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Journal of Advanced Manufacturing SystemsVol. 5, No. 1 (2006) 27–44c World Scientific Publishing Company

A GENETIC ALGORITHM APPROACH FOR MACHINE

CELL FORMATION

RAVISHANKAR RAJAGOPALAN∗ and DANIEL J. FONSECA†

Department of Industrial Engineering, The University of Alabama

Tuscaloosa, AL 35487 — 0288, US ∗[email protected] †[email protected]

Cellular Manufacturing Systems (CMS) have been the key to the success of manufac-turing industries in the recent past. Machine cell design, which involves formation of machine cells and component groups, represents the most important step in the designof CMS. Even though a tremendous amount of research has been conducted in thisarea, the gap between theoretical research and practice is widening primarily becauseof the lack of consideration of key production data such as production volumes, oper-ations sequences, machine sequence inside the cells, processing times, setup times, andmachine costs during the cell design stage. This paper discuses the development of aGenetic Algorithm Model (GAM), designed to assist in the formation of manufacturingcells. The GAM aims at the minimization of the material handling and the penalty costswhile considering the effects of inter-cell, intra-cell, backtracking, and machine skippingmovements.

Keywords: Genetic algorithms; cellular manufacturing; cell formation.

1. Introduction

Increased competition and fluctuating market demands have driven many manu-

facturing firms to consider novel approaches to improve productivity and eliminatewaste. In the past two decades, manufacturing industries have undergone a revo-

lution, widely considered as the third industrial revolution.1 Many innovative con-

cepts have surfaced, and only a few among them has been successful. The concept

of Group Technology (GT) is one of such successful principles embraced by most

industries.

Group Technology (GT) is the exploitation of the similarities among processes

and component designs in such a way that it increases the utilization of resources,

and eliminates/reduces nonvalue added activities, i.e., material handling, scraps,

downtime, etc. GT exploits similarities in three different ways: (1) by performing

alike activities together, (2) by standardizing similar tasks, and (3) by efficiently

storing and retrieving information about recurring problems 2 GT forms the basis



28 R. Rajagopalan & D. J. Fonseca

of Cellular Manufacturing Systems (CMS). Cellular manufacturing is a practice

that involves grouping similar machines into cells, simultaneously grouping sim-ilar components into groups. The CMS offer a great deal of benefits including

reduction in material handling times, setup times, batch sizes, and throughput

times.3

2. Drawbacks of Current Cell Formation Techniques

The formation of machine cells and component groups has been the main focus of

most of the research performed in the field of CMS. The complexity, in terms of

the size of the problem, makes it difficult for researchers to present a comprehen-

sive method that simulates the exact manufacturing system. The initial methods

that attempted to solve the problem of machine and component grouping failed

to consider any practical constraints.4–7 Most of these methods work with the 0-1

incidence matrix, in which the entries are either 0 or 1 depending on whether a

part is processed in a machine or not, respectively. In these methods, the incidence

matrix is rearranged to obtain a diagonal structure that facilitates the identifica-

tion of machine cells and their corresponding component groups. Another group

of solution techniques known as the similarity coefficient methods involves com-

puting the value of similarity coefficients between all the machines or components

and grouping the ones with the highest similarity.3,4 This process is repeated until

all the machines or components are grouped into cells. These methods, though

quick in obtaining machine cells and component groups, do not consider sev-

eral important production data that have significant effect on the cell formation

process.

Since the late eighties, researchers have included several production data such as

production volume, processing sequence, processing times, alternate process plans,

and capacity of machines etc., during the cell design stage. References 8–14 are the

few of the works that have taken into consideration the effects of some of the previ-

ously mentioned production data during machine cell formation. These productiondata have been found to impact the machine cells and component groups formed.

The last decade has seen a steep rise in the number of publications considering

various production data in arriving at a practical solution to the cell formation

problem. Many of the techniques proposed by these researchers have the objective

of minimizing the material handling costs while forming the machine cells and com-

ponent groups. The composition of material handling costs affects the cells designed.

The early researchers15,16 considered the effect of inter-cell material handling alone

and neglected the effects of intra-cell material handling. Even though, the magni-

tude of the intra-cell material handling is less when compared to inter-cell materialhandling, the frequency of intra-cell material handling is very high when com-

d t i t ll t i l h dli H id i th i t ll t



A Genetic Algorithm Approach for Machine Cell Formation 29

handling in their material handling cost calculation.9,17 However, many of them

have failed to capture precisely the different components of intra-cell materialhandling namely the intra-cell, backtracking, and machine skipping movements.

Reference 12 made an attempt to capture these factors in their research. However,

the nonconsideration of machine sequence inside the cells, another factor repeatedly

neglected by the researchers, makes the material handling costs calculated unreal-

istic. This machine sequence inside the cells has a significant impact on the three

components of the intra-cell material handling cost, and hence, on the cell design

process.

Considering these factors simultaneously in the cell formation stage will cer-

tainly affect the machine cells and component groups formed. Hence, there is a

need to develop a one step method that will address all these issues effectively in a

timely manner. The Genetic Algorithm Model (GAM) discussed here is a one-step

model that captures all these factors effectively and provides the optimal/near-

optimal machine cells, component groups and machine sequences inside the cells.

3. The Genetic Algorithm Model

The main goal of the study was to develop a Genetic Algorithm (GA) based model

(GAM) to tackle the machine cell formation problem in CMS, considering various

production data such as production volume of components, processing sequences,

machine sequence inside the cell, processing times, setup times, and machines

costs. The computer code developed in Visual C++ enables the determination

of optimal/near-optimal solutions in a timely manner.

3.1. Assumptions behind the GAM

The GAM has been designed based on the following assumptions:

1. The number of cells is predefined.2. There is only one machine of each type, i.e., no duplicate machines are allowed.

3. Each component visits a machine only once during its processing.

4. Every component has a fixed operation sequence.

5. The layout of the cells is assumed to be linear and has a single row.

6. The transfer batch size is one.

7. Each machine can belong to one and only one cell.

3.2. Notation used in the GAM

Following is the notation used in the development of the model:

1 IRC T t l i t ll t ($)




4. MSC: Machine skipping cost ($).

5. PC: Total penalty cost ($).6. ST: Setup time per batch (min).

7. MR: Machine rate per hour ($/h).

8. PT: Processing time per unit (min).

9. PV: Production volume (units).

3.3. The model

The GAM identifies the machine cells, machine sequences inside each cells, and

component groups. The objective of the GAM is to minimize the sum of material

handling and penalty costs. The material handling cost encapsulates the variousmaterial handling movements namely the inter-cell, intra-cell, backtracking, and

machine skipping. The penalty cost consists of the setup and the processing costs

and accounts for the formation of component groups. Its impact on machine cells

and component groups formation is explained in detail in the subsequent section.

3.4. Penalty cost

The total material handling cost controls the formation of machine cells, but has

no influence on the component group formation. For a specific machine cell formed,

there might be a number of different component groups. For instance, consider a

component that requires only two operations. If these two operations are performed

in two different cells, the only material handling cost associated with it is the inter-

cell cost. All other costs namely intra-cell, backtracking, and machine skipping are

zero. However, assigning the components to either of these cells would not influence

the calculated inter-cell material handling cost. Hence, the same material handling

cost will be arrived at irrespective of whether the component is assigned to one

cell or another. To overcome this problem of multi-solution component grouping,

a penalty cost is associated with each component that visits a cell other than the

one to which it is assigned. Such a cost factor is required to effectively accountfor the grouping of components. The penalty cost is the sum of the setup and the

processing costs. In this regard, each cell is considered as a separate cost center.

Hence, any processing in the cell to which the part is assigned will incur in no extra

cost. However, if the part is assigned to another cell, the setup and the processing

costs are treated as extra costs. This in turn restricts most of the operations on a

part to be assigned to the same cell, thus reducing the inter-cell movement. The

penalty cost is calculated as given in Eq. (1).

PC = (ST ×MR/60) + (PT×MR× PV/60). (3.1)

It thus can be said that the objective function of the study involves obtaining

th hi ll t d hi i h th t




For Each Component Repeat These Steps;

PC=0; IRC=0;IAC=0; BC=0

compcellno=cell nu

mber to which component belongs;

operation no=1

operation no

=1

machcellno=co

mpcellno

machno=machine

in which operation is carried out

machcellno=cell to which this machine belongs

operation no= operation no+1

PC=PC+(ST*MR/60)+(PT*MR*PV/60)


YES

YES

NO

machcellno=

compcellno

NO

machcellno(current)=

machcellno(previous)

PC=PC+(ST*MR/60)+(PT

*MR*PV/60)

IRC=IRC+(PV*Interc

ell_cost)


Step-3

Current Machine Postion

> Prev

ious Machine

Position


IAC=IAC+(Current Position-Previous

Position)*Intra_cell_cost*PV


Step-3


BC=BC+(Previous Position-Current

Position)*Backtrack_cost*PV


Step-3

machcellno(c

urrent)=

machcellno(p

revious)

IRC=IRC+(PV*Intercell_cost)

ope

ration no= operation no+1

Step-3

Current Machine Postion

> Previous Machine

Position

IAC=IAC+(Current Pos

ition-Previous

Position)*Intra_cell_

cost*PV


Step-3

BC=BC+(Previous Position-Current

Position)*Backtra

ck_cost*PV

operation no= op

eration no+1

Step-3

YES

NO

NO

YES

YES

NO

NO

YES

YES

NO

Fig.1.

Costcalculation

heuristic.




5 Machine, 6 Component Problem

Sequence Matrix

Machines1 2 3 4 5

1

2

3

4

5

6

Production Volume = {100, 300, 200, 250, 150, 175}

Processing Time Matrix (Minutes)

Machines

1 2 3 4 5

1

2

3Components

4

5

6

Setup Time in Each Machine (Minutes) = {120, 75, 100, 60, 100}

Machine Cost for Each Machine ($/Hour) = {25, 35, 50, 20, 40}

1 2 3 0 0

1 2 0 3 0

2 1 0 0 0

0 0 0 1 2

0 0 1 2 3

0 0 0 2 1

5 4 3 0 0

6 2 0 3 0

4 5 0 0 0

0 0 0 4 6

0 0 4 3 2

0 0 0 3 4

Fig. 2. Overall cost calculation example.

5 Machine – 6 Component Problem2 Cell Solution

Cells Machines in Order Components

1 1, 3, 2 1, 2, 3

2 4, 5 4, 5, 6

Cell 1 Cell 21 3 2 4 5




Machines 1 2 3 4 5 6

1 2 1 1 2 1Cells

Fig. 4. Sample chromosome for machine cells.

Similarly, component 2 has a production volume of 300, and follows a processing

sequencing of 1-2-4. From Fig. 4, machines 1 and 2 are located in cell 1, whereas

machine 4 is located in cell 2. Moreover, component 2 belongs to cell 1. This compo-

nent incurs in an inter-cell material handling while being moved from machine 2 to

machine 4. An intra-cell cost, along with a machine skipping factor of 2, is incurred

when the component is transferred from machine 1 to 2. However, there are no

backtracking costs associated with this part’s movement. Moreover, component 2

belongs to cell 1, but machine 4 is located in cell 2; hence, its processing in machine

4 implies a penalty cost. In such a case, the setup and processing costs in machine

4 are considered as penalty costs. The Setup (ST) and Processing Times (PT) for

component 2 in machine 4 are 60 and 3 min, respectively, thus:

Inter-cell cost [2-4] = 300× 5 = 1500

Intra-cell cost [1-2] = 300× 2× 1 = 600

Backtracking cost = 0

Setup cost = (60 × 20)/60 = 20

Processing cost = (3 × 300× 20)/60 = 300

Penalty cost = 300 + 20 = 320.

In a similar fashion, the different cost elements can be calculated for all thecomponents as shown in Table 1. The overall cost incurred by all the components

is $5628.33. This cost is treated as the fitness function for the GAM, and this

effectively guides the GAM toward the optimal/near-optimal solution.

Table 1. Overall cost calculation summary.

Comp No. Material Handling Costs ($) Penalty Costs ($) Overall Cost ($)

Inter Intra Back Total Setup Process Total

1 0 200 200 400 0 0 0 400

2 1500 600 0 2100 20 300 320 24203 0 0 800 800 0 0 0 8004 0 250 0 250 0 0 0 250




4. Genetic Algorithm Design for the GAM

4.1. Coding scheme for the GAM

In the GAM, the objective is to find optimal machine cells, machine sequences inside

each cell, and component groups. The coding is designed to properly capture these

three decision variables. A three-set coding scheme is used in this model. One set

to code the machine cells, one to code the machine sequences inside the cells, and

the other to code the component groups. A set of real numbers, strictly integers,

are used to code the sets.

Figure 5 shows a sample chromosome that represents the machine cells. In this

chromosome, the position of each bit represents the machines and its value cor-

responds to the cell number to which the machine belongs. The total number of positions is equal to the number of machines available. The shaded chromosome

shown in Fig. 5 corresponds to a 6-machine, 2-cell scenario with machines 1, 3, 4,

and 6 placed in cell 1, and machines 2 and 5 placed in cell 2. This set is formed

randomly by generating values between 1 and the number of cells. A subroutine is

used to check and remove empty cells, if present.

The second coding corresponds to the machine sequence inside the cells. Figure 5

shows a sample chromosome representing the machine sequences. The number of

bits corresponds to the number of machines and the value of these digits pro-

vides the sequence of machines inside each cells. However, the interpretation of this chromosome requires knowledge on the machine cell chromosomes. Figure 6

illustrates the decoding of the machine sequences chromosome in conjunction with

the machine cells chromosome.

The decoding (interpretation) of the machine sequence chromosome is done in

two steps. In the first step, the machines are rearranged according to the cells they

belong to, as well as their machine sequence values. In Fig. 6, machines 1, 3, 4,

and 6 which belong to cell 1, are grouped together, as well as their corresponding

machine sequence values 1, 5, 2, and 6. Afterward, each cell has one set of machines

and sequences associated with it. In stage two, the machine sequence values in acell are arranged in ascending order, and thus, the machines are too. This machine

arrangement, interpreted in the ascending order, gives machine sequence inside each

cell. In Fig. 6, machine sequence numbers 1, 5, 2, and 6 in cell 1 are arranged in

ascending order as 1, 2, 5 and 6. Hence, machines are rearranged as 1, 4, 3 and 6,

Machines 1 2 3 4 5 6

1 4 5 2 3 6MachineSequence




1 2 3 4 5 6

1 2 1 1 2 1

1 4 5 2 3 6

Machines (Stage 1) 1 3 4 6 2 5

1 1 1 1 2 2

1 5 2 6 4 3

Machines (Stage 2) 1 4 3 6 5 2

1 1 1 1 2 2

1 2 5 6 3 4

1 4 3 6 5 2

Machines

Cells

MachineSequence

Cells

Grouped

Corresponding

Sequence

Cells

Grouped

Sequence inAscendingOrder

Final MachineSequence

Cell 1 Cell 2

Fig. 6. Decoding of machine sequence chromosome.

which corresponds to the sequence of machines inside the cell 1. Similarly, the

sequence of machines inside cell 2 is 5 and 2.

The coding scheme used for component grouping is very similar to the one

defined for the machine cells. The only difference being that the total num-




4.2. Fitness function design for the GAM

The GAM’s main objective is to minimize the overall cost, which is the sum of the material handling and penalty costs as defined previously. The total material

handling cost consists of the inter-cell cost, the intra-cell cost, and the backtracking

cost. The penalty cost is made out of the setup and processing costs. The fitness

function in the GAM corresponds to the overall cost. The heuristic designed (Fig. 1)

is used to calculate the fitness function. The fitness function values are computed for

every member of the population, and these values are used to perform the selection

operation.

4.3. Selection of mating chromosomes for the GAM

A selection operator exploits the information available about the fitness of each

chromosome, and it is responsible for propagating good chromosomes thorough the

subsequent generations. The most widely used selection operators are the roulette-

wheel selection and the tournament selection.18 Roulette-wheel selection is best

suited for maximization problems. Tournament selection is easier to apply and

more efficient than roulette-wheel selection for minimization problems. Since the

problem at hand involves minimization of the overall cost, tournament selection

was chosen.In tournament selection, four chromosomes are chosen at random from the

machine cell population. Each of these four chromosomes has an overall cost

associated with it. A tournament is conducted among the four chromosomes to

detect the one with the least overall cost. The chromosome corresponding to the

minimum overall cost is copied to the subsequent generation.18 This process is

repeated as many times as the population size to obtain a set of machine cells. Sim-

ilar tournament selection is conducted to obtain a population of machine sequences,

and component groups.

4.4. Crossover operator design for the GAM

Genetic Algorithms are mainly driven by the crossover operator. The crossover

operator is responsible for effective exploration of the solution space, and hence, it

is applied with a high probability. Crossover is complicated in the case of the GAM

since three crossover operators need to be applied: one for the machine cell pop-

ulation, one for the machine sequence population, and another for the component

group population.

A single point crossover was designed for the machine cell population.18 In

it, two chromosomes are selected at random from the machine cell population. Acrossover position, between 1 and the number of machines, is randomly selected,

d li d t th t h Th t il l th f th h ft




procedure is implemented to check for empty cells every time the crossover operation

is implemented. If an empty cell is detected, the chromosome is removed, and

the crossover operator is applied again to generate a valid chromosome. The same

crossover operator with a similar checking procedure is applied for the component

population.

For the machine sequence population, a crossover operator called Partially

Matched Crossover (PMX) is applied. This operator ensures that the continuity

of number sequence is maintained. In this PMX, two chromosomes are randomly

selected for crossover, and two crossover sites are picked at random along the length

of the strings. A matching section is formed between the two crossover sites, and a

position-by-position exchange is executed to perform the crossover operation along

the matching section. PMX crossover is illustrated in Fig. 7. In this position wise

exchange, 5 from chromosome 1 is exchanged with 2 of chromosome 2. To avoid

repetition of sequence numbers, 5 also replaces 2 in chromosome 1. In this way,

PMX crossover is carried out between each position in the matching zone. The

probability of applying these crossover operators dictates the effectiveness of the

GA under consideration. A crossover probability of 0.8 was found to be effective in

most of the problems.

4.5. Mutation operator design for the GAM

A mutation operator, even though applied sparingly in a GA, induces fresh genetic

material, and hence, aids in the effective exploration of the solution space.18 As in

the case of crossover, three mutation operators were designed in the GAM: a muta-

tion operator for the machine cell population, a mutation operator for the machine

sequence population, and a mutation operator for the component group popula-

tion. In the GAM, a simple exchange mutation operator is applied in all the three

cases. This operator ensures that only valid offspring are generated. In the simple

exchange mutation, two bits of a chromosome are chosen randomly, and the posi-

tions of the bits are exchanged. The same mutation operator is applied for machinesequence and component group populations. While applying this to the machine

sequence population, care needs to be taken to ensure that corresponding machines

Before Crossover

9 8 4 5 6 7 1 3 2 108 7 1 2 3 10 9 5 4 6

After Crossover

9 8 4 2 3 10 1 6 5 7

8 10 1 5 6 7 9 2 4 3




are also exchanged along with their sequences. The probability of mutation usually

is kept very low, and in the GAM, a probability of mutation of 0.001 was found to

be effective.

4.6. Termination condition for the GAM

The termination condition for a GA is usually specified as a pre-established number

of generations. If the number of generations is less, the solution obtained might be

suboptimal, and if larger than necessary, significant amount of computation time

would have been wasted. In the GAM, a run of 5000 generations was found effective

to obtain satisfactory solutions. The number of generations can be modified by

the user.

5. Model Validation

For validating the GAM, several examples from the literature were used. The results

obtained from one such example are discussed here. The problem under considera-

tion is a 10 — machine, 16 — component problem.19 Figure 8 shows the sequence

matrix of this problem. This defines the sequence of operations followed by each

component. For example, component 1 is processed in machine 3 first, then in

machine 10, and finally in machine 2.

The 3-cell solution generated by the conventional methods, which do not take

into account any of the production data discussed before, is shown in Fig. 9. Accord-

ing to the solution, the designed cell accounts for one inter-cell movement as part 15

moves from machine 5 to 8. The number of voids, number of zeros, in the main diag-

onal is 16. The resulting grouping efficacy20 is 68.51%.

Figure 10 shows the inputs used for the GAM, and Fig. 11 displays the solution

generated by the GAM. Figure 12 shows the machine arrangements inside each

MC1 MC2 MC3 MC4 MC5 MC6 MC7 MC8 MC9 MC10

PR1 3 1 2PR2 1 2

PR3 1 3 2

PR4 1 2

PR5 1 3 2

PR6 2 1

PR7 1 2

PR8 1 2

PR9 2 1

PR10 3 1 2

PR11 1 2

PR12 2 1

PR13 1 2PR14 1 2

PR15 1 2 3




MC10 MC3 MC6 MC2 MC5 MC4 MC1 MC8 MC7 MC9PR1 3 1 0 2

PR7 0 1 2 0PR5 2 1 3 0

PR3 0 3 2 1

PR6 0 0 1 2

PR4 2 0 1

PR9 0 1 2

PR16 3 1 2

PR2 2 1 0

PR11 0 2 1

PR15 2 1 0 3

PR13 2 1 0PR8 1 0 2

PR12 0 2 1

PR10 1 3 2

PR14 0 1 2

Fig. 9. Reported 10-machine 16-component problem solution.

Process Time Matrix (Minutes)

MC1 MC2 MC3 MC4 MC5 MC6 MC7 MC8 MC9 MC10

PR1 3 4 5

PR2 5 6

PR3 7 4 3

PR4 8 3

PR5 2 4 3

PR6 2 2

PR7 3 2

PR8 8 7

PR9 3 4

PR10 7 2 2

PR11 2 4

PR12 3 3

PR13 2 3

PR14 2 2

PR15 3 7 4

PR16 4 2 3

Production Volume

{100, 50, 150, 250, 600, 400, 200, 75, 300, 250, 50, 100, 500, 250, 150, 100}

Setup Time in Each Machine (Minutes)

{0, 60, 75, 100, 80, 45, 70, 120, 75, 100, 45,}

Machine Rate per Hour ($/Hr)

{25, 20, 15, 30, 35, 25, 40, 45, 20, 25}

Material Handling Cost per Unit

Inter-Cell Material Handling Cost per Unit = $ 5.00Intra-Cell Material Handling Cost per Unit = $1.00




MC3 MC10 MC6 MC2 MC8 MC7 MC9 MC4 MC1 MC5PR1 1 2 0 3

PR3 3 0 2 1PR5 1 2 3 0PR6 0 0 1 2

PR7 1 0 2 0

PR8 1 0 2

PR10 1 2 3

PR12 0 2 1

PR13 2 1 0

PR14 0 1 2

PR2 1 0 2

PR4 0 1 2

PR9 1 2 0

PR11 2 1 0PR15 3 1 0 2

PR16 1 2 3

Fig. 11. Solution generated by the GAM.

M/c3

M/c10

M/c6

M/c2

M/c8

M/c7

M/c9

M/c4

M/c5

M/c1

Cell 1 Cell 2

Cell 3

Fig. 12. Cell configurations generated by the GAM.

cell as generated by the GAM. As far as the machine cells and the component

groups are concerned, the solution generated by the GAM is the same as that

generated by the conventional method. The number of inter-cell moves is 1 due

to part movement from machine 5 to 8; and the number of voids inside the main

diagonal is unchanged from the conventional- method solution at 16, resulting in

the same grouping efficacy of 68.51%.

However, the effect of intra-cell, backtracking, and machine skipping costs, andthe consideration of machine sequences inside the cells is evident in the difference

b t th ll t i d b th t th d T bl 2 i th i




Table 2. Comparison of conventional method versus GAM.

Sl. No. Description Conventional Method’s Results GAM ResultInputs

1 Number of machines 10 102 Number of components 16 163 Number of cells 3 34 Inter-cell cost per unit($) 5 55 Intra-cell cost per unit ($) 1 26 Backtracking cost per unit ($) 2 27 Crossover rate — 0.88 Mutation rate — 0.0019 Number of generations — 10000

10 Population size — 50

Results11 Number of inter-cell movements 1 112 Number of voids 16 1613 Number of backtracking moves 12 414 Number of machine skipping 7 615 Total inter-cell cost ($) 750 75016 Total intra-cell cost ($) 3300 435017 Total backtracking cost ($) 5500 270018 Total penalty cost ($) 506.25 506.2519 Overall cost ($) 10056.25 8306.25

as well as the number of machine skippings from 7 to 6. This reduction is reflectedin the reduction of the overall cost from $10,056.25 to $8,306.25. Even though

there is no change in the machine cells formed by the conventional method and the

GAM, the reduction in the overall cost justifies the superiority of the GAM over

the conventional methods. It can be concluded that this difference in the overall

cost is not considerable enough to bring about changes in the machine cells formed.

However, a significant difference in the overall cost would make a marked change

in the machine cells formed. As the GAM captures all the costs effectively, it is

expected to provide better results than the existing methods as the problem size

and complexity increases.The number of generations to arrive at this result was approximately 2000.

Data on the number of generations is required to assess whether the number of

generations chosen are sufficient enough for the GAM to reach the optimal/near-

optimal solution. In this case, the number of generations chosen was 10 000, which

was more than sufficient for the GA to arrive at the optimal solution.

6. Conclusions

The GAM has several advantages over the existing methods. In the GAM, theconsideration of the machine sequences at the cell design stage itself gives a more

li ti ti t f th t i l h dli t M t f th i ti th d




Also, most of the existing cell formation techniques do not consider the effects of

backtracking and machine skipping in arriving at the material handling costs. Many

of them just consider the inter-cell costs alone. The GAM, however, considers all

the elements of the material handling costs in the right magnitude. Moreover, the

methods developed earlier involved stages of complex computations. The GAM,

on the other hand, is a one-step method that is computationally less tedious, and

provides effective solutions in minimal time.

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