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Aggregate PlanningAggregate Planning
Planning the overall use of the Planning the overall use of the organization’s assetsorganization’s assets
Applied Management Science for Decision Making, 1e Applied Management Science for Decision Making, 1e © 2012 Pearson Prentice-Hall, Inc. Philip A. Vaccaro , PhD© 2012 Pearson Prentice-Hall, Inc. Philip A. Vaccaro , PhD
OVERVIEWOVERVIEW
ObjectivesObjectives
Definition of the Definition of the Quasi-UnitQuasi-Unit
StrategiesStrategies
Computer ApplicationsComputer Applications
Master Production ScheduleMaster Production Schedule
Aggregate Planning Aggregate Planning DefinitionDefinition
The overall employment of the firm’s facilities and other resources over the next 3 to 18 months so as to satisfy customer demand for all goods and services at minimum cost, as well as certain corporate policies such as “no layoffs” and “no overtime pay”.
Corporate PolicyCorporate Policy Requirements Requirements EXAMPLESEXAMPLES
A stable work force 100% in-house production Sufficient inventories to reduce the
likelihood of stockouts to =< 5% Overtime labor hours not to exceed
10% of all regular labor hours
The The Quasi-UnitQuasi-Unit
A unit of product that is representative of
all the firm’s goods and services.
Examples are appliances and vehicles in manufacturing.
Examples are airline passenger miles flown and restaurant meals in the service sector.
The Meal Quasi-UnitThe Meal Quasi-Unit
x ounces of meat x ounces of fish x ounces of poultry x gallons of water for
cooking / cleaning x amount of gas and
electricity for cooking
x amount of labor time and cost for cooking
x amount of labor time and cost for serving
x ounces of vegetables of various types
And much more!
RESTAURANT
The Quasi - UnitThe Quasi - Unit
Gallons of Beer
Not individual brands, bottles, kegs, cans, varieties
Tons of Steel Not ingots or beams of varying tensile strength
MANUFACTURING
The Quasi - UnitThe Quasi - Unit
Faculty-to-Student Contact Hours
Transcends the number of hours of classroom
instruction, student advising, directed studies,
internships, and so on.
Airline Passenger Miles Flown
Transcends the number of flights by specific
aircraft over specific routes.
SERVICE SECTOR SERVICE SECTOR
The Pseudo / Composite UnitThe Pseudo / Composite UnitALTERNATE NAMES FOR THE QUASI - UNIT
Sometimes, the unit does not exist at all!
It is a collection of square feet of sheet metal,several dozen screws or bolts, a variety ofcomponents, assemblies, ounces of glue,
paint, fabric, and so on.
STRICTLY USED FORPLANNING PURPOSES
The The NewNew Quasi - Unit Definition Quasi - Unit Definition
A SINGLE PRODUCTSINGLE PRODUCT representing a family of individual products that:
are processed on the same machines are processed by the same workers share the same general machine setup have similar cost structures, carry costs, and output rates share more / less the same parts and assemblies as well as physical charac- teristics
Quasi-Unit InterpretationsQuasi-Unit Interpretations
Mid-sized ProductMid-sized Product in a line of similar products ( autos, refrigerators )
Only ProductOnly Product made in a particular manufacturing plant
Basic ProductBasic Product with minor differences between models
Hybrid ProductHybrid Product or “cross” between several types of products produced in one or more plants
Other
Basic Product with Minor Differences
UNITED STATESUNITED STATES
MEXICOMEXICO
Basic Product with Minor Differences
2013 Ford Fusion
2013 Lincoln MKZ
Basic Product with Minor Differences
2013 Ford Fusion
2013 Lincoln MKZ
Overview of the ProcessOverview of the Process
A quasi-unit demand forecast is developed for 3 to 18 months into the future.
The firm then manipulates production rates, inventory levels, and work force levels to generate a series of aggregate plans that meet the forecasted demand.
AGGREGATE PLANNINGAGGREGATE PLANNING
Overview of the ProcessOverview of the ProcessAGGREGATE PLANNINGAGGREGATE PLANNING
Cost estimates are developed and the lowest cost aggregate plan is adopted.
Plan is then decomposed or disaggregated into a series of master production schedules that specify the exact number of products and services to be generated on a daily, weekly, or monthly basis. ( by make, model, color, and options )
The Aggregate PlanThe Aggregate Plan
I. Specified production rate for each time period.
II. Specified level of inventory for each time period.
III. Specified labor force size for each time period.
* ( USUALLY 1 MONTH OR 1 QUARTER )
*
MINIMUM DATA REQUIREMENTSMINIMUM DATA REQUIREMENTS
The Three Principal Strategies
Inventory Cushion or Level Work Force
Skeleton Force or Cadre
Chase or Matching
AGGREGATE PLANNING
Inventory Cushion StrategyInventory Cushion Strategy
Labor force size is fixed. Production rate is fixed. Inventories riserise during slowslow demand periods. Inventories shrinkshrink during highhigh demand periods. Inventory stockout costs are reduced. Overtime pay, hiring, firing, subcontracting, and
production rate change costs are eliminated.
The Inventory CushionThe Inventory Cushion
DURINGHIGH
DEMANDDECREASESDECREASES
DURINGLOW
DEMANDINCREASESINCREASES
THE INVENTORY CUSHION INSULATES THE FACTORY FROM DEMAND FLUCTUATIONS
Skeleton Force or Cadre Skeleton Force or Cadre StrategyStrategy
The permanent labor force size is usually set for the lowest monthly or quarterly forecasted quasi- unit demand.
Higher demand must then be met by scheduling overtime, hiring temporary workers, subcontract- ing, and so on.
Lower demand, if any, is tolerated as paid idle time.
SKELETON FORCE SKELETON FORCE STRATEGYSTRATEGY U.S. ARMYU.S. ARMY
ACTIVE DUTY480,000
46%
RESERVE / NATIONAL GUARD563,000
54%
$100,000.TO PAY
AND EQUIPEACH
SOLDIERPERMANENT
WORK FORCE
$25,000.TO PAY
AND EQUIPEACH
SOLDIERPART-TIME
WORK FORCE
*
RETIRED AND STANDBY RESERVES ACTIVATED ONLY IF ABSOLUTELY NECESSARY - 12,000,000 TROOPS
SKELETON FORCE SKELETON FORCE STRATEGYSTRATEGY HIGHER HIGHER
EDUCATIONEDUCATION
In 1984, full-time faculty were 80% of all faculty
In 1987, full-time faculty were 67% of all faculty
In 2001, full-time faculty were 55% of all faculty
In 2003, full-time faculty were 50% of all faculty
BETWEEN 1995 – 1997, 67% OF ALL NEW PROFESSORSWERE HIRED AS ADJUNCTS, IN ORDER TO SAVE $$$
Chase Chase oror Matching Strategy Matching Strategy
Calls for monthly / quarterly adjustment of the
labor force size as necessary to match produc-
tion to demand.
Eliminates or reduces inventory carry costs and stockout costs.
It generates substantial hiring, training, and termination costs and risks the degradation of employee morale and loyalty.
Two Types of Two Types of CostsCosts
Those that Those that WILLWILL change from one change from one
developed plan developed plan
to the nextto the next
Those that Those that WILL NOTWILL NOT change from one change from one developed plandeveloped plan
to the nextto the next
NON-RELEVANTNON-RELEVANTRELEVANTRELEVANT
THEIR INCLUSION WOULD NOT DIFFERENTIATE ONE PLAN FROM ANOTHERTHEIR INCLUSION WOULD NOT DIFFERENTIATE ONE PLAN FROM ANOTHER
NON-RELEVANT COSTS ARE OMITTED FROM THE AGGREGATE PLANNING ANALYSIS SINCE THEY DO
NOT ASSIST THE PLANNER IN IDENTIFYING THE MOST COST- EFFECTIVE PLAN.
Possible Plan CostsPossible Plan Costs
Regular Hourly Labor Rate
Overtime Hourly Labor Rate
Direct Labor Unit Cost Direct Materials Unit
Cost Overhead Unit Cost Labor Severance Cost
per Unit
Subcontracting Unit Cost
Inventory Unit Carry Cost
Inventory Unit Stockout Cost
Production Rate Change Costs
Labor Hire/Train Cost per Unit
AGGREGATE PLANNINGAGGREGATE PLANNING
Possible Data InputPossible Data Input
Productivity per worker per day
Number of production days in the plan
Accurate monthly or quarterly demand forecasts
Existing plant capacity
Required labor hours per unit
Required direct materials per unit
Corporate policy regarding overtime,
subcontracting,
backordering, etc. Machine processing
hours per unit
AGGREGATE PLANNING
Possible Possible Decision VariablesDecision VariablesAGGREGATE PLANNINGAGGREGATE PLANNING
Production Rate Changes Production Subcontracting Overtime Labor Hours Equipment Rental Backordering Temporary Employees Part-time Employees
USEFUL FOR DEVELOPINGUSEFUL FOR DEVELOPINGALTERNATIVE PLANSALTERNATIVE PLANS
UNDER VARIOUSUNDER VARIOUSSTRATEGIESSTRATEGIES
The Selected Aggregate PlanThe Selected Aggregate Plan
MODERATE INVENTORY LEVELS MODERATE STOCKOUT COSTS A SMALL NUMBER OF PRODUCTION
RATE CHANGES WITH RELATIVELY
SMALL MAGNITUDES
ALMOST ALWAYS IT IS A MIXED STRATEGY CHARACTERIZED BY :
The The “ “ 44thth “ “
StrategyStrategy
Aggregate PlanningAggregate PlanningTWO STARTING ASSUMPTIONSTWO STARTING ASSUMPTIONS
PASSIVEPASSIVE
ASSUMES THE PRODUCTDEMANDPATTERN
CANNOT BEALTERED
AGGRESSIVEAGGRESSIVE
ASSUMES THEPRODUCTDEMANDPATTERNCAN BE
ALTEREDIF NECESSARY
Product Demand PatternProduct Demand Pattern PRE - STABILIZATIONPRE - STABILIZATION
THE DEMAND RATE MAY VARY DRAMATICALLYFROM THE NORMAL PRODUCTION RATE,
MAKING AGGREGATE PLANNING DIFFICULTAND LESS COST EFFECTIVE
( time )
( u
nit
s )
Normal Production Output
Variable Product Demand
Product Demand PatternProduct Demand Pattern
Normal Production Output
( u
nit
s )
( time )
Variable Product Demand
STABILIZATIONSTABILIZATION
THE LEVELING OF DEMAND TO APPROACHTHE NORMAL PRODUCTION RATE MAKESAGGREGATE PLANNING MUCH EASIER
AND MORE COST EFFECTIVE
Some Some Demand Demand Leveling Leveling TacticsTactics
Heavy advertising, price discounts, coupons, and contests during periods of low demand.
Little or no advertising and price increases during periods of high demand.
Production of countercyclic, similar products.
Reservation systems.
Aggregate Planning withQM for Windows
We Select Aggregate Planning
From The Menu
WE SELECTAGGREGATE
PLANNINGFROM THE MENU
WE DESIRE TOSET UP A
NEW PROGRAM To
We Select The1st
Menu
WE SELECT THEFIRST OPTION
THE DIALOGUEBOX APPEARS
WE SELECT SIX PERIODSFOR THE AGGREGATE PLAN
AND LABEL THEM“JANUARY” THROUGH
“JUNE”
IF DEMAND EXCEEDSPRODUCT SUPPLY IN
ANY MONTHLY PERIOD,IT IS ASSUMED THOSE
SALES ARE LOST FOREVER
THE DATA TABLE APPEARS
Inventory Cushion StrategyInventory Cushion StrategyEXAMPLEEXAMPLE
OBJECTIVE
TO MAINTAIN A CONSTANT-SIZE WORK FORCE AND UNIFORM PRODUCTIONRATE OVER THE SPECIFIED PLANNING PERIOD.
ASSUMPTIONS
DEMAND FORECAST OF 6,200 QUASI-UNITS OVER THE NEXT SIX MONTHS ONE-HUNDRED-TWENTY- FOUR AVAILABLE PRODUCTION DAYS QUASI-UNIT INVENTORY CARRY COST IS $5.00 PER MONTH EACH WORKER PRODUCES FIVE QUASI-UNITS PER DAY EACH WORKER IS PAID $120.00 PER DAY
CALENDAR
MONTH
ACTUAL
PRODUCTION
QUASI-UNIT
FORECAST
CUSHION NET CHANGE
ENDINGINVENTORY
JAN 1100 900 +200 200
FEB 900 700 +200 400
MAR 1050 800 +250 650
APR 1050 1200 - 150 500
MAY 1100 1500 - 400 100
JUN 1000 1100 - 100 0
6200units
6200units
1850 units
22 DAYSAVAILABLE
X 50 UNITS
DAILY
18 DAYSAVAILABLE
X50 UNITS
DAILY
FIRM MUST PRODUCE 50 UNITS DAILY IN ORDER TOMEET THE SIX-MONTH DEMAND ( 6,200 / 124 DAYS )
∑21 DAYS
AVAILABLEX
50 UNITSDAILY
Inventory Cushion StrategyInventory Cushion Strategy
1.6 hours of labor per quasi-unit1.6 hours of labor per quasi-unitXX
$15.00 / hour average labor rate$15.00 / hour average labor rate
Quasi-UnitQuasi-UnitDemandDemand
ForecastsForecasts
Quasi-UnitQuasi-UnitInventoryInventory
Carry CostCarry Costperper
MonthMonthPlannedPlannedMonthlyMonthly
ProductionProduction
Inventory Inventory Cushion StrategyCushion StrategyEXAMPLE
TOTAL COSTS: $158,050.00
INVENTORY CARRY COSTS…………...….$9,250.00 ( 1,850 units x $5.00/unit )
OVERTIME, HIRE/FIRE, SUBCONTRACTING..............$0.00 ( fixed work force )
PRODUCTION RATE CHANGE COSTS………$0.00 ( uniform production rate )
LABOR COSTS..$148,800.00…..( 50/5 = 10 workers x $120.00/day x 124 days)
Strategy Total CostStrategy Total Cost Total Labor CostTotal Labor Cost Total Inventory Carry CostsTotal Inventory Carry Costs
Quasi-Unit DemandQuasi-Unit DemandRegular TimeRegular Time
Quasi-Unit ProductionQuasi-Unit Production
The Inventory CushionThe Inventory Cushion( peaks at mid-term of plan )( peaks at mid-term of plan )
Skeleton Force StrategySkeleton Force StrategyEXAMPLE
OBJECTIVE
TO BUILD A PERMANENT LABOR FORCE AROUND A SPECIFIC LEVEL OF DEMAND, TOLERATING PAID IDLE TIME DURING LOWER DEMAND
PERIODS AND INCURRING COSTS OF OVERTIME LABOR OR SUBCONTRACTING DURING HIGHER DEMAND PERIODS.
THE SPECIFIC LEVEL OF DEMAND IS USUALLY THE LOWEST LEVEL OF DEMAND
Skeleton Force StrategySkeleton Force StrategyEXAMPLEEXAMPLE
ASSUMPTIONS
A PERMANENT LABOR FORCE BUILT AROUND THE LOWEST DEMAND PERIOD IN ORDER TO SAVE ON RETIREMENT BENEFITS, HEALTH INSURANCE , PAID VACATIONS, LEAVE, ETC.
FEBRUARY HAS THE LOWEST FORECASTED QUASI-UNIT DEMAND (700 units)
FEBRUARY HAS EIGHTEEN (18) AVAILABLE PRODUCTION DAYS
FIRM WANTS TO SUBCONTRACT PRODUCTION TO AN OUTSIDE COMPANY WHENEVER QUASI-UNIT DEMAND EXCEEDS THE PERMANENT LABOR FORCE CAPABILITY
SUBCONTRACTED QUASI-UNITS COST THE FIRM $10.00 EACH
Skeleton Force StrategySkeleton Force StrategyEXAMPLE
CALCULATIONS
DAILY FEBRUARY PRODUCTION…....700/18 days = 39 units daily
IN-HOUSE PRODUCTION…..39 units/day x 124 days = 4,836 units
SUBCONTRACTED PRODUCTION…….6,200 – 4,836 = 1,364 units
REQUIRED WORKERS……..…39/5 units per worker per day = 7.8
Quasi-UnitQuasi-UnitSubcontractSubcontract
CostCost
In February, in-house production was 39 units per day for 18 days = 702 quasi-unitswhich resulted in overproduction of 2 quasi-units
In March, in-house production was 39 units per day for 21 days = 819 quasi-unitswhich resulted in overproduction of 19 quasi-units
In April, in-house production was 39 units per day for 21 days = 819 units.The shortfall seems to be ( 1200 - 819 ) = 381 units, but it was reduced to
360 quasi-units, due to the 21 quasi-unit surplus generated in February and March
Over Production in Regular TimeOver Production in Regular Time
Skeleton Force StrategySkeleton Force StrategyEXAMPLE
COSTS: $129,704.00
LABOR COST...$116,064.00 ( 7.8 workers x $120.00 per day x 124 days)
SUBCONTRACT COST………..$13,640.00 (1,364 units x $10.00 per unit)
OVERTIME, HIRE/FIRE, TRAINING COSTS……..$0.00 (rejected options)
INVENTORY CARRY COST……..$0.00 (all demand satisfied exactly via house production or subcontracting)
RT - Regular Time Production
Sub - Subcontracted Production
SubcontractingSubcontracting
Over ProductionOver ProductionInIn
Regular TimeRegular Time
In-House ProductionIn-House ProductionShortfallShortfall
( Subcontracted )( Subcontracted )
Chase or Matching StrategyChase or Matching StrategyEXAMPLE
OBJECTIVE
TO HIRE OR TERMINATE PERSONNEL AS NEEDED IN ORDER TO MATCH PRODUCTION TO DEMAND, PERIOD-BY-PERIOD, RESULTING IN THE ELIMINATION OR DRASTIC REDUCTION OF BOTH INVENTORY CARRY AND STOCKOUT COSTS.
Chase or Matching StrategyChase or Matching StrategyEXAMPLE
ASSUMPTIONS
EACH QUASI-UNIT REQUIRES 1.6 HOURS OF DIRECT LABOR
PERSONNEL TERMINATION COST IS PRORATED AT $15.00 PER MANUFACTURED QUASI-UNIT CANCELLED
PERSONNEL RECRUITING AND TRAINING COST IS PRORATED AT $10.00 PER MANUFACTURED QUASI-UNIT ADDED
EACH WORKER EARNS $15.00 PER HOUR ON AVERAGE.
EXAMPLE: If sales were forecasted to be 100 units lower in the next period, then the prorated employee termination costs would be ( 100 x $15.00 ) $1500.00 If sales were forecasted to be 100 units higher in the next period, then the prorated employee hiring and training costs would be ( 100 x $10.00 ) $1000.00
PRORATED TERMINATION COSTPRORATED TERMINATION COST
PRORATED HIRE/TRAIN COSTPRORATED HIRE/TRAIN COST
MONTH DEMANDFORECAST
PRODUCTION
COSTS
FORECASTCHANGE
HIRE/FIREFIRE
COSTS
TOTALCOSTS
JANJAN 900900 $21,600.$21,600. $21,600.$21,600.
FEBFEB 700700 $16,800.$16,800. (200)x$15 $3,000. $19,800.$19,800.
MARMAR 800800 $19,200.$19,200. 100 x $10100 x $10 $1,000.$1,000. $20,200.$20,200.
APRAPR 12001200 $28,800.$28,800. 400 x $10400 x $10 $4,000.$4,000. $32,800.$32,800.
MAYMAY 15001500 $36,000.$36,000. 300 x $10300 x $10 $3,000.$3,000. $39,000.$39,000.
JUNJUN 11001100 $26,400.$26,400. (400)x$15 $6,000. $32,400.$32,400.
∑∑ $148,800.$148,800. $8,000. $8,000.
$9,000.$9,000.
$165,800.$165,800.
900 UNITS x
1.6 HOURS x
$15.00 =
$21,600.00
700 UNITSX
1.6 HOURSX
$15.00=
$16,800.00
TOTAL MONTHLY COST = PRODUCTION + HIRE( TOTAL MONTHLY COST = PRODUCTION + HIRE( FIRE FIRE ) COSTS) COSTS
The Chase StrategyThe Chase Strategy
Chase or Matching StrategyChase or Matching StrategyEXAMPLE
COSTS : $165,800.00
REGULAR TIME LABOR COST……………………………..$148,800.
HIRE / TERMINATION COSTS………………………………..$17,000
INVENTORY CARRY AND STOCKOUT COSTS………………... $ 0.
6200 UNITS x 1.6 HOURS/UNIT = 9,920 HOURS x $15.00/HOUR
$8,000.00 HIRE COSTS + $9,000.00 TERMINATION COSTS
PRODUCTION MATCHES DEMAND EXACTLY PERIOD-BY-PERIOD
$17,000.00 totalbroken downinto hire/fire
andtermination
Period Demand = Period Production
CUMULATIVE PRODUCTION
EQUALSCUMULATIVE
DEMAND( ONE IN THE SAME LINE )
Aggregate Plan ExamplesAggregate Plan ExamplesPOSTSCRIPT
I. If only three strategies or plans were generated and
evaluated, the firm would select the skeleton forceskeleton force since it has the lowest projected total costs.
II. Direct material cost, direct machine hour cost, and applied overhead per quasi-unit were identical under all three plans. Hence, they are non-relevant costs and routinely omitted from the analysis.
The Relevant Range of ActivityThe Relevant Range of Activity
0 1000 2000 3000 4000 5000 6000 7000 80000 1000 2000 3000 4000 5000 6000 7000 8000
CUMULATIVE PRODUCTION ( CUMULATIVE PRODUCTION ( IN UNITS )IN UNITS )
CCOOSSTTSS
SEMI-VARIABLE COSTS
VARIABLE COSTS
Relevant Range 1
Relevant Range 2
Relevant Range 3
X6200
FIXED COSTS
PRODUCTION OF 6200 QUASI-UNITSFALLS JUST WITHIN THE RELEVANTCOST RANGE OF 6000-8500 UNITS.THEREFORE, UNIT DIRECT LABOR,
DIRECT MATERIALS, AND OVERHEADREMAIN THE SAME
6000 8500
Aggregate Plan ExamplesAggregate Plan ExamplesPOSTSCRIPT
III. The mix of resources—labor force size, production rate, and inventory level as well as subcontracting ----and their timing allowed the development of 3 unique aggregate plan proposals and associated costs.
IV. In the skeleton force strategy, the firm elected to augment the capacity of its small permanent labor force by subcontracting exclusively. Variations of this strategy could, and usually are generated us- ing overtime hours, temporary labor hours, and subcontracting exclusively or in combination.
Aggregate Plan ExamplesAggregate Plan ExamplesPOSTSCRIPT
V. Corporate policies may impose limitations on the use of subcontracting, overtime hours, inventory levels, production rates, machines, available days for production, and so on.
Aggregate Planning withQM for Windows
TransportationAlgorithm
Transportation Algorithm Transportation Algorithm Approach to Aggregate PlanningApproach to Aggregate Planning
When aggregate planning is viewed as an allocation of capacity to meet forecasted demand.
Produces an optimal plan for minimizing costs !
Can specify regular, overtime, and subcontracting production in each time period.
Can specify inventory carryover from period to period.
Will not handle non-linear costs such as hiring and layoff.
Applied Management Science for Decision Making, 1e Applied Management Science for Decision Making, 1e © 2011 Pearson Prentice-Hall, Inc. Philip A. Vaccaro , PhD© 2011 Pearson Prentice-Hall, Inc. Philip A. Vaccaro , PhD
ForecastedQuasi-UnitDemand
700 Quasi-Units can beproduced onregular timeeach month
50 Quasi-Units can beproduced on overtime
each month
The number of quasi-unitsthat can be
subcontracted outeach month
Beginning Inventory ( from May )
Per Unit Labor Costs
Inventory Carry Costsper Quasi-Unit
per Month
June demand of 800 is met by 50 units of beginning inventory, 700 units of June regular production,and 50 units of June subcontracted production. July demand of 1000 is met by 50 units of beginning inventory, 50 units of June overtime production,700 units of July regular production, 50 units of July overtime production, and 150 units of subcontractedJuly production.August demand of 750 is met by 700 units of August regular production, and 50 units of August overtimeproduction.
This shows the costs and headings to be inserted in each cell for the
normal transportation tableau,if there had been one.
Note that cells that are notallowed to be filled, have
a prohibitive cost of $9,999.00 !
Also note that the dummy columnfor unused capacity in each
month is missing in the originaltransportation tableau !
For each month that a quasi-unit remains in inventory, an additional$2.00 carry (holding) cost is added to its original cost
Shows the total number of quasi-unitsthat should be made underregular-time, overtime, and
subcontracting over the life of the3-month aggregate plan.
Total quasi-unit productionover the 3-month
aggregate plan
The only carry costs were for theinitial inventory of 100 quasi-units
Here, we are using the regulartransportation algorithm module to solve the same
aggregate planning problem
For each month that a quasi-unit is kept in inventory, a $2.00 carry cost will be
added to itsoriginal production
cost
June demand of 800 was met by 100 units of beginning inventory (from May) and 700 units of regular time production in June itself.
July demand of 1,000 was met by 50 units made overtime in June, 50 units subcontracted in June, 700 units of regular time production in July itself, 50 units made overtime in July, and 150 units subcontracted in July.
August demand of 750 was met by 700 units of regular time production in August and 50 units made overtime in August.
The 1st feasible solution
The 2nd feasible solution
The 3rd feasible and
optimal solution
Aggregate PlanningAggregate Planning
Sample Data +
Basic Template
The Simplex MethodThe Simplex Method
An alternative to the transportation method of linear programming.
Must be employed where non-linear costs are involved, such as hiring and layoff.
Minimum and maximum constraints can be put on the desired amounts of regular labor, overtime labor, subcontracting, backordering, and many other factors on a monthly, bi-monthly, quarterly, or semi-annual basis.
The Simplex MethodThe Simplex Method
Constraint formulation is quite complex.
The optimal solution virtually always must be obtained via computer.
Dozens or hundreds of variables are involved.
The Simplex MethodThe Simplex Method
A production manager must develop an aggregate plan for the nexttwo quarters of the year. The plant produces computer terminals.
700 terminals need to be shipped to customers in the 1st quarter and3,200 in the 2nd quarter. It is the firm’s policy to ship orders in thequarter in which they are ordered.
It takes 5 hrs labor to produce each terminal, and only 9,000 hours of straight-time labor is available in each of the two quarters.
Overtime can be used, but the firm limits overtime in each quarterto 10% of straight-time labor available. Labor costs $12.00 per hourat the straight-time rate and $18.00 per hour at the overtime rate.
EXAMPLE
The Simplex MethodThe Simplex Method
If a terminal is produced in one quarter and shipped in the nextquarter, a carrying cost of $50.00 is incurred.
Requirement:
How many terminals should be produced on straight-time andovertime in each of the two quarters to minimize straight-timelabor, overtime labor, and carrying costs?
The market requirements, straight-time labor availability, andovertime policy must be adhered to.
The Simplex MethodThe Simplex Method
X1 = terminals made on straight-time in 1st quarter and shipped in 1st quarter.
X2 = terminals made on overtime in 1st quarter and shipped in the 1st quarter.
X3 = terminals made on straight-time in 1st quarter and shipped in the 2nd quarter.
X4 = terminals made on overtime in 1st quarter and shipped in the 2nd quarter.
X5 = terminals made on straight-time in 2nd quarter and shipped in the 2nd quarter.
X6 = terminals made on overtime in 2nd quarter and shipped in the 2nd quarter.
Q1 = 1st quarter , Q2 = 2nd quarter, Z = total cost of the plan
Defining the Decision Variables
The Simplex MethodThe Simplex Method
Minimize Z = 60X1 + 90X2 + 110X3 + 140X4 + 60X5 + 90X6
Subject to:
X1 + X2 => 700 Q1 demand
X3 + X4 + X5 + X6 => 3,200 Q2 demand
5X1 + 5X3 =< 9,000 Q1 straight-time labor
5X5 =< 9,000 Q2 straight-time labor
5X2 + 5X4 =< 900 Q1 overtime labor
5X6 =< 900 Q2 overtime labor
The Model
Aggregate Planning withQM for Windows
SimplexLinear
Programming
X1 = 580 units made and shipped on straight- time in 1st QtrX2 = 120 units made on overtime and shipped in 1st QtrX3 = 1,220 units made on straight-time in 1st Qtr and shipped during 2nd QtrX5 = 1,800 units made and shipped on straight- time in 2nd QtrX6 = 180 units made on overtime in 2nd Qtr and shipped in 2nd Qtr
Aggregate PlanningAggregate Planning
Applied Management Science for Decision Making, 1e Applied Management Science for Decision Making, 1e © 2012 Pearson Prentice-Hall, Inc. Philip A. Vaccaro , PhD© 2012 Pearson Prentice-Hall, Inc. Philip A. Vaccaro , PhD