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Development of the MAIN algorithm for a cellular manufacturing machinelayoutW. M. Chana; C. Y. Chana; C. K. KwongaaDepartment of Industrial & Systems Engineering, The Hong Kong Polytechnic University, Kowloon,Hong Kong

To cite this ArticleChan, W. M. , Chan, C. Y. and Kwong, C. K.(2004) 'Development of the MAIN algorithm for a cellularmanufacturing machine layout', International Journal of Production Research, 42: 1, 51 65

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int. j. prod. res.,2004, vol.42, no.1, 5165

Development of the MAIN algorithm for a cellular manufacturing

machine layout

W. M. CHANy, C. Y. CHANy* and C. K. KWONGy

When a static machine layout is simply optimized to a fixed quantitative demand,it may not be able to cope with demand fluctuations. The development of aheuristic approach called the MAIN (Machines Allocation INter-relationship)algorithm for intracellular machine layout design is introduced. It begins byanalysing a single period with a fixed quantitative demand and machine assign-ment is based on a set of proposed objective functions together with mergingtechniques. To simulate the demand fluctuations in a multiple periods planninghorizon, layouts are generated to fit different demand profiles. Each layout is thenprocessed further. First, at every periodic transition, there is re-layout to minimizethe material-handling cost. Second, we will examine the condition of using alayout right through all the periods to keep away from the machine rearrange-ment cost with some scarifications of the material-handling cost. Comparisonswill be done to seek out good machine layout(s). In terms of a single-periodlayout, the experimental results show that the proposed heuristic algorithm canachieve an average deviation of 4.8% in contrast with optimal solutions.However, to opt for re-layout or not depends very much on the relations betweenthe machine rearrangement and material-handling costs. Moreover, the variationsin the qualitative aspects in material handling will also be considered as it has

significant influence on the design of the machine layout.

1. Introduction

Group Technology (GT) has been applied to generate machine groups and

corresponding part families for cellular manufacturing (CM). In an ideal situation,

each cell is independent of another and, in practice, the main idea is to reduce the

intercellular movements. This results in an intracellular flow dominance arrange-

ment, and there are often similarities in processes in a cell (Chan et al. 1999,Yasuda and Yin 2001). To have the full benefits of CM, efficient layout design is

a key element (Massoud 1999, Taho and Brett 1999). In a manufacturing cell, each

part family has its own operating sequences and, in reality, the quantitative demands

can also vary periodically. This paper is to investigate the Dynamic Machine Cellular

Layout (DMCL) in an environment with multiple periods planning horizon.

Initially, the machine layout will be generated based on a fixed quantitative

demand profile and this is referred to the Static Machine Cellular Layout (SMCL).

Each static layout makes a good fit for a planning period but, in real situation, the

product mix is a function of demand, and it may well change as demand fluctuates

Revision received June 2003.y Department of Industrial & Systems Engineering, The Hong Kong Polytechnic

University, Hung Hom, Kowloon, Hong Kong.*To whom correspondence should be addressed. e-mail: [email protected]

International Journal of Production Research ISSN 00207543 print/ISSN 1366588X online# 2004 Taylor & Francis Ltd

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

DOI: 10.1080/00207540310001598456

DownloadedBy:[NationalInstituteof

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(Seifoddini and Djassemi 1997). Nicol and Hollier (1983) also mentioned that the

changes of radical layout happened frequently and management should always con-

sider this in the forward planning. DMCL is an attempt to address the demand

changes with unchanged product operating sequences in a cell.

The qualitative flow dominance represents considerable changing attributes

in parts whilst the quantitative flow dominance means that the movements (e.g.

transportation frequencies and distances) of the parts between machines are more

significant. In fact, most of the current approaches pay little attention to the quali-

tative aspects. In this paper, the MAIN (Machines Allocation INter-relationship)

algorithm is formulated to optimize the machine layout by considering both the

qualitative and the quantitative characteristics of a cell. This algorithm will address

the problem in view of the machine rearrangement cost and the part travelling cost.

In addition, the total part travelling score will be used as the SMCL performance

indicator and the dynamic layout(s) in DMCL is obtained by searching the layouts

generated by SMCL to cope with the multiple periods planning horizon.

In brief, the objective of this research is to exploit the machine layout with

varying periodic demand in a CM environment. The intention is to minimize the

total part travelling cost by taking into the consideration of the closeness of

machines, the handling efficiency, the part travelling distance, the materials flow

frequency and the machine rearrangement cost in a dynamic environment. First,

we will look into how to assign machines within a cell effectively based on several

factors like the operation sequences, the part flow frequencies, and the customer

demands of a part family in order to determine the required closeness of machines

in the layout. Then, the total travelling score will be calculated by accumulatingvalues of all related pair-wise machines, each of which incorporates information

such as the distance, the frequency of part flow, and the part handling efficiency.

As mentioned before, this score is also used to represent the SMCL performance for

comparison purpose. In terms of DMCL, the ultimate goal is to shrink the overall

layout cost and this can be achieved by having a good balance between the total

machine rearrangement cost and the total part travelling cost.

2. Literature review

Static machine layout problems have being studied for decades and the solution

layout is only good fit for a planning period. Currently, most of the availabletechniques tackle static layout problems by minimizing the total travelling cost of

parts. This can be done by working out a suitable arrangement for machines under

predefined locating zones (Tanchoco and Lee 1999, Urban et al.2000). For example,

the Quadratic Assignment Problem (QAP) technique uses the number of locations as

the number of facilities, and Koopmans and Beckmann (1957) are the pioneers of the

QAP technique. However, the QAP is NP-complete, and the size of a problem that

can be solved by optimal methods is very limited (Kusiak and Heragu 1987). In

SMCL, if n machines are grouped into a cell, there are as many as n! potential

layouts. In case of DMCL, the same machine group may have to be rearranged to

suit for m periods in a planning horizon. As the result, the probable combina-tions are as large as (n!)m and it is difficult to obtain the optimal solution based

on QAP approach (Rosenblatt 1986, Balakrishnan and Chun 1998). Indeed, purely

mathematical iterations will not be a feasible method for dealing with this sort of

problems (Jajodia et al. 1992) and, moreover, QAP usually works only with little

constraints. Instead, the heuristic approach can be useful in SMCL and DMCL.

52 W. M. Chan et al.



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Although heuristic approach cannot guarantee optimal result, it requires relatively

little time and effort to achieve an acceptable solution (Heragu and Kusiak 1988).

Apart from using the QAP technique, Montreuil (1990) developed a static layout

solving method using mixed-integer linear programming, which focuses on the load/

unload point along aisles. Tam and Li (1991) also formulated a three-phase

hierarchical approach that attempted to minimize the geometric constraint.

Nevertheless, the key limitation of static layout is that it only focuses on a single

planning period and will not be able to fulfil the changing customer demands today.

The dynamic layout problem usually assumes that machines could be economi-

cally relocated in order to cope with a new demand profile. Rosenblatt (1986) first

introduced a layout problem-solving technique for multiple planning periods. His

dynamic programming model attempts to find out the best layout for each prede-

termined period. The aim is to minimize the sum of deterministic rearrangement cost

through the entire planning periods. One limitation of Rosemblatts approach is the

cost of rearrangement, which does not consider the distance from a machine location

zone to another. Secondly, the discrete best layouts may not give a good overall

performance and the assumption that machines could always economically relocated

is also debatable. To resolve the problem, Kouvelis et al. (1992) presented a similar

algorithm to determine a layout, which would suit for multiple planning periods,

and, of course, this resulted in some scarifications in the material-handling cost.

Rather than switching from two extremes, there are often some rooms in between

worth exploring. Actually, constraints always exist in layout design. For example,

Balakrishnan et al. (1992) added the budget constraint for machine rearrange-

ments and solved the problem by using the shortest path algorithm. In fact, otherrealistic constraints such as the location restrictions, designers preferences, etc. are

indispensable in determining machine layout (Massoud 1999). Still, there is not much

concern in the product attributes. Clearly, the design of material-handling devices

plays a very important role in the material-handling system and the operational

efficiencies can quite vary with different handling facilities. Thus, the effort spent

on moving parts should not be uniformly assumed. In terms of layout determination,

Conway and Venkataramanan (1994) applied the genetic search technique to evolve

a population with a premature initial solution. Optimal solution layouts were also

computed for comparison purpose. Two cases were tested by this approach, and an

optimum could be obtained in the case with six machines. It hints that with areasonable complicated problem, looking for optimal solution will be impractical.

Again, heuristic algorithms are usually more suitable for cases of larger size.

Based to the studies, intracellular machine layout problem associated with

changing in part attributes in both SMCL and DMCL will be essential to look

into, and the significance of machine rearrangement cost in a multiple periods

planning horizon will also be a sensible issue to be examined. In addition, the

material-handling efficiency notably affecting the layout design should be included

to reflect the real-world situations.

3. Problem definitionsThis research aims on developing a method to undertake the static and the

dynamic machine layouts in a manufacturing cell where the machine location site

is a regular grid; similar to Tanchoco and Lee (1999) and Urban et al. (2000), each

machine cluster contains machines requiring equal floor space areas. The maximum

number of machines can be assigned into a grid is limited to nine machines as a

53MAIN algorithm for a cellular manufacturing machine layout



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3 3 grid is going to be used and there are only nine potential machine location

zones on it (figure 1). This is considered to be adequate for a machine cell as the

average machine size in a cell is around seven machines. For the model, we also

assume that a machine can be assigned to any location and the part travelling

distance is estimated by measuring the rectilinear distance from the centre of the

source machine to the centre of the destination machine. This implies the travelling

distance between machines j and k will be identical, and the size of any machine

location zone (x,y) should be able to accommodate the largest machine in a cell.

SMCL is designed to work with a fixed quantitative demand for a given partfamily. Besides targeted on the part flow between pair-wise machines such as

machines with larger number of in between flow would be allocated more closely,

the variations in part handling efficiency will also counted. As mentioned, it is

important as the attributes of a part will change from process to process. For

example, in an assembly cell, a part can have changes in size, weight, shape and

so on. It is not a surprise to see an initial 1 kg part increased to 5 kg after some

assembly operations or, the opposite, a finished part may reduce in weight in com-

parison with its earlier state if there is a material removal action involved. As a

result, even though the quantitative demand of a part remains unchanged, the best

possible layout can be different if the part handling efficiency is taken into account.DMCL is the extension of SMCL. It aims at obtaining machine layout that goes

well with periodic variations. In the MAIN algorithm, DMCL is further divided

into two branches namely the multiple-DMCL (mDMCL) and the single-DMCL

(sDMCL). mDMCL works with changing layouts whilst sDMCL keeps a unique

layout over periods. In the former case, machine locations will be rearranged as

the part flow frequencies change so as to maintain the lowest total part travelling

scores in the subsequent periods (the lowest the score the better the layout).

Generally, four potential quantitative demand profiles in a planning horizon

would have four possible optimal layouts ideally. However, owing to the similarity

in processing natures in a cell, we may have identical layout for a succeeding plan-ning period. Of course, this depends on the conditions but the potential is always

here. To measure the performance of the proposed algorithm, the total cell layout

cost is used as the performance indictor in the dynamic stage while the total part

travelling score is employed in the static stage. The formulation of the total cell

layout cost includes two basic elements: the total machine rearrangement cost and

j k

Measuring

points

Measuring

distance

n = 3

Machine

m = 3

x

y

Maximum size of

machine location

Figure 1. Nine zones location site.




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the total part travelling cost over all periods. The total part travelling cost is devised

from the part travelling score, which is determined by the proposed objective func-

tions to be discussed in the next section. In terms of the machine rearrangement cost,

figure 2 shows nine machines at the first period (p1). If machinesEand A are going

to be swapped to suit for the second planning period (p2), the rearrangement cost

(R1!2) must be introduced into the total machine rearrangement cost at the

dynamic state.

In some cases, machine relocation may not be practical due to prohibitive

rearrangement cost on moving machines and so on. Consequently, only the same

machine layout will be used for throughout all periods. Under these circumstances,

some relinquishes in part moving distances have to be made in order to keep the

layout and this is where the sDMCL takes place. Obviously, there is no machine

rearrangement cost but the part travelling cost may be higher.

4. MAIN algorithm

This section provides a brief description of the mathematical model presented by

Chan et al. (2002); the interested reader can refer to Chan et al. for details and

explanations about the handling of the SMCL. Basically, SMCL covers the data

collection and matrix-based data manipulations along with the application of the

formulated objective functions. Then, pair-wise machines are inserted into the 3 3

space grids in accordance with the ranking orders. Possible layouts are evaluated and

the total part travelling scores calculated to represent the preferences of the machine

layouts. SMCL can produce a good layout for a single period while DMCL needsa series of static layouts for multiple planning periods correspondingly, or a parti-

cular layout in case of machine rearrangement is impractical. Figure 3 shows the

skeleton of the MAIN model.

Rtotal = R12+R23+R34 (> 0)

p-1

A B C

D E F

G H I

p-2

E B C

D A F

G H I

p-3

F B C

D E A

G H I

p-4

A F C

D E G

B H I

Changing in quantitative demands on parts

There is machine rearrangement costs incurred in four periods (p-1 to p-4).

Figure 2. mDMCL with four planning periods.

SMCL mDMCL

sDMCL

Dynamic StageStatic Stage

Figure 3. Skeleton of the conceptual MAIN model.




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4.1. Static stage: SMCL

The static stage of the MAIN algorithm is to determine the total part travelling

score (p) in a cell in a period (p) with a particular layout. The purpose is to minimize

the total travelling score and this is analogue to the cost on making part movements.

The objective function is defined as:

min p Xm

j1

Xm

kj1

Dj$ k Fpj$ k 1

where

Dj$ k Xj Xk Yj Yk

: 2The Manhattan method has been chosen for calculating the distance (Dj$ k)

between two points where (Xj, Yj) and (Xk, Yk) are the coordinates of the measuring

points of machines jand k with reference to the 3 3 grid.

Fp, j $ x Tp, j ! k Tp, k !j, 3

whereFp,j$ kis the merged part flow weight for period p. It combines the unidirec-

tional basic part flow weights (Tp,j!k andTp,k!j) to form a generic correlation of

two machines. A basic part flow weight (e.g.Tp,j!k) is the mean by which parts are

transported from one machine to another in unidirectional (say, from machine jto

machinek) within a cell. The characteristics of intracellular part flows are that they

are usually rushed and short distances. These weights directly affect the positioning

of machines. In other words, a pair of machines with higher merged part flow weight

should be more closely placed. The determination of the basic and the merged part

flow weights are intimately related to the quantitative demand of a part (i) in a familyin a period (Qp,i) and the part transportation quantity per move (Hi,j!k). The later is

needed because some transportation devices may have the ability to carry several

items in one transaction. This suggests that the transportation frequency is equal to

the quantitative demand of a part divided by the transportation quantity per move.

Lastly, the part-handling factor (li,j!k) is introduced to signify the levels of

difficulty in moving a part between a machine pair. In this research, a simple relative

mode is used to quantify this factor. For examples, 1 represents the easiest in

transporting and 2 means double the effort of 1, etc. The equation for determine

the basic part flow weight is:

Tp, j ! k Xn

i1

Qp, i

Hi,j! k li,j! k 4

4.2. Dynamic stage: DMCL

At this point, two situations would be faced, namely the mDMCL and the

sDMCL in a multiple periods planning horizon. Figure 3 illustrates the two

alternative routes of the MAIN algorithm. In mDMCL, the part travelling cost

and the machine rearrangement cost are needed to be determined. In case of the

travelling cost, it will be obtained by converting the total travelling scores generatedin SMCL into monetary terms; fortunately, this is a linear conversion only. The

function used for calculating the total cell layout cost () over multiple periods is:

XP

p1

p ! XP1

p1

Rp $p1 5




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There are at most three machine rearrangement costs involved in a four periods

planning horizon. !represents the cost per unit travelling score and it is a constant.

However, the establishment of this value must be taken reference to the formulation

of the part-handling factor. In the period-to-period machine rearrangement cost

(Rp!p 1), it consists of two portions; they are the basic cost for machine relocation

such as the set-up/installation cost (Mj) and the cost per unit machine movement

(Cj). The calculation of this cost is based on:

Rp !p1 Xm

j1

Mj Dj$ k Cj 6

Note that Rp!p 1 is equal to 0 if all machines remain in the same locations

becauseMj 0 and Dj$ k 0.

Remember, sDMCL tends to keep all machines stationary. This signifies that the

layout determined by sDMCL may not be the optimal solution in all periods. In theMAIN algorithm, the cell layout cost derived from sDMCL is the aggregation of the

part travelling cost over all periods. This is done by evaluating every static layout

generated in SMCL to find out the best one, which is going to be used as the final

layout for a cell. The equation for working out the total part travelling cost for each

SMCL generated layout is:

Total part travelling cost !Xn

p1

0

p 7

For example, if there are four periods, then SMCL may generate four layouts, each

of which fits for a particular period. The iteration of using each of these four layouts

exclusively throughout all periods yields new sets of part travelling scores (0p), and

the new part travelling costs can be found. Normally, one of them will have the

lowest value and this becomes the selected layout of sDMCL.

5. Numerical analysis establishment

Numerical information provided by established research cases in machine layout

is used to evaluate the proposed MAIN algorithm. Some related data are obtained

from Yaman et al. (1993) and Tang and Abdel-Malek (1996). In essence, both

Yaman et al. and Tang and Abdel-Malek used the same data set. Besides, Yamanet al.also used a 3 3 grid for locating machines. In the process operation side, there

were five parts processed by nine machines. For each part in this family, the opera-

tional sequence and quantitative demands in a five-period planning horizon were

proposed (tables 1 and 2). Although they provided some basic requirements, there

was still information missing for the MAIN algorithm to operation. These include

the cost per unit part movement, the part transportation quantity per move, the part-

handling factor and those that related to machine rearrangement, etc. Therefore, we

assigned a fixed cost (! $10/unit travelling score) to deal with part movements. To

test the effect of the part-handling factor, a set of part-handling factors had also been

proposed (table 3); parts 1 and 3 gradually decease in part-handling factors, whilstthe others increased. Table 4 shows the machine rearrangement costs. They are

required in the conditions with multiple planning periods.

In the static stage, all the part transportation quantity per move and the part-

handling factors were set to 1s. This is required with the purpose of fulfilling the

needs of the MAIN and also is capable of going for comparisons to see the effect of




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having taken into the consideration of part-handling effort. As a result, the part flow

weights (Fp,j$ k) generated by applying the static stage of the MAIN when dealing

with the period (p1) are presented in the third column in table 5. After the part flowweights were ranked, the layout designer can start pulling the machines to form a

3 3 machine layout grid according the rankings. Once the pulling operations have

been completed, the distances among machines (Dj$ k) can be obtained by referring

to the Manhattan method (equation 2). Then, the travelling score for each machine

pair can be determined accordingly and the summation of these travelling scores give

Part

Period

p-1 p-2 p-3 p-4 p-5

1 10 35 90 40 552 30 50 25 65 203 45 15 40 70 154 70 80 55 90 855 85 60 70 20 30

Table 2. Demand profiles in Yamanet al.s and Tanget al.s cases.

Part Machine operational sequence

1 01 ! 03 ! 05 ! 07 ! 02 ! 07 ! 092 01 ! 04 ! 02 ! 05 ! 06 ! 08 ! 09

3 01 ! 05 ! 07 ! 08 ! 05 ! 06 ! 02 ! 094 01 ! 02 ! 04 ! 06 ! 07 ! 08 ! 02 ! 03 ! 095 01 ! 07 ! 06 ! 04 ! 02 ! 08 ! 03 ! 05 ! 06 ! 09

Table 1. Original data of Yamana et al.s and Tang et al.s cases.

Part Part-handling factor

1 6 ! 5 ! 4 ! 3 ! 2 ! 12 1 ! 2 ! 3 ! 4 ! 5 ! 63 6 ! 5 ! 4 ! 4 ! 3 ! 2 ! 14 1 ! 1 ! 2 ! 2 ! 2 ! 3 ! 3 ! 45 1 ! 2 ! 3 ! 4 ! 5 ! 5 ! 5 ! 5 ! 6

Table 3. Proposed part-handling factors forYamanet al.s and Tang et al.s cases.

Machine 01 02 03 04 05 06 07 08 09

Basic cost for machine relocation (Mj) for case five($) 150 100 200 320 180 90 240 130 90

Cost per unit machine movement (Cj) for case five($) 15 10 20 32 18 9 24 13 9

Table 4. Proposed machine rearrangement costs for Yamanet al.s andTang et al.s cases.




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the total travelling score (p) of this layout. The second iteration begins by examining

the part travelling scores. For example, table 5 shows that machines 0708 (F1,7 $ 8)

contributed a significant influence to the part travelling score (see the greyed row)

and this was due to the lengthy distance (D7 $ 8) in between. As the result, it is likelyto make some improvements by bringing machines 07 and 08 closer. The rule of

thumb for doing this part of the job is that that one should always check for those

with high merged part flow weights and far distances (say, Dj$ k>2) to seek for

improvements. To simplify the discussions, the layouts for all five periods are shown

in tables 6 and 7 for the first and the second iterations, respectively. Note that

layouts suggested by the second iteration may not always be better than the first

iteration, such as inp4 andp5. The layout designer can make the selection easily by

looking at the figures and, moreover, based on our experiences, two iterations are

adequate to provide very good solutions.

Two more test cases had been created arbitrarily with 10 parts and ninemachines. In each test case, five periods with varying quantitative demands were

generated to simulate the production fluctuations (tables 8 and 9). In table 10,

operational sequences and part-handling factors were also proposed for the self-

developed test cases. Finally, the basic costs for machine relocation and cost per

unit machine movement were assumed as in tables 11 and 12.

Ranking (j$ k) Fp,j$ k Dj$ k

Iteration 1(Fp,j$ k Dj$ k) Dj$ k

Iteration 2(Fp,j$k Dj$k)

1 02,04 185 1 185 1 185

2 05,06 160 1 160 1 1603 02,08 155 1 155 1 155

04,06 155 1 155 1 15506,07 155 1 155 1 155

4 07,08 115 4 460 2 2305 03,05 95 1 95 1 956 01,07 85 1 85 1 85

03,08 85 1 85 1 8506,09 85 3 255 2 170

7 01,02 70 2 140 2 14002,03 70 2 140 2 14003,09 70 1 70 2 140

8 05,07 55 2 110 2 1109 01,05 45 1 45 3 135

02,06 45 2 90 2 9002,09 45 3 135 4 18005,08 45 2 90 2 90

10 01,04 30 3 90 1 3002,05 30 1 30 3 9006,08 30 3 90 1 3008,09 30 2 60 3 90

11 02,07 20 3 60 3 6012 01,03 10 2 20 4 40

07,09 10 2 20 1 101 2980 2850

* Greyed values are machines 07, 08 with high part-travelling score at Iteration 1.

Table 5. Part travelling scores in the first planning period(p-1, li, j$k 1, Hi, j$k 1).




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Part

Period

Totalp-1 p-2 p-3 p-4 p-5

1 100 200 300 700 900 22002 200 610 800 440 650 27003 340 300 980 670 320 26104 450 450 450 450 450 22505 590 370 740 870 1100 36706 500 210 180 120 80 10907 770 800 900 530 790 37908 1120 1500 1400 1600 1210 68309 960 300 200 720 530 2710

10 440 110 680 90 880 2200

Table 8. Demand profiles for self-developed case one [S1].

Part

Period

Totalp-1 p-2 p-3 p-4 p-5

1 1200 1450 1670 1890 1940 81502 400 520 460 930 210 25203 980 460 270 380 740 28304 450 450 450 450 450 22505 610 220 1000 880 370 3080

6 270 160 150 340 130 10507 650 790 530 460 230 26608 1720 1440 1380 1690 2130 83609 810 150 130 240 1170 2500

10 410 320 60 700 530 2020

Table 9. Demand profiles for self-developed case two [S2].

p-1 p-2 p-3 p-4 p-5

09 07 07 09 03 05 09 08 06 07 05 06 05 07 0603 05 06 01 07 06 01 03 05 08 02 04 08 02 04

08 02 04 08 02 04 04 02 07 09 01 03 03 01 091 2980 2 2880 3 3710 4 3165 5 2275

* Greyed values are the lowest total part-travelling score at each period.

Table 6. First iterative results of the MAIN algorithm (p-1 top-5, li, j$k 1,Hi, j$ k 1).

p-1 p-2 p-3 p-4 p-5

02 04 01 02 04 01 01 08 03 01 02 04 01 02 0408 06 07 08 06 07 02 07 05 09 08 06 09 08 06

03 05 09 03 05 09 04 09 06 03 07 05 03 05 071 2850 2 2790 3 3160 4 3225 5 2475

* Greyed values are the lowest total part-travelling score at each period.

Table 7. Second iterative results of the MAIN algorithm (p-1 to p-5, li, j$ k 1,




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6. Results and analysisFor evaluation purposes, MATLAB was used to work out the optimal solutions

for static layouts using an exhaustive search. However, there is little chance to get the

optimal layouts for DMCL due to the very large number of combinations involved.

This is also why a heuristic approach is the feasible technique to determine the

dynamic layouts. Referring to the information presented in tables 6 and 7, the

static layouts generated by the SMCL of MAIN for all five periods are given in

table 13 based on the data sets from Yaman et al.s and Tang and Abdel-Maleks

cases. Table 14 summarizes the results from various approaches. Note that all

preliminary results generated by the proposed MAIN algorithm were better than

Yaman et al.s approaches, although some results might not be more superior toTang and Abdel-Maleks method such as in planning periodsp1 andp4. Among all

tested heuristics, the proposed algorithm was best in overall performance and the

average error was least, i.e. it was only 4.8% in comparison with the optimal

solutions. Furthermore, in operating MAIN, one important feature was virtually

disabled at this stage as all part-handling factors were set to 1 s. This was done

Parttype Operational sequence Part-handling factor

1 01 ! 04 ! 06 ! 04 ! 05 ! 03 ! 09 5 ! 5 ! 4 ! 3 ! 2 ! 1

2 01 ! 06 ! 04 ! 07 ! 08 ! 09 4 ! 2 ! 2 ! 1 ! 13 01 ! 05 ! 03 ! 02 ! 05 ! 09 1 ! 1 ! 2 ! 3 ! 44 01 ! 02 ! 03 ! 05 ! 04 ! 06 ! 09 1 ! 2 ! 3 ! 3 ! 4 ! 45 01 ! 08 ! 04 ! 06 ! 05 ! 02 ! 03 ! 05 ! 09 1 ! 1 ! 1 ! 1 ! 1 ! 2 ! 2 ! 26 01 ! 03 ! 04 ! 07 ! 09 7 ! 6 ! 5 ! 47 01 ! 06 ! 05 ! 02 ! 06 ! 08 ! 03 ! 09 1 ! 1 ! 1 ! 2 ! 2 ! 3 ! 38 01 ! 02 ! 04 ! 06 ! 05 ! 03 ! 05 ! 09 1 ! 1 ! 1 ! 1 ! 1 ! 2 ! 29 01 ! 04 ! 05 ! 07 ! 03 ! 08 ! 09 4 ! 3 ! 2 ! 1 ! 1 ! 1

10 01 ! 07 ! 08 ! 02 ! 06 ! 04 ! 05 ! 03 ! 09 5 ! 4 ! 3 ! 2 ! 1 ! 2 ! 3 ! 4

Table 10. Operational sequences and part-handling factors for [S1] and [S2].

M/C 01 02 03 04 05 06 07 08 09

Basic cost for machine relocation (Mj) for S1($) 780 650 930 820 620 670 770 910 860

Cost per unit machine movement (Cj) for S2($) 78 65 93 82 62 67 77 91 86

Table 11. Machine rearrangement cost for [S1].

M/C 01 02 03 04 05 06 07 08 09

Basic cost for machine relocation (Mj) for S1($) 940 640 1100 450 390 780 990 420 520

Cost per unit machine movement (Cj) for S2($) 94 64 110 45 39 78 99 42 52

Table 12. Machine rearrangement cost for [S2].




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because other approaches had not considered the affect of this parameter and the

comparison might not be fair if it was included.

The sDMCL looks for a sole layout for all periods by picking the mostappropriate static layout. Since there are five periods, five static layouts produced

by the SMCL will be examined. Naturally, the one with a minimum overall total

part-travelling score should be chosen; to ease the comparison with mDMCL, we

multiplied them with the cost per unit travelling score (!) to yield the total cell layout

cost. Referring to table 15, the smallest value is 145 700; it was the static layout

generated by SMCL for period p5 and it is called SMCL5 in this case.

In mDMCL, all SMCL generated static layouts were used to minimize the parts

travelling due to periodic changes and the machine rearrangement cost is brought in

to finance the re-layout. We also observed that in some cases it might not be

necessary to rearrange the machines if the proposed successive layout was alsoidentical to the one in use. The chance of having this is always there as parts assigned

to a cell are from the same family. Similarly, in this case, there was no machine

rearrangement cost incurred between p1 and p2 (table 16).

For better illustration, the overall results are summarized in table 17. Note

that the total cell layout cost of the mDMCL (146 351) was greater than the best

layout generated by sDMCL (145 700) when using Yaman et al.s and Tang and

Abdel-Maleks data sets, in which part-handling factors were set to 1s. Therefore,

sDMCL (grey) should be applied in this case. Moreover, the figures generated by

including part-handling factors were significantly larger (up to two-to-three times in

our cases) than those with the part-handling factors disabled. This also indicates thatthe effect of the part-handling factor can be striking and this will surely influence

planning of the machine layout. In addition, referring to the first self-developed case

[S1] in table 17, it is clear that if the part-handling factors were taken into account,

the decision would be quite different. In this case, the most suitable layout strategy

changed from sDMCL to mDMCLs.

Method

Part travelling score

Per cent ofdeviation

p-1(1)

p-2(2)

p-3(3)

p-4(4)

p-5(5)

Total(P

)

Optimal 2780 2640 2950 3020 2200 13 590 Yaman et al. (1) 3630 3180 3690 3975 3045 17 520 28.9Yaman et al. (2) 3470 3350 3570 4065 2975 17 430 28.3Tang et al. 2820 2980 3200 3100 2355 14 455 6.4MAIN 2850 2790 3160 3165 2275 14 240 4.8

Table 14. Part traveling scores generated by various approaches.

p-1 p-2 p-3 p-4 p-5

02 04 01 02 04 01 01 08 03 07 05 06 05 07 0608 06 07 08 06 07 02 07 05 08 02 04 08 02 04

03 05 09 03 05 09 04 09 06 09 01 03 03 01 091 2850 2 2790 3 3160 4 3165 5 2275

Table 13. Static layouts generated by MAIN (li, j$ k 1, Hi, j$ k 1).




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7. Discussion

Although we did not incorporate the data for part transportation quantity in this

research, the establishment of the part-handling factor could imitate the importance

of the part transportation quantity. In practice, both can be valuable when reflectingtrue situations. In view of the MAIN algorithm, the number of machines and the

orientation of the location zones should not be the definite constraints. In addition,

more than nine machines and irregular machine disposition zones are also possible.

However, these require further investigation. Readers interested in this area can

refer to Massoud (1999) and Taho and Brett (1999).

Total part travellingcost ( !) ($)

PeriodTotal

(a)p-1 p-2 p-3 p-4 p-5

Static layout SMCL1 28 500 27 900 35 100 36 100 25 300 152 900SMCL2 28 500 27 900 35 100 36 100 25 300 152 900SMCL3 31 400 29 700 31 600 35 150 24 650 152 500SMCL4 32 600 30 200 35 900 31 650 24 550 154 900SMCL5 29 400 28 200 31 700 33 650 22 750 145 700

Minimum totalcell layout cost ()

(b) Total machine rearrangement cost 0 (a) (b)

145 700

*Grayed values are generated static layouts by SMCL.

Table 15. Total cell layout costs for sDMCL.

Data Set

Total cell layout cost

sDMCL(l 1)

mDMCL(l )

sDMCL(l vary)

mDMCL(l vary)

Averagevariations between

(l 1) and (l vary)

Tang et al.s

Yamanet al.s

145 700 146 351 456 550 457 326 3.13 times

S1 3 243 600 3 548 260 7 060 400 6 983 514 2.07 timesS2 2 899 000 3 180 960 6 052 000 6 057 874 1.99 times

* Greyed values are the lowest total cell layout costs.

Table 17. Summary of total cell layout costs.

Period p-1 p-2 p-3 p-4 p-5 Total

Total parttravelling cost( !) ($)

28 500 27 900 31 600 31 650 22 750 142 400 (a)

Machinerearrangementcost (Rp!p 1) ($)

g 0 1829 1660 1671 g 3951 (b)

Minimum totalcell layout cost ()

(a) (b) 146 351

Table 16. Total cell layout cost from mDMCL.




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Referring to the analysis, one may observe that the ratios of total part travelling

cost to total cell layout cost and of total machine rearrangement cost to total cell

layout cost are very important factors when deciding on layout tactics (e.g. sDMCL

or mDMCL). Hence, future research could involve the investigation of these

ratios and the development of a methodology for the quick determination of a

proper layout strategy could save much calculation effort. Additionally, Taho and

Brett (1999) presented an idea of putting the probability of occurrence on demand

profiles. This can be valuable when designing a machine layout if there are some

kinds of uncertainties. In fact, this always happens in real life. Basically, MAIN

can absorb probability into the objective functions and this is surely another area

worth investigating.

At first, we tended to take out the machine rearrangement cost from the layout

from the dynamic layouts to yield a lower bound to assist in the searching for better

solutions. However, it was also noticed that the effect of the machine rearrangementcost was not significant in our cases. Moreover, due to similarities in processing

a part family, it was also observed that in a lot of cases an identical layout could

be used effectively throughout multiple periods. However, this can act against our

intention of expanding the use of the MAIN algorithm to handling more than nine

machines. This is because a layout with more than nine machines cannot follow the

characteristics of CM anymore and, thus, the similarity in processes cannot exist in

these cases.

8. ConclusionsMachine layout problems in manufacturing have received considerable

attention. For instance, using a computer can hardly solve problems with more

than 15 machines in the static stage with limited constraints, according to a literature

review. MAIN can overcome this problem as it is based on a heuristic approach.

The proposed MAIN algorithm addresses the problems in both static and

dynamic layouts by incorporating practical factors such as the part-handling

factor, the basic cost for machine relocation and the cost per unit machine

movement, etc. MAIN makes a best compromise of the above-mentioned factors

with the closeness of machines in order to minimize the total cell layout cost. This

algorithm also caters for the possibility of allowing a single layout for multiple

periods with demand fluctuation. The algorithm works well for a maximum of

nine machines, which are assigned into a 3 3 matrix-like layout by using a pulling

technique based on a set of objective functions developed under MAIN. Referring to

the experimental results, the MAIN algorithm achieved an average of 95.2%

performance (4.8% deviation) in comparison with optimal solutions in the case of

a static layout. In terms of multiple planning periods, the selection of either sDMCL

or mDMCL depends on the proportion of the total machine rearrangement cost

and the total part travelling cost. Moreover, the role of the part-handling factor in

the layout design is inevitable. The difference in cell layout cost could be more thanthree times in the cases we studied when the part-handling factor was involved. In

addition, it was assumed that the transportation quantity per move (Hi,j!k) kept

constant and relied on the part-handling factor to simulate the effect. Finally, it can

be observed that the layout decision can be totally different if this factor is taken

into consideration.




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Acknowledgements

The work was substantially supported by a grant from the Department of

Industiral & Systems Engineering, The Hong Kong Polytechnic University,

Research Grants Council of the Hong Kong Special Administrative Region

(Project No. G-V524).

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