Eqpto carga: equipamento de carga, Quant. Caminhões: quantidade de caminhões alocados

Em ambos casos, a qualidade da mistura e a relação estéril/minério atendem às especificaçõescomo pode ser observado na tabela 6. Como pode ser observado o exemplo admite mais de umasolução. Além disso, não houve necessidade, para operacionalizar este plano, de se utilizar todos oscaminhões disponíveis, apenas 11 deles.

Tabela 6 – Resultados de qualidade e relação estéril/minérioVariável Modelo Alocação Estática Modelo Alocação Dinâmica

Ferro 52,15 49,89Fósforo 0,039 0,043Alumina 1,03 1,11

Sílica 4,12 4,19Rel. Est/Min 0,30 0,33

Rel. Est/Min: relação estéril/minério

6) Conclusões

Os modelos apresentados contemplam diversos aspectos operacionais do planejamento delavra de curto prazo e seu uso simplifica substancialmente a programação da lavra. A implementaçãocomputacional dos modelos, apesar de não trivial, devido ao grande número de restrições, pode serfeita utilizando qualquer software de programação matemática. Na maioria das minas brasileiras, aresolução de problemas deste tipo ainda é feita pelo método de tentativas e erros, utilizando planilhaseletrônicas, o que não garante uma solução otimizada e demanda muito tempo. Espera-se que, embreve, muitas dessas empresas adotem soluções deste tipo visando à otimização de suas atividades, deforma a atender às exigências de um mercado cada vez mais competitivo.

Referências bibliográficas

PINTO, L. R. Uso de técnicas de pesquisa operacional na otimização das operações de lavra. In:Congresso Brasileiro de Mineração, VI, 1995. Salvador. Coletânea de trabalhos técnicos. Salvador:IBRAM, 1995. p. 53-61

INTRODUCCIÓN A LA INGENIERÍA

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“LA TECNOLOGÍA MODERNA, A PARTIR DE LA REVOLUCIÓN INDUSTRIAL, CONFIGURA DE FORMA DECISIVA TODO EL ÁMBITO DE LA EXPERIENCIA HUMANA. ALTERA LA REALIDAD, NUESTRA FORMA DE REPRESENTARLA Y EXPLICARLA Y NUESTROS CRITERIOS PARA VALIDARLA”

M.A. QUINTANILLA. 1988


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“Lo que nadie puede dudar es que, desde hace mucho tiempo, la técnica se ha insertado entre las condiciones ineludibles de la vida humana de suerte tal que el hombre actual no podría, aunque quisiera, vivir sin ella. Es pues, hoy, una de las mayores ingredientes que integran nuestro destino”

Ortega y Gasset, JoséSantander, 1932


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SOBRE LA TECNOLOGÍA

D.R.A.E.

ETIMOLOGÍA

“Conjunto de los conocimientos propios de un oficio o arte industrial

Estudio racional de la técnicaCiencia tratada según las normas del arte

CARÁCTER ANFIBOLÓGICO ACTUALCARÁCTER ANFIBOLÓGICO ACTUALUTILIZACIÓN INTERESADAUTILIZACIÓN INTERESADA

¡ TO GET MORE OUT OF LESS ¡


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TECNOLOGÍA

TÉCNICAProcedimientos

CIENCIAConocimientos TECNOLOGÍATECNOLOGÍA

PROCESOSINDUSTRIALES

+


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TTEECCNNOOLLOOGGÍÍAA

ÁMBITO CULTURAL

Fines, valores, creencias,costumbres, ideas, creatividad,

progreso

ÁMBITO ORGANIZATIVO

Actividad económica, actividadindustrial, organizacionesprofesionales, sindicatos

consumidores

ÁMBITO CIENTÍFICO -TÉCNICO

Ciencia, conocimientos, máquinas,aparatos, productos, recursos

TTEECCNNOOLLOOGGÍÍAA

ÁMBITO CULTURAL

Fines, valores, creencias,costumbres, ideas, creatividad,

progreso

ÁMBITO ORGANIZATIVO

Actividad económica, actividadindustrial, organizacionesprofesionales, sindicatos

consumidores

ÁMBITO CIENTÍFICO -TÉCNICO

Ciencia, conocimientos, máquinas,aparatos, productos, recursos

Tecnología:Tecnología: “Aplicación del conocimiento científico y de los procedimientos técnicos a la realización de tareas prácticas por medio de sistemas organizados que comprenden personas y organizaciones, seres vivos y máquinas”

[Pacey, 1983]


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Un concepto que serelaciona con otros:

- CIENCIA

- TÉCNICA

- TECNOLOGÍA

- UN TÍTULO ACADÉMICO

- UNA ACTIVIDAD PROFESIONAL

- UNA MANERA DE ACTUAR:“EL MÉTODO INGENIERIL”

INGENIERÍA

INTRODUCCIÓN:

Problemas que plantea la definición de Ingeniería


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INGENIERÍA: Arte de transformar las materias primas y usar las fuentes de energía de la naturaleza en la producción de bienes y servicios para el bienestar del hombre. [“Engineering and Western Civilization”, James H. Finch. MGH, 1952]

PROCREAD Y MULTIPLICAOS

Y HECHID LA TIERRA.

Y SOJUZGARLA, Y DOMINAD

EN LOS PECES DEL MAR

Y EN LAS AVES DEL CIELO

Y EN TODO ANIMAL

QUE SE MUEVA SOBRE LA TIERRA

[Génesis 1,28]


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OTRA DEFINICIÓN DE INGENIERÍA:Aplicación creativa de los principios científicos al diseño de estructuras, máquinas, aparatos y procesos de fabricación, y al manejo de todo ello con un buen conocimiento de sus usos y propiedades, pudiendo predecir su funcionamiento bajo condiciones específicas de trabajo.

DIMENSIÓN:DIMENSIÓN: FÁBRICA, MÁQUINAS, APARATOS, ...

PERFILPERFIL:: INGENIERO REVOLUCIÓN INDUSTRIAL (1825)


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INGENIEROS INDUSTRIALES: ESPAÑA 1855

DIMENSIÓN:DIMENSIÓN: SERVICIOS

PlanificaciónGestiónAdministraciónOrganizaciónDirección

DIMENSIÓNDIMENSIÓN:: ECONÓMICA

CosteTiempoMercado


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DEFINICIÓN SINTÉTICA QUE “ACEPTAREMOS”EN ESTE CURSO

INGENIERÍA: Es la actividad profesional que consiste en la aplicación creativa de los conocimientos científico-técnicos a la invención, desarrollo y producción de bienes y servicios, transformando y organizando los recursos naturales para resolver las necesidades del hombre, haciéndolo de una manera óptima, tanto económica como socialmente.


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DEFINICIÓN “PROVOCADORA”: La ingeniería es el arte de modelar materiales que no entendemos plenamente en formas que no podemos analizar con precisión, para que soporten fuerzas que no sabemos evaluar correctamente, de modo que la opinión pública no tenga motivos para sospechar el alcance de nuestra ignorancia.


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DEFINICIÓN DE INGENIERÍA COMOACTIVIDAD PROFESIONAL:

Actividad profesional que usa el método científico para transformar de una manera económica y óptima los recursos naturales en formas útiles para el uso del hombre.

ACTIVIDAD PROFESIONAL

Empleo, facultad u oficio que se ejerce públicamenteNo confundir titulación con profesión


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DEFINICIÓN DE “INGENIERO” SEGÚN FEANI(Federación Europea de Asociaciones Nacionales de Ingenieros):

Un ingeniero es una persona que ha adquirido y sabe utilizar conocimientos científicos, técnicos y cualesquiera otros necesarios que le capacitan para crear, operar y mantener sistemas eficaces, estructuras, instalaciones o procesos, y para contribuir al progreso de la ingeniería mediante la investigación y el desarrollo.

CONOCIMIENTOCONOCIMIENTO (Posesión y utilización)CAPACITACIÓNCAPACITACIÓN (Legal y profesional)INNOVACIÓN INNOVACIÓN (I+D, optimización)


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INNOVACIÓNINNOVACIÓNJ. Soluciones que combinen calidad-sencillez-costeK. Actitud innovadora y creativa, apreciación positiva del cambio técnicoM. Consideración y respeto por los factores medioambientales

INGENIERO

(FEANI)

CAPACITACIÓNCAPACITACIÓNA.Responsabilidad profesionalE. Uso de modelos teóricos de

simulación del mundo físicoF. Enjuiciar problemas técnicosG.Trabajo multidisplinarI. Comunicarse oralmente y por

escritoL. Solución ingenieril más favorable

(costes/calidad/tiempos)

CONOCIMIENTOCONOCIMIENTOB. Física, matemáticas y

fundamentos de su especialidadC. Práctica de su rama de

ingenieríaD. Instrumentación en nuevas

tecnologías y manejo de información técnica y estadística

H.Relaciones industriales, dirección empresarial

O.Dominio de otra lengua europeaForm

ación Universitaria

Práctica Profesional


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E J E M P L O

FARADAY

PRINCIPIO DE INTRODUCCIÓN ELECTROMAGNÉTICA (1831)

SIEMENS(1816-1842)

EDISON(1847-1931)

DINAMO(1879)

DINAMO(1867)

EMPRESA EMPRESA


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1. Observación de un fenómeno

2. Conocimiento existente

3. Formulación de hipótesis

4. Deducción:lógica,matemáticas, etc

5. Contraste teorías-hechos

6. Comunicación a la comunidad científica

7. Aceptación por la comunidad científica

8. Nuevo conocimiento, mejora del existente

MÉTODO CIENTÍFICOMÉTODO CIENTÍFICO MÉTODO INGENIERILMÉTODO INGENIERIL

1. Identificación de un problema

2. Recopilación de información

3. Búsqueda de soluciones creativas

4. Diseños preliminares: modelización, simulación, cálculos, etc

5. Evaluación y selección de soluciones

6. Elaboración del proyecto: planos, mediciones, pliegos.condiciones, etc.

7. Producción, construcción, etc.

8. Mercado, público, sociedad.


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HOMBREHOMBREPIENSA (H. SAPIENS)HACE (H.FABER)

SUJETOSUJETO

NATURALEZANATURALEZADIFICULTADESFACILIDADES

MEDIOMEDIO

ACTIVIDADTÉCNICA

REFORMA

ADAPTACIÓN

ANIMALESANIMALESPLANTASPLANTASSUJETO

NATURALEZANATURALEZAMEDIO

ACTIVIDADBIOLÓGICA

ADAPTACIÓN

REFORMA


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NATURALEZA

+

PROGRAMA HUMANO

TÉCNICA

OBJETO: “EL QUE”

FINALIDAD: “PARA QUE”

REFORMA DE LA NATURALEZA


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NECESIDADNECESIDAD ........................................

ACTO NATURAL ...............ACTO NATURAL ...............

ACTOS TÉCNICOS ............ACTOS TÉCNICOS ............

INGENIERÍA .......................INGENIERÍA .......................

HAMBRE

COMER LO QUE SE ENCUENTRA

CAZAR, SEMBRAR, RECOLECTAR, SEGAR, MOLER, ETC

SISTEMAS Y REDES DE RIESGOS

UTILIZACIÓN DE MAQUINARIA

PLANIFICACIÓN, PRODUCCIÓN

BIOTECNOLOGÍA

TRANSGÉNICOS, ETC

¿Existe hambre en el mundo?


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NECESIDADNECESIDAD ........................................

ACTO NATURAL ...............ACTO NATURAL ...............

ACTOS TÉCNICOS ............ACTOS TÉCNICOS ............

INGENIERÍA .......................INGENIERÍA .......................

DESPLAZARSE

ANDAR, CORRER, SALTAR

USO DE ANIMALES

NAVEGACIÓN

ENERGÍAS NATURALES:

AGUA, VIENTO

FERROCARRIL, BARCOS, AUTOMÓVIL

ENERGÍAS ARTIFICIALES

MÁQUINAS

Volar,¿Era necesario?


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OPTIMIZACIÓN ECONÓMICO-SOCIAL

LA TOMA DE DECISIONES SOBRE:LA TOMA DE DECISIONES SOBRE:

OPCIONES CON ALTO GRADO DE CERTEZAFactores y variables cuantificablesModelos, simulación, etc.Consecuencias conocidas

OPCIONES CON RIESGO E INCERTIDUMBREFactores y variables no cuantificablesAusencia de modelosConsecuencias conocidas con un margen de seguridad

OPCIONES CON RESULTADOS DESCONOCIDOS

Largo plazoSistemas complejos


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CONCEPTO DE INGENIERÍA

DEFINICIÓN GLOBAL: DIMENSIONESDEFINICIÓN GLOBAL: DIMENSIONES

I. DIMENSIÓN CIENTÍFICO-TÉCNICAAplicación creativa: innovaciónPrincipios científicosDiseño, desarrollo, construcciónEstructuras, máquinas, aparatos, sistemasFuncionalidad, utilidad

II. DIMENSIÓN ECONÓMICO-SOCIALOrganización Recursos: materiales – económicos - humanosOrganización y dirección empresasPlanificación y gestión de serviciosOptimización costes: económicos - sociales


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RESOLVER PROBLEMASRESOLVER PROBLEMASTÉCNICOSTÉCNICOS ECONÓMICOSECONÓMICOS SOCIALESSOCIALES

ECONÓMICOS: “Un ingeniero es una persona capaz de hacer por una peseta lo que un no ingeniero haría por cien”Hacer que una cosa funcione bien de la forma más barata posible

COMPROMISO: CALIDAD / COSTECOMPROMISO: CALIDAD / COSTE

SOCIALES. Importancia deLA SEGURIDADLA SALUDEL MEDIO AMBIENTE

CALIDAD TÉCNICACALIDAD TÉCNICACOMPROMISOCOMPROMISO COSTE ECONÓMICOCOSTE ECONÓMICO

COSTE SOCIALCOSTE SOCIAL

CONCEPTO DE INGENIERÍA

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TECHNICAL CORNER by Greg Sitek Introducing the …...Five forward gears.An additional forward speed is provided between the normal working and hauling ranges. Softer steps between