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FMS design model withmultiple objectives usingcompromise programmingTaeho Park , Hochang Lee & Heeseok LeePublished online: 14 Nov 2010.

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int. j. prod. res., 2001, vol. 39, no. 15, 3513 ± 3528

FMS design model with multiple objectives using compromiseprogramming

TAEHO PARKy*, HOCHANG LEEz and HEESEOK LEE§

There has been a great change in manufacturing systems toward computer-con-trolled ¯ exible manufacturing systems (FMS). The design and operation of theFMS involve intricate and interconnected decisions that result in the maximumperformance of the system. However, the design and operational decisions havebeen made separately in consideration of a single-system performance measure.This paper presents a method for simultaneously determining design and controlparameters of an FMS with the multiple performance objectives via full-factorialdesign of experiments, regression analysis and compromise programming. For anumerical example, the SIMAN simulator models a hypothetical FMS with sixworkstations. Eight design and control parameters are simultaneously determinedby compromising four performance measures that are formulated using regres-sion analysis.

1. Introduction

There has been an important change in manufacturing systems toward computer-

controlled ¯ exible manufacturing systems (FMS). An FMS is an integrated and

automated system of numerically controlled (NC) machine tools, a material-hand-

ling system (e.g. automatically guided vehicles, AGV), and a system controller (i.e. a

decentralized or centralized computer system) designed to provide bene® ts of

reduced work-in-process inventory and shortened production lead time.

The design and operation of the FMS involve intricate and interconnected deci-

sions that result in the maximum bene® t of the system: (1) some design-related

decisions include part types to be produced, the type and size of buŒers, the

number of pallets, and the number and design of ® xtures, and (2) operation-related

problems are input sequence of parts into the system, scheduling parts to machines

based upon alternative routings, sequencing parts on a machine, and scheduling

material-handling devices such as AGV. The design and operational decisions

have been made separately even in most simulation models. Park and Steudel

(1989) advocated to take into account both design- and operation-related decision

parameters simultaneously to achieve a global optimization in the development of an

FMS.

International Journal of Production Research ISSN 0020± 7543 print/ISSN 1366± 588X online # 2001 Taylor & Francis Ltd

http://www.tandf.co.uk/journals

DOI: 10.1080/00207540110062381

Revision received January 2001.{ Organization and Management Department, San Jose State University, One Washington

Square, San Jose, CA 95192-0070 , USA.{ School of Business, Kyung Hee University, Kyunggi-Do 449-701, Korea.} Department of Management Information Systems, Korea Advanced Institute of Science

and Technology, Seoul 130-012, Korea.* To whom correspondence should be addressed. e-mail: park_t@cob.sjsu.edu

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The choice of performance measures in a manufacturing system depends highly

on management policy and decision-making. The literature on the design and opera-

tion of the FMS has shown that most past research used only a single performance

measure its their objective. However, optimizing one performance objective may lead

to sacri® cing the other objective(s). For example, the objective of minimizing in-

process inventory might be in con¯ ict with that of maximizing a production rate.

From this point of view, the multi-objective approach has recently been of interest in

a wide range of design and control problems for FMS, such as machine selection

(Tabucanon et al. 1994), choice of the FMS system con® guration architecture

(D’Angelo et al. 1996), the control of automated storage and retrieval systems

(Chincholkar and Chetty 1996) and FMS scheduling (Belton and Elder 1996, Yu

et al. 1999).

Mathematical models with multiple objectives, such as a goal programming

(GP), linear multi-objective programming (LMP), compromise programming (CP),

etc., have been developed to resolve the dilemma of the con¯ icting objectives occur-

ring in many areas: manufacturing, engineering design, publishing, tax shelters and

investment, and capital budgeting. The CP is a relatively recent methodology. It is

much more ¯ exible than GP and LMP in that it combines the best and most useful

features of both. It is not limited to linear cases; it can be used for identifying non-

dominated solutions under the most general conditions; it allows prespeci® ed goals;

and, most importantly, it provides an excellent base for interactive programming

(Zeleny 1992).

The performance measures of an FMS need to be presented in mathematical

formula that will be used as multiple-objective functions in the CP. A regression

analysis approach has been a popular method to obtain mathematical equations for

describing the characteristics of a manufacturing system that are usually di� cult to

model in a mathematical form. Chanin et al. (1990) used the regression method to

obtain a mathematical equation for the average equipment utilization (EU) of a

maintenance ¯ oat system, and embedded the EU equation into a mathematical

programming formula to ® nd an optimal combination of standby units and techni-

cians. Schmidt and Meile (1989) employed a similar approach to shorten the product

development cycle time for a new photoresist from concept to marketplace. They

obtained linear responses of key characteristics of the new photoresist by using the

regression model, and then optimized the linear response function via linear pro-

gramming.

In summary, the objective of this research is to present a hybrid FMS design

approach by (1) considering both design and operational parameters simultaneously,

(2) modelling performance measures of the FMS using design of experiments (e.g.

full-factorial design) and a regression analysis, and then (3) achieving compromised

levels of multiple performance measures through a compromise programming prob-

lem with the regression equations of performance measures. For a numerical ex-

ample, a hypothetical FMS with six workstations is employed, and the following

eight design and control parameters are to be determined: (1) number of AGV, (2)

speed of AGV, (3) number of pallets, (4) buŒer sizes, (5) routing scheduling rules, (6)

loading scheduling rules, (7) sequencing rules and (8) AGV scheduling rules. The

FMS design problem considers four performance measures simultaneously: (1) mini-

mizing job tardiness, (2) maximizing system utilization, (3) minimizing in-process

inventory and (4) maximizing a production rate.

3514 T. Park et al.

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2. Issues on FMS design and control problems

As indicated in Stecke (1984), the construction of an FMS involves many deci-

sions during the design and operation phases. Some of the decisions are given below.

Design-related problems:

. Part types to be produced.

. Process plan including tooling and tool magazine capacity.

. Type and capacity of a material-handling system.

. Type and size of buŒers.

. Number of pallets.

. Number and design of the ® xtures.

. Selection of a subset of part types for immediate and simultaneous manu-

facture.

. Part-mix ratios.

. Allocation of pallets and ® xtures to part types, etc.

Operation-related problems:

. Input sequence of parts into the system.

. Scheduling parts to machines based upon alternative routings.

. Sequencing parts on a machine.

. Scheduling material-handling devices such as AGV.

. Policy to handle machine tools and other breakdowns.

. Preventive maintenance policy.

. Inspection policy, etc.

The above design and operational decisions have been made separately due to the

complexity of system formulation. Furthermore, most simulation and analytical

modelling research completed thus far has focused on mainly one or two decision

problems among part selection, machine grouping, system loading, part allocation

(machine loading), tool allocation, and scheduling parts. (See Co et al. (1990) for the

machine loading and tool allocation problems, Kumar et al. (1990) for a joint con-

sideration of machine grouping and loading problems, Stecke and Kim (1991) for the

part selection problems, Liu et al. (1995) for the part type selection and scheduling,

and Atmani and Lashkari (1998) for machine tool selection and operation alloca-

tion.)

According to Smith et al. (1986), the following measures have been most likely

used in the FMS environment: due dates, job tardiness, system utilization, work-in-

process inventory, production rate, set-up time and tool changes, ¯ ow time, balance

of machine usage. Most past research on the design and operation of the FMS used

only a single performance measure as their objective performance to optimize. In

contrast with the past research, however, several researchers have applied multi-

objective decision-making approaches to solving FMS production planning and

control problems with more than one objective performance measure. Dean et al.

(1990) employed a goal-programming (GP) approach to modelling an FMS produc-

tion-planning problem in the context of multi-objectives, such as production rate,

3515FMS design model with multiple objectives

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machine utilization, throughput time, tool usage time and value of parts. Gangan et

al. (1987) also used the GP to determine the most e� cient part routing in an FMSthat satis® es multiple objectives of (1) meeting the forecasted demand, (2) minimizing

material movements and (3) minimizing workload imbalance on all machines.

Unlike the above research applying the GP to multi-objective FMS problems, Ro

and Kim (1990) applied a simple lexicographically ordering comparison to a prob-lem of identifying the most e� cient process selection rule which could satisfy all

multiple objectives, such as makespan, mean ¯ ow time, mean tardiness, maximum

tardiness and system utilization. Min et al. (1998) applied a neural network approach

to scheduling jobs for an FMS in consideration of multiple-objective performance

measures.

3. Design model for an FMS with multiple objectives

In human goal-seeking behaviour, decision-making is not just to maximize or

minimize a single goal but to search for stable patterns of harmony among all goalsbecause some goals are in con¯ ict with others (Zeleny 1974). Thus, this research

employs CP (Shi and Yu 1989, Romero 1991) to make the best decision through an

iterative target setting process, which attempts to reduce deviations of goal values

from their target values. A CP-based FMS design method with multiple performance

objectives is given in ® gure 1.

The ® rst phase is to identify design parameters and performance measures ofinterest. Since the early 1980s, many researchers have developed various mathemat-

ical models for the design and control of the FMS with a given system con® guration.

(For a review of the analytical models, see Buzacott and Yao 1986.) Using the

various mathematical models, most past research focused on one or two design or

operational issues and had many limitations in use due to their inherent assumptionsand the complexity of the system formulation. Thus, computer simulation has been

widely used to alleviate the restrictions of the analytical models for designing and

analysing the FMS (Jeong and Kim 1998, Bilberg and Alting 1991, Vujosevic 1994,

Yim and Barta 1994). From this point of view, the simulation is employed in this

research to extract the FMS performance measures.The performance of the FMS is measured by running the FMS simulation model

via a design of experiments method, such as a full-factorial design or Taguchi

method (TM). As computer technology advances much faster than we imagined,

the speed and cost of computation become relatively unimportant in the choice of

simulation methods as an evaluation tool for determining the performance of a

manufacturing system. For instance, it took ¹3 s to run an FMS with six machinesfor 167 simulation-h, described in Section 4, on Pentium II 233-MHz computer. The

full-factorial design is employed in this research to design an experimental scheme

for the multiple-objective FMS design problem. Since the full-factorial design eval-

uates all combinations of the levels of design factors, it has been an unpractical

design tool as the number of design factors increases. However, from the light ofincredibly reduced computation time per simulation run, it is now a viable design

device for experiments to extract the performance characteristics of an FMS.

After performance measures of the FMS are obtained using the simulation model

and full-factorial design method, statistical tests are conducted by analysis of vari-

ance (ANOVA) to identify signi® cant main and interaction eŒects of the designfactors. The FMS performance measures are then formulated in a mathematical

form with the identi® ed signi® cant main and interaction eŒects through a regression

3516 T. Park et al.

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analysis. After that, a multi-objective mathematical programming problem should be

constructed by setting the performance measure functions as objective functions and

including necessary constraints associated with the FMS problem. Finally, the most

appropriate values of design parameters in the mathematical programming problem

should be determined using the CP. A brief explanation for CP will be provided in

appendix A. (For more details, see Shi and Yu 1989, Romero 1991 and Lee et al.

1994.)

After the design parameters are determined, it is necessary to validate the per-

formance of the FMS with the determined design parameter settings because they are

obtained from regression equations. The validation test ought to be conducted via t-

test with the following hypothesis after a con® rmation simulation run with the

determined design settings: null hypothesis (the performance measure is statistically

the same as the one obtained from the regression equation) versus alternative

hypothesis (it is not the same). If the null hypotheses for all performance measures

3517FMS design model with multiple objectives

Are all goals met with the design

parameters?

Not Validated

Validated

Identify design parameters and performance measures of interest.

Develop a simulation model for evaluating performance of an FMS.

Run the FMS simulation model via a design of experiments.

Determine statistically significant design parameters using an analysis of variance technique.

Formulate the FMS performance measures through a regression analysis.

Construct a compromise programming problem.

Determine desired design parameters by solving the compromise programming problem.

Validate the determined design parameters through a confirmatory simulation run.

Stop Yes

No

Revise a statistical method or the domain of variables to formulate the equations of FMS performance measures better.

Figure 1. Model for designing an FMS with multiple performance objectives.

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are true at a given signi® cance level (e.g. 5% ), the determined design settings from

the compromise programming are the most appropriate values for design parametersto meet the designer’s goals for the FMS performance measures. Otherwise, addi-

tional testing is needed to check if the design settings generate better performance in

all measures than the desired performance goals pre-set by a designer based upon the

previous experience or the requirements for meeting market demands of products.The rejected null hypothesis of a performance measure means that the performance

measure obtained from its regression equation is not statistically the same as that

from con® rmation simulation runs. However, if the con® rmation simulation runs

show better performance measures than their desired goals, the FMS design settings

determined through compromise programming are acceptable.

If both tests fail to accept the design settings obtained from compromise pro-

gramming, the applications of statistical methods (i.e. design of experiments,ANOVA, regression analysis) should be checked and revised, if needed, to formulate

regression equations for the FMS performance measures better. For example, the

design of experiment method should be changed to obtain more statistical informa-

tion (e.g. from TM to full-factorial design); the number of levels for some design

factors should be increased (e.g. two levels to three levels); the signi® cant level mightbe relaxed to include more main/interaction eŒects (e.g. from 5 to 10% ).

After revising the regression equations for the FMS performance measures, new

design settings should be determined again through compromise programming. The

above procedures have to be repeated until the design settings satisfy the designer’s

performance goals.

4. Numerical example of the FMS design problem

This section describes an FMS design problem with multiple performance objec-

tives and presents design processes for the problem using a multiple-objective FMS

design model shown in Section 3.

4.1. Description of an FMS design problemA manufacturing system studied in this research is a random FMS which allows a

random process routing of parts to work centres with the capability of processing the

next operation. There are six machine centres with two separate local buŒer storages

for incoming and outgoing parts. Parts in this system are moved via AGV on

bidirectional paths, and processed at any one of the available alternative machines.

A schematic picture of the system is given in ® gure 2.The tracks of the AGV in the system are bidirectional. If there is no work waiting

for the AGV upon its completion of the current service, then it stays idle at the

current machining centre. One of the unique characteristics of the FMS system is its

routing ¯ exibility, which allows parts to be processed on more than one alternative

machine per operation. Consequently, the system controller must decide where tosend a part for the next operation upon completion of the current operation, based

upon queues, processing times required, and tool availability on the alternative

machines at that moment.

The alternative machines for a speci® c operation of a part are predetermined via

prior analysis to balance the workloads among machines. (See Shanker andSrinivasulu 1989 for the allocation of parts to machines and balancing of workloads

among machines.) Thus, when a job enters the system, the alternative machines for

3518 T. Park et al.

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each operation are already known based on the part type of the job. The same buŒer

sizes are used in this study to reduce the complexity of decision problems.

4.2. System modelling of the FMS via simulation

The FMS presented in ® gure 3 is modelled using the SIMAN/CINEMA simu-lator. Parts enter the system based upon exponential distribution with a mean of ½*

EOSSR, where EOSSR (expected overall system service rate) is approximately cal-

culated from the processing requirements and the number of machines, and ½ is a

parameter (ranging from 0.0 to 1.0) that indicates the amount of workload in the

system in comparison with the expected overall system service rate. The number ofoperations required for each part type is predetermined in the range of two to three

operations, and then when a part comes into the system, the predetermined opera-

tions are assigned depending upon the part type. In addition, for the simulation

experiments presented here, the number of part types and ½ are set at 13 and 0.9,

respectively.The processing times in FMS vary from minutes to hours depending upon the

nature of production systems. Here, the times are assigned uniformly over 10± 30

3519FMS design model with multiple objectives

Figure 2. System con® guration of a random FMS.

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min. Like the number of operations, the processing times of operations are prede-

termined and ® xed for each part type. Transportation time is calculated by dividingthe rectangular distance by AGV speed. For this purpose, the DISTANCES block in

the EXPERIMENT section of the SIMAN simulator is used. To avoid the initial

transient system performance, collection of statistics of the simulation results begins

after 1000 min, and the data collection ends at 10 000 min.

4.3. Design of experiments

Eight decision variables are involved in the FMS design problem to optimize fourperformance measures of job tardiness (h), machine utilization, WIP inventory, and

throughput rate (units/h). They include four our design parameters (number of

AGV, speed of each AGV (feet/min), number of pallets, and buŒer size) and four

operational parameters (loading rules for jobs to the FMS, routing rules for parts to

machine centres, sequencing rules for parts at each machine centre, and AGV dis-patching rules).

The design of experiments for the FMS design problem includes eight factors and

two levels in each factor (table 1). The values of two levels of four design-related

factors are determined through a preliminary simulation analysis for the FMS, and

two scheduling rules for each operation-related factor are selected based on theirperformance reports published in the literature. For instance, while Shanker and

Tzen (1985) asserted that SPT rule performed best, based upon the machine utiliza-

tion criterion, Choi and Malstrom (1988) found that SLACK and LWIQ for part

launching and routing, respectively, show high performance in terms of a WIP

inventory measure. Montazeri and van Wassenhove (1990) presented a comprehen-

sive study on the performance of 14 dispatching rules for an FMS with severaldiŒerent measures.

4.4. Statistical analysis for identifying signi® cant design parameters

Using the full-factorial experimental design, 256 (i.e. 28) simulation runs were

conducted on a Pentium II 233-MHz and 64 MRAM. It took ¹3 s to run an FMS

3520 T. Park et al.

Factors Levels

Symbol Content Low High

X1 no. of AGVs 1 3X2 speed of AGVs 75 125X3 no. of pallets 20 30X4 buŒer size 2 4X5 loading rule SPT SLACKX6 routing rule SPT LWIQX7 sequencing rule SPT LWKRX8 AGV dispatching FCFS LOQS

Abbreviations of scheduling rules are: SPT, shortest processingtime for the imminent operation; SLACK, least slack remainingtime; LWIQ, least work in the queue of a machine where the nextoperation will be processed; LWKR, least work remaining; andLOQS, assigning an AGV to a machine with the largest numberof outgoing parts. Unit of AGV speed is feet/min.

Table 1. FMS design factors and their levels.

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simulation. The ANOVA technique is employed to investigate the signi® cance of

main and interaction eŒects of the eight design factors. The interaction eŒects of

three or more factors are assumed negligible so that the mean squares associated

with the interaction eŒects are pooled into an error term. The results of ANOVA are

given in table 2 with F and p where signi® cant eŒects at 5% signi® cance level are

indicated in bold. It should be noted that since the signi® cance level is set at 5% ,

3521FMS design model with multiple objectives

Throughput Tardiness Utilization WIP

Source F p F p F p F p

X1 7.77 0.0058 43.85 0.0001 10.23 0.0016 43.29 0.0001

X2 57.77 0.0001 311.78 0.0001 112.34 0.0001 473.6 0.0001

X*1X2 0.66 0.4179 12.76 0.0004 0.16 0.6939 5.24 0.0230

X3 0.00 0.9466 7.84 0.0056 0.14 0.7072 4.93 0.0274

X*1X3 0.22 0.6395 0.09 0.7658 1.21 0.2729 0.25 0.6176

X*2X3 0.59 0.4434 0.83 0.3618 0.28 0.5359 2.31 0.1298

X4 147.40 0.0001 15.98 0.0001 30.07 0.0001 81.00 0.0001

X*1X4 2.95 0.0872 0.74 0.3894 0.21 0.6436 2.27 0.1333

X*2X4 28.99 0.0001 39.95 0.0001 10.95 0.0011 0.42 0.5167

X*3X4 0.04 0.8445 0.04 0.8492 0.84 0.3597 0.01 0.9110

X5 45.86 0.0001 4.02 0.0463 0.78 0.3796 29.54 0.0001

X*1X5 1.59 0.2089 0.92 0.3390 0.93 0.3351 0.39 0.5308

X*2X5 2.52 0.1135 4.80 0.0294 0.02 0.8934 0.35 0.5571

X*3X5 0.46 0.5005 1.82 0.1785 0.10 0.7531 0.06 0.8055

X*4X5 40.81 0.0001 5.94 0.0156 0.15 0.6998 18.15 0.0001

X6 127.68 0.0001 15.35 0.0001 46.02 0.0001 217.78 0.0001

X*1X6 0.06 0.8004 0.67 0.4127 0.08 0.7821 0.13 0.7167

X*2X6 20.00 0.0001 0.04 0.8461 19.96 0.0001 17.65 0.0001

X*3X6 0.75 0.3882 0.00 0.9441 1.32 0.2521 0.57 0.4510

X*4X6 100.32 0.0001 17.53 0.0001 22.25 0.0001 44.01 0.0001

X*5X6 21.79 0.0001 0.74 0.3908 0.07 0.7851 10.38 0.0015

X7 31.99 0.0001 27.00 0.0001 0.03 0.8450 9.19 0.0027

X*1X7 0.62 0.4324 16.47 0.0001 0.76 0.3840 1.40 0.2388

X*2X7 0.23 0.6342 33.61 0.0001 0.16 0.6893 10.06 0.0017

X*3X7 0.00 0.9926 0.21 0.6497 0.20 0.6561 0.26 0.6088

X*4X7 38.89 0.0001 2.74 0.0991 1.20 0.2744 43.18 0.0001

X*5X7 0.42 0.5178 1.10 0.2948 14.47 0.0002 8.20 0.0046

X*6X7 18.94 0.0001 6.21 0.0135 0.47 0.4943 68.88 0.0001

X8 4.38 0.0376 3.75 0.0540 3.50 0.0626 19.31 0.0001

X*1X8 0.98 0.3222 1.03 0.3112 0.51 0.4771 1.38 0.2422

X*2X8 0.05 0.8213 0.01 0.9077 0.00 0.9592 0.11 0.7365

X*3X8 0.52 0.4715 0.01 0.9420 0.96 0.3290 0.19 0.6632

X*4X8 2.17 0.1421 0.87 0.3527 0.45 0.5018 0.97 0.3256

X*5X8 0.18 0.6737 0.03 0.8725 0.00 0.9783 0.07 0.7940

X*6X8 1.69 0.1949 1.51 0.2202 2.31 0.1296 6.67 0.0104

X*7X8 1.06 0.3053 0.41 0.5230 0.68 0.4090 1.88 0.1717

Table 2. Results of ANOVA (signi® cant eŒects at the 5% level are indicated in bold).

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eŒects with a p µ 0:05 signi® cantly contribute to the corresponding FMS perform-

ance measure.Functions of four FMS performance measures (i.e. job tardiness, WIP, through-

put rate and machine utilization) are obtained using regression analysis with identi-

® ed signi® cant main and interaction eŒects. They are:

(1) Job tardiness (y1): y1 ˆ 7:905 3:529X1 5:784X2 ‡ 0:827X1X2 ‡0:324X3 3:010X4 ‡ 1:463X2X4 ‡ 0:102X5 0:254X2X5 ‡ 0:282X4X5 ‡0:252X6 ‡ 0:485X4X6 0:117X7 ‡ 0:094X1X7 ‡ 0:134X2X7 0:029X6X7.

(2) WIP (y2): y2 ˆ 43:092 10:522X1 57:306X2 ‡ 5:433X1X2 ‡ 2:635X3 ‡2:603X4 ‡ 3:976X5 5:054X4X5 ‡ 5:443X6 ‡ 4:984X2X6 7:870X4X6 ‡1:911X5X6 ‡ 2:192X7 ‡ 0:752X2X7 ‡ 1:559X4X7 0:340X5X7

0:985X6X7 0:227X8 ‡ 0:061X6X8.(3) Throughput rate (y3): y3 ˆ 7:364 ‡ 0:468X1 ‡ 1:874X2 4:288X4 ‡

1:808X2X4 ‡ 0:816X5 ‡ 1:072X4X5 0:168X6 0:751X2X6 ‡ 1:681X4X6

0:392X5X6 0:136X7 0:209X4X7 ‡ 0:073X6X7 ‡ 0:007X8.

(4) Machine utilization (y4): y4 ˆ 75:897 ‡ 3:065X1 ‡ 15:552X2 17:468X4 ‡6:342X2X4 ‡ 3:132X6 4:282X2X6 ‡ 4:521X4X6 ‡ 0:003X5X7.

4.5. Design of the FMS with multiple performance objectives using the CP

With the regression equations for four performance measures presented insubsection 4.4, the FMS design problem can be formulated via a multi-objective

quadratic mixed-integer programming technique as follows:

Problem 1 (P1):

(1) Objective functions:(i) Job tardiness (y1): y1 ˆ 7:905 3:529X1 5:784X2 ‡ 0:827X1X2 ‡

0:324X3 3:010X4 ‡ 1:463X2X4 ‡ 0:102X5 0:254X2X5 ‡0:282X4X5 ‡ 0:252X6 ‡ 0:485X4X6 0:117X7 ‡ 0:094X1X7 ‡0:134X2X7 0:029X6X7,

(ii) WIP (y2): y2 ˆ 43:092 10:522X1 57:306X2 ‡ 5:433X1X2 ‡2:635X3 ‡ 2:603X4 ‡ 3:976X5 5:054X4X5 ‡ 5:443X6 ‡ 4:984X2X6

7:870X4X6 ‡ 1:911X5X6 ‡ 2:192X7 ‡ 0:752X2X7 ‡ 1:559X4X7

0:340X5X7 0:985X6X7 0:227X8 ‡ 0:061X6X8,

(iii) Production rate (y3): y3 ˆ 7:364 ‡ 0:468X1 ‡ 1:874X2 4:288X4 ‡1:808X2X4 ‡ 0:816X5 ‡ 1:072X4X5 0:168X6 0:751X2X6‡1:681X4X6 0:392X5X6 0:136X7 0:209X4X7 ‡ 0:073X6X7 ‡0:007X8,

(iv) Machine utilization (y4): y4 ˆ 75:897 ‡ 3:065X1 ‡ 15:552X2

17:468X4 ‡ 6:342X2X4 ‡ 3:132X6 4:282X2X6 ‡ 4:521X4X6 ‡0:003X5X7,

(2) Constraints:

1 µ X1 µ 4; 60 µ X2 µ 150; 15 µ X3 µ 40; 1 µ X4 µ 5;

where X1, X3, and X4 are integers, X2 is a real value, and X5; . . . ; X8 are

binary (0 or 1).

3522 T. Park et al.

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The boundaries of variables in (P1) are set through prior analysis. Since preliminary

tests with the regression equations showed that better production rate and machineutilization might be located slightly beyond the domain of variables set in table 1 for

the experiment design, we expanded the boundaries of variables. It should also be

noticed that in a real manufacturing system, these boundaries should include physi-

cal constraints, such as investment budget, space limitation in buŒer storage, anFMS design policy on the buŒer storage in consideration of work-in-process inven-

tory, and AGV speed restriction based upon technology availability and potential

tra� c hazard.

A model for designing the FMS with four multiple performance objectives is then

formulated in a CP mathematical form (appendix A). Let F be a constraint set as

shown above, and denote the function of ith performance measure and its target

value by yi ˆ fi…x† and y*i, respectively. The CP model for the FMS design problemis:

Minimize r…yjp; w† ˆX4

iˆ1

!i

ki

³ ´p

…di ‡ d‡i †p

subject to y¤i fi…x† ˆ di d‡

i ; for i ˆ 1; . . . ; 4

x 2 F ;

where

x ˆ …x1; x2; x3; x4; x5; x6; x7; x8†:

An eigenvalue method is used to measure !i’ s. Such a method has been success-

fully used for the Analytic Hierarchy Process (AHP) (Saaty 1977), and a computer

software called the Expert Choice (Forman et al. 1985) is available. To obtain the

weights of !i ’ s, the following matrix A is constructed through the pairwise compar-

isons of four objectives. aij…i ˆ 1; . . . ; n; j ˆ 1; . . . ; n) in the matrix A ˆ ‰aijŠ indicatesthe relative importance of goal i compared with goal j. For example, since a12 ˆ 2,

job tardiness is twice as important as WIP.

A ˆ

1 2 4 512

1 2 314

12

1 215

13

12

1

2

6664

3

7775;

where the rows and columns represent performance measures in the same order as

those listed in the objective functions.

Expert Choice has generated the weights of !1 ˆ 0:507, !2 ˆ 0:264, !3 ˆ 0:143

and !4 ˆ 0:086 using matrix A and an engenvalue method. Normalization factors,

ki ’ s, are calculated by |best value ± worst value| of goal measures shown in table 4,resulting in k1 ˆ 7:48, k2 ˆ 67:50, k3 ˆ 8:02 and k4 ˆ 59:97. The regret function to

be minimized is then:

r…y† ˆ 0:07212 ¤ d‡1 ‡ 0:00391 ¤ d‡

2 ‡ 0:01783 ¤ d3 ‡ 0:00391 ¤ d4 :

With an initial target of y* ˆ …1:0, 20.0, 8.0, 97.0) and p ˆ 1, a compromise design isobtained such that X ˆ …3, 125, 25, 2, SLAK, LWIQ, SPT, LOQS). The goal is

achieved at y ˆ …0:97, 16.67, 8.65, 93.66). To improve the level of WIP down to

15, a new target goal is set at y* ˆ …1:0, 15.0, 8.0, 93.0) by making a compromise

3523FMS design model with multiple objectives

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with a reduction of machine utlization to 93% . Then, a new design is obtained at

X ˆ …1, 67, 18, 1, SLAK, LWIQ, SPT, FCFS) with a new achieved goal of y ˆ …1:01,

15.09, 8.54, 93.42). WIP has been enhanced by 9.48% with the detriment of through-put and utilization by 1.27 and 0.26% , respectively. Now, the FMS designer

attempts to see the possibility of improving the level of tardiness down to 0.8 bysacri® cing utilization to 90. For this purpose, a new target is set at y* ˆ …0:8, 15.0,

8.0, 90.0). A new design is then X ˆ …2, 99, 17, 2, SLAK, LWIQ, SPT, LOQS) with a

new achieved goal of y ˆ …0:52, 15.09, 8.26, 90.24). The throughput and utility are

traded for the improvement of the tardiness.

The current design is accepted as a satisfactory solution, and the compromising

process terminates. Thus, the FMS is designed as follows:

. Number of AGV: 2.

. Speed of each AGV: 99 feet/min.

. Number of pallets: 17.

. BuŒer size: 2.

. Loading rule: SLACK.

. Routing rule: LWIQ.

. Sequencing rule: SPT.

. AGV dispatching rule: LOQS.

The above iterative processes including setting targets and searching for better sol-

utions are likely to better represent an FMS designer’s compromising behaviour for

trade-oŒs among multiple goals in con¯ ict.

Thirty simulation runs are conducted with the above design settings for con® rm-

ing that the FMS performance measures (tardiness 0.52, WIP 15.09, throughput rate

8.26, utilization 90.24) can be achieved as calculated using the regression equations.

Table 3 illustrates the results of t-tests for the con® rmation procedure. From the t-

tests with performance measures obtained from regression equations, the null

hypotheses for tardiness, WIP, and throughput rate are rejected. However, as

shown in table 3, the solution obtained from the CP problem could generatebetter Td, WIP and Th than the designer’s pre-set performance goals, and the null

hypothesis for Ut is not rejected from the t-test. Therefore, the entire FMS design

procedures are completed with the above design settings that are acceptable as a

satisfactory solution.

3524 T. Park et al.

Source ofperformance Performance Null Alternativemeasures measure hypothesis hypothesis Mean t p

Calculation tardiness (Td) 5 0.52 h 6ˆ 0:2 0.68 4.06 0.0003using WIP 5 15.09 items 6ˆ 15:09 13.61 3.23 0.0031regression throughput (Ut) 5 8.26 items/h 6ˆ 826 8.44 3.78 0.0007equations utilization (Ut) 5 90.24% 6ˆ 90:24 89.34 1.71 0.097

Designer’s tardiness 5 0.8 h . 0.8 2.90 1.00pre-set WIP 5 15 items . 15 3.03 1.00performance throughput 5 8 items/h , 8 9.23 1.00goals utilization 5 90% , 90 1.25 0.11

Table 3. Results of t-test for the con® rmation procedure (CP).

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5. Conclusions

This paper presents a hybrid design model for simultaneously determining design

and control parameters of an FMS with multiple performance objectives via the

Compromise Programming. A hypothetical FMS was modelled using the SIMAN

simulation language to illustrate eŒectiveness of the FMS design model. Although

the FMS was designed with four design and four control parameters for a numerical

example, more parameters as well as sensitivity analysis for the parameters (e.g. ½ : an

indicator of system workload) might be necessary to be included to solve real world

FMS problems.

A full-factorial design is employed in this research to design an experimental

scheme for the multiple-objective FMS design problem. A Pentium II 233-MHz

and 64 MRAM was used to run the simulation, requiring ¹3 s per a simulation

run. Considering fast computer technology advances and declining computer prices,

the use of the full-factorial design that can provide more ample statistics is getting

more reasonable. Then, design and control parameters associated with the multiple-

objective FMS problem are determined simultaneously using compromise program-

ming, which can resolve the dilemma of the con¯ icting objectives.

This is the ® rst kind of a new approach to solving a multi-objective FMS design

problem by employing a design of experiments method, regression analysis, and a

multi-objective decision method of compromise programming all together. It allows

FMS designers to compromise interactively among con¯ icting performance objec-

tives while determining system design parameters. The multistep approach with a

combination of statistical analysis and optimization methodology, shown this

research, can be applied to other optimization problems that are too complicated

to obtain a mathematical formula of an objective function in a closed form. For

future research, the FMS design model can be expanded to incorporate the econom-

ical perspectives (e.g. the return on investment for AGV and buŒer storage) and

dynamic manufacturing environments (e.g. machine reliability, utilization of facil-

ities, mix of part types, and logistical consequences of design changes).

Appendix A: Compromise Programming (CP)

The objective of CP technique is to de® ne human goal seeking behaviour under

multiple-objective situations. Each goal in a decision-making process is expressed as

a function with respect to decision variables, and its target value is a determined

value of the goal function that a decision-maker attempts to achieve. Once target

values of goals are set, CP is to reach the best decision through an iterative target

setting process which attempts to reduce deviations of goal values from their target

values. Thus, the CP model is to minimize a regret function that combines all devi-

ations of goals from their target values. For given n goals, suppose that a vector

y ˆ …y1; . . . ; yn) is a set of goal functions. Let y* be a target vector that is initially set

by a decision-maker. The regret of having y instead of achieving the target y* is

represented by the distance between y and y*. Thus, the regret function is de® ned by

r…y† ˆ ky y*k:

It is thereby presented in the following form of Lp metric (p ¶ 1), which represents a

distance with p as a parameter de® ning the family of distance functions:

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r…yjp† ˆXn

iˆ1

jyi y¤i j

ki

³ ´p" #1=p

;

where ki is a normalization value for the ith goal measure. Since goals in multiple

criteria decision-making situations often have diŒerent degrees of importance, im-

portance weights (!is) should be assigned to goals, yis, wherePn

iˆ1 !i ˆ 1. Thus,

r…yjp; w† ˆXn

iˆ1

! pi

jyi y¤i j

ki

³ ´p" #1=p

; where w ˆ …!1; . . . ; !n†:

Estimation of the weight vector w is not a trivial task. First of all, each goal shouldbe compared with the others in its importance. The results from all pairwise com-

parisons are recorded in a matrix A ˆ ‰aij Š, where aij…i ˆ 1; . . . ; n; j ˆ 1; . . . ; n† indi-

cates the relative importance of goal i compared with goal j. For instance, if goal i is

twice as important as goal j, then aij ˆ 2. All diagonal elements of the matrix A areset to 1, and its lower triangle is the inverse of its upper triangle. Then, weight vector

w can be calculated by applying an eigenvalue method to A. (Refer to Saaty 1977 for

a detailed explanation of the eigenvalue method.)

The absolute value sign in the above regret function can be removed by intro-

ducing new values of d‡i and d‡

i as follows: for i ˆ 1; . . . ; n:

d‡i ˆ

yi y¤i ; if yi > y¤

i

0; otherwise;

(

di ˆy¤

i yi; if yi < y¤i

0; otherwise:

(

Then, jyi y¤i j ˆ di ‡ d‡

i ; y¤i yi ˆ di d‡

i , and di £ d‡i ˆ 0.

Combined with the above result, the regret function can be rewritten as

r…yjp; w† ˆXn

iˆ1

!i

ki

³ ´p

…di ‡ d‡i †p

" #1=p

:

It is noted that minimization of the above regret function is equivalent to minimiza-tion of

r 0…yjp; w† ˆXn

iˆ1

!i

ki

³ ´p

…di ‡ d‡i †p:

Therefore, design problems with multiple objectives can be presented in the follow-ing form of compromise programming (for simplicity and without loss of generality,

r 0 is replaced by r):

Minimize r…yjp; w† ˆXn

iˆ1

!i

ki

³ ´p

…di ‡ d‡i †p

Subject to y¤i fi…X† ˆ di d‡

i ; for i ˆ 1; . . . ; n

BX ˆ C ;

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where X is a decision vector, (x1; . . . ; xn), with decision variables of xi…i ˆ 1; . . . ; n†;fi…X† is an ith goal function, yi, such that yi ˆ fi…X†, B is a constraint coe� cientmatrix, and C is a right-hand side vector of constraints.

After solving the above CP problems with multiple goals, a system designer will

check if the target values of goals are achieved. If target values of some goals are

not obtained at the satisfactory level, the system designer will attempt to improve the

goals by adjusting target values of other goals until a certain satisfactory solution isreached (see Shi and Yu 1989 for further details of CP).

References

Atmani, A. and Lashkari, R. S., 1998, A model of machine-tool selection and operationallocation in FMS. International Journal of Production Research, 36, 1339.

Belton, V. and Elder, M. D., 1996, Exploring a multicriteria approach to production sched-uling. Journal of the Operation Research Society, 47, 162± 174.

Bilberg, A. and Alting, L., 1991, When simulation takes control. Journal of ManufacturingSystems, 10, 179.

Buzacott, J. A. and Yao, D. D., 1986, Flexible manufacturing systems: a review of analyticalmodels. Management Science, 32, 890± 905.

Chanin, M. N., Kuei, C. and Lin, C., 1990, Using Taguchi design, regression analysis, andsimulation to study maintenance ¯ oat systems. International Journal of ProductionResearch, 28, 1939± 1953.

Chincholkar, A. K. and Chetty, O. V. K., 1996, Simultaneous optimisation of controlfactors in automated storage and retrieval systems and FMS using stochastic colouredPetri nets and the Taguchi method. International Journal of Production Research, 12,137.

Choi, R. H. and Malstrom, E. M., 1988, Evaluation of traditional work scheduling rules ina ¯ exible manufacturing system with a physical simulator. Journal of ManufacturingSystems, 7, 33± 45.

Co, H. C., Biermann, J. S. and Chen, S. K., 1990, A methodical approach to the ¯ exible-manufacturing-system batching, loading and tool con® guration problems. InternationalJournal of Production Research, 28, 2171± 2186.

D’Angelo, A., Gastaldi, M. and Levialdi, N., 1996, Multicriteria evaluation model for¯ exible manufacturing system design. Computer Integrated Manufacturing Systems, 7,171± 178.

Dean, B. V., Yu, Y. and Schniederjans, M. J., 1990, A goal programming approach toproduction planning for ¯ exible manufacturing systems. Journal of Engineering andTechnology Management, 6, 207± 220.

Forman, E. H., Saaty, T. L., Selly, M. A. and Waldron, R., 1985, Expert Choice(Pittsburgh, PA: Decision Support Software Ind.).

Gangan, S., Khator, S. K. and Babu, A. J. G., 1987, Multiobjective decision makingapproach for determining alternative routing in a ¯ exible manufacturing system.Computers in Industrial Engineering, 13, 112± 117.

Jeong, K. C. and Kim, Y. D., 1998, A real-time scheduling mechanism for a ¯ exible manu-facturing system: using simulation and dispatching rules. International Journal ofProduction Research, 36, 2609± 2626.

Kumar, P., Tewari, N. K. and Singh, N., 1990, Joint consideration of grouping and loadingproblems in a ¯ exible manufacturing system. International Journal of ProductionResearch, 28, 1345± 1356.

Lee, H., Shi, Y. and Stolen, J., 1994, Allocating data ® les over a wide area network: goalsetting and compromise design. Information and Management, 26, 85± 95.

Liu, C.-Y. Tang, L. L. and Yih, Y., 1995, A framework for part type selection and schedulingin FMS environments. International Journal of Computer Integrated Manufacturing, 8,102.

Min, H. S., Yih, Y. and Kim, C. O., 1998, A competitive neural network approach to multi-objective FMS scheduling. International Journal of Production Research, 36, 1749± 1765.

3527FMS design model with multiple objectives

Dow

nloa

ded

by [

Tem

ple

Uni

vers

ity L

ibra

ries

] at

16:

01 1

6 N

ovem

ber

2014

Montazeri, M. and Wassenhove, L. N., 1990, Analysis of scheduling rules for an FMS.International Journal of Production Research, 28, 785± 802.

Park, T. and Steudel, H. J., 1989, The need to consider job sequencing policy when deter-mining buŒer capacity for FMC ¯ ow lines. Proceeding of the Third ORSA/TIMSSpecial Interest Conference on FMS, Cambridge, MA, pp. 173± 178.

Ro, I. and Kim, J., 1990, Multi-objective operational control rules in ¯ exible manufacturingsystems. International Journal of Production Research, 28, 47± 63.

Romero, C., 1991, Handbook of Critical Issues in Goal Programming (Oxford: Pergamon).Saaty, T. L., 1977, A scaling method for priorities in hierarchical structures. Journal of Maths

Psychology, 15, 234± 281.Shanker, K. and Srinivasulu, A., 1989, Some solution methodologies for loading problems

in a ¯ exible manufacturing system. International Journal of Production Research, 27,1019± 1034.

Shanker, K. and Tzen, Y. J., 1985, A loading and dispatching problem in a random ¯ exiblemanufacturing system. International Journal of Production Research, 23, 579± 595.

Shi, Y. and Yu, P. L., 1989, Goal setting and compromise solutions. In G. Karpak and S.Zionts (eds), Multiple Criteria Decision Making and Risk Analysis UsingMicrocomputers (Berlin: Springer).

Smith, M. L., Ramesh, R., Dudek, R. A. and Blair, E. L., 1986, Characteristics of U.S.¯ exible manufacturing systems Ð a Survey. Proceedings of the Second ORSA/TIMSConference on FMS, Ann Arbor, MI, pp. 477± 486.

Stecke, K. E., 1984, Design, planning, scheduling, and control problems of ¯ exible manu-facturing systems. Proceeding of the First ORSA/TIMS Special Interest Conference onFMS, Ann Arbor, MI.

Stecke, K. E. and Kim, I., 1991, A ¯ exible approach to part type selection in ¯ exible ¯ owsystems using part mix ratios. International Journal of Production Research, 29, 53± 75.

Tabucanon, M. T., Batanov, D. N. and Verma, D. K., 1994, Decision support system formulticriteria machine selection for ¯ exible manufacturing systems, Computers inIndustry, 25, 131± 143.

Vujosevic, R., 1994, Visual interactive simulation and arti® cial intelligence in design of¯ exible manufacturing systems. International Journal of Production Research, 32,1955± 1971.

Yim, D. and Barta, T. A., 1994, A Petri net-based simulation tool for the design and analysisof ¯ exible manufacturing systems. Journal of Manufacturing Systems, 13, 251± 261.

Yu, L., shih, H. M. and Sekiguchi, T., 1999, Fuzzy inference-based multiple criteria FMSscheduling. International Journal of Production Research, 37, 2315.

Zeleny, M., 1974, A concept of compromise solutions and the method of the displaced ideal.Computers and Operations Research, 1, 479± 196.

Zeleny, M., 1992, An essay into a philosophy of MCDM: a way of thinking or anotheralgorithm? Computers and Operations Research, 19, 563± 566.

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