1

A. Azadeh, M. Haghnevis and Y. KhodadadeganDepartment of Industrial Engineering and

Research Institute of Energy Management and PlanningFaculty of Engineering, University of Tehran

ASSESSMENT OF A COMPLEX MACHINE MIX PROBLEMASSESSMENT OF A COMPLEX MACHINE MIX PROBLEM BY INTEGRATED SIMULATION AND AHP MODELING BY INTEGRATED SIMULATION AND AHP MODELING

2

Objectives and FeaturesObjectives and Features

The objectives :Introduce an integrated simulation AHP model for modelingAssessment and improvement of a machine mix problem with complex queue priorities and service times

The unique feature :Integrated simulation AHP modeling of a production system with complex service times and queue prioritiesThe integrated simulation AHP approach of this study may be applied for other similar production systemsThere is no closed form expression for such situations, as previous studies show no mathematical models exists for machine mix with such complex service times and queue priorities Introduction of a hybrid simulation AHP approach for alternative analysis. The hybrid approach of this study for such complex settings may be easily extended to other similar production systemsThe hybrid approach of this study is applied to actual production system discussed in the next section

3

IntroductionIntroduction

Queuing systems require controlling and maintaining a list of events to determine next occurrences.

Most of queuing problems can be modeled and solved by closed form mathematical methods (Gross & Harris, 1984; Kleinrock, 1975; White, Schmidt and Bennett, 1975; Ross, 1983; Jaiswal, 1968) but in few cases because of severe complexity and variety of constraints does not have closed form expressions. Therefore, computer simulation approach can be used in these rare cases (Shannon, 1975).

Priority queues have been studied since the early days of queuing theory Stidham (2002). The monograph on queues by Cox and Smith (1961) gives a concise summary of the early works. The book by Jaiswal (1986) provides a compendium of known result as of the late `60s. Most of the research until then concerned single-server queues with fixed priorities. Operating under preemptive or nonpreemptive disciplines.

4

The general hybrid simulation AHP modelThe general hybrid simulation AHP model

Identify a production system with n order types, and complex service and queue disciplines

Compare existing system with other alternatives by AHP

Verify and validate simulation model

Develop a simulation model for simulation model

Identify a meaningful set of performance measures

Can be used for different kinds of productions with various orders and complex service and queue priorities (chemical, military and food industries).

5

General ModelGeneral Model

The entity (order): determined with that has just received service

The priority : entities which have the same order as the entity being serviced

If the waiting entities have different orders than the entity being serviced, the priority is with the entity with the highest rank

The arriving entities are ranked numerically from 1 to n depending on the priority of the order

To prevent severe waiting times of entities, the maximum time allotted for a particular order type is ta for a = 1,...,n representing the n orders, respectively

If ta is reached, the entity with higher ranking is prepared for production immediately after service completion

6

General ModelGeneral Model

The complex service and queue priorities for such systems are defined as:

Orders are classified with respect to their type (The orders are numbered from a= 1 to n) Orders are then placed in the queue according to the order which is being processed and current positioning of orders in the queue (the services turn over moves clockwise)Each order type has a limited total production timeDifferent setup times are required between order type changes

7

Schematic DiagramSchematic Diagram

Machine

Arrivalof orders

Customer

a

i

a: Order type (Atrib[6])i: Manufacturing priority (Atrib[8])

n

n

n

n

3

3

2

2

2

2

1

1

2

n+2

2

n+2

1

n+1

5

5

5

5

3

3

3

3

Set priority by Order type

Set priority by Manufacturing

Production time control

3

3

If a order is continuously produced and total production time is grater than or equal to ta

If total production time is less than ta

The production priority will be given to the next prioritized order and remove all entities to be re-ordered for prioritization in the queue

Production process of existing order is ended and a new order is initiated

.....

n

n .....

2

n+2

2

n+2

1

n+1

5

5

5

5

3

n+3

n

n .....

8

General Logical ChartGeneral Logical Chart Start

Is the priority of a new entity

greater than or equal to entity which is being

serviced?

Arrangement of entities in a queue with particular length

Occupation of a particular machine "i"(save machine

number)

Expiring the production time

Saving the priority and type of produced entity

Adding to entity priority equal to order type number (entity is placed at the end of the queue)

Implement of production process

K

Yes

No

A

9

General Logical ChartGeneral Logical Chart

Saving the priority and type of produced entity

Is the order type of present entity equal

to order type of previous entity? (Is a

particular order continuously produced?)

Adding the process time of present entity to length of total

production time

Is the production time of the entity with particular

order type (total production time) greater

than determined constraint ta?

Saving new time as production time of the particular entity

and saving order type number of new production

Expiring of the set up time of production change

Production priority will be given to the next prioritized order

Expiring of the set up time of production change

Remove all entities in queue of machine "i" to be re-ordered for

prioritization in the queue (transfer to K)

Finish

Release machine i

Collect required information

yes

yes

no

no

A

10

Attributes and VariablesAttributes and Variables

The simulation model was developed by Visual SLAM (Pritsker, Oreilly & LaVal, 1997; Pritsker, 1990; Pritsker, Sigal, & Hammesfahr, 1989).

Variable Description of variableATRIB[1] Arrival time

ATRIB[6] Order type

ATRIB[8] Manufacturing priority

LTRIB[1] Utilized machine in production line

XX(4) Order priority variable in line of production

XX(7) Order code variable produced in line

XX(8) Previous order produced in line

XX(9) Maximum allotted time to a specific order type in line

XX(10) Production time of machine

11

Visual SLAM NetworkVisual SLAM Network

12

The Case StudyThe Case Study

The above phenomena are used as production planning and scheduling of a spray coatings manufacturer.

The manufacturer is capable of producing different spray coatings (from faint color to dark color).

The faintest and darkest colors are ranked one and n, respectively.

There is a set-up time if a new order must be started for any of the machines.

There is no set-up time as long as the same order is prepared by any machines.

13

The Case StudyThe Case Study

ta = 600

a = 3 to 6

n=4

C=15

Machine

Arrivalof orders

Customer

a

i

a: Order type (Atrib[6])i: Manufacturing priority (Atrib[8])

44

44

33

66

66

55

48

48

37

66

66

55

55

55

Set priority by Order type

Set priority by Manufacturing

Production time control

55

If a order is continuously produced and total production time is grater than or equal to 600

If total production time is less than 600

The production priority will be given to the next prioritized order and remove all entities to be re-ordered for prioritization in the queue

Production process of existing order is ended and a new order is initiated

48

48

37

66

66

55

55

14

ExampleExampleAfter passing some of simulation time, below state may be occurred

I:

In this state if order type of arrival entity was 4 (a=4) then manufacturing priority became 16 (i=16) and if a=5 or 6 then i =17 and 18 sequentially and if order type of arrival entity was 3 (a=3) then manufacturing priority became 19 (i=19)

3+4+4+4+4>16Also in below state if order type of arrival entity was 3 (a=3) then manufacturing priority became 19 (i=19).

II:

In all state if entities have similar manufacturing priority earlier arrival entity was product.

Machine

4

16

4

16

5

17

6

18

6

18

4

16

Machine

4

16

4

16

4

16

15

Verification and ValidationVerification and Validation Verification:

The movements of entities compared with the movement of orders in the actual production system.

Validation: The most important performance measure of the production system which is number of completed orders in a two weeks period was selected and verified by the management.Run for two working weeks and replicated twenty times.The results compared with 20 random samples of the actual system.Independent t-test has been used to compare the production system with simulation model with respect to total number of completed orders.H0: µ1 = µ2 at α = 0.01 level of significance.

Alternative

No. of completed orders in two weeks

to P-value

MeanStandard deviation

Simulation 33.55 5.33

1.07 0.297Actual system

31.15 6.72

16

Results of production planning alternativesResults of production planning alternatives

The verified and validated simulation model was used as production planning and scheduling tool to identify the optimum alternatives (lowest

set-up and waiting times).

Performance measure

Considered conditions (alternatives)

a b c d e

1 25.62 8.82 42.99 1.38 46.99

2 27.02 29.1 54.91 8.43 58.53

3 8.27 3.6 11.64 2.26 8.92

4 13.55 2.16 16.92 5.99 15.47

5 5.57 1.73 16.86 2.39 18.39

6 26.6 14.68 21.02 18.39 25.22

17

AHP rankingsAHP rankings

Analytic Hierarchical Process (AHP).The decision maker models a problem as hierarchy of criteria, sub criteria, and alternatives. After the hierarchy is constricted, the decision maker assesses the importance of each element at each level of the hierarchy.

By generating entries in a pair wise comparison matrix where elements are compared to each other.

For each pair wise, the decision maker typically uses the eigenvector method (EM) to generate a priority vector hat gives the estimated, relative weights of the elements at each level of hierarchy.

Weights across various levels of the hierarchy are then aggregated using the principle of hierarchic composition to produce a weight for each alternative (Chandrana et al, 2005).

a b c d e

AHP score 14.67 7.33 19.47 6.74 20.17

AHP rank 3 4 2 5 1

18

Value AnalysisValue Analysis By noting value performance = (worth)/ (cost) in context of value engineering

VE (Value engineering) is an organized, creative technique directed at analyzing the functions of a product, service or system with the requirements which comprise its value-such as performance, reliability, maintainability, appearance, etc.VE is not constrained to produce the same design at least cost but rather to search out methods of achieving a superior product at least cost (Parker 1998 and Shellito 1992).

Low performance alternatives are discarded from further considerations and the results of value analyze analysis shows the superiority of alternative "c" over all other alternatives.

High performance Low performance

a c e b d

Parametric Cost 6α 7α 10α α 3α

Value performance 2.446 2.781 2.017 7.333 2.247

Value rank 2 1 3 1 2

19

ConclusionConclusion

The bottlenecks and sensitive points of the system are identified.

Sensitivity analysis could be easily performed.

Customer satisfaction may be enhanced due to introduction of an optimum model with lowest set-up and waiting times

20

A. Azadeh, M. Haghnevis and Y. KhodadadeganDepartment of Industrial Engineering and

Research Institute of Energy Management and PlanningFaculty of Engineering, University of Tehran

ASSESSMENT OF A COMPLEX MACHINE MIX PROBLEMASSESSMENT OF A COMPLEX MACHINE MIX PROBLEM BY INTEGRATED SIMULATION AND AHP MODELING BY INTEGRATED SIMULATION AND AHP MODELING

FINISH