CHAPTER 2

DESIGN OF CELLULAR MANUFACTURING

SYSTEMS - A LITERATURE REVIEW1

Machine-component cell formation and its related issues have

been investigated over the last three decades. Several research papers

on cell formation have appeared in various journals. The following

methods have been proposed by different authors

1. Part characteristics approach to part family formation

2 . Evaluative methods

3. Array sorting or Analytical methods

4. Graph theoretic approach

5. Mathematical programming

6. Fuzzy clustering approach

7. Pattern recognition methods, knowledge-based and

Al-based techniques

8. Cluster analysis - Hierarchical clustering

9. Cluster analysis - Nonhierarchical clustering

10. Search methods

1 1 . Heuristics and other methods.

* A paper entitled, "Design of cellular manufacturing systems - a literature review" based in this part of the research work was presented in the International Conference on Operations Managamant for Global Economy: Chal bnges and Prospact., Indian Institute of Technology, New Delhi and Production and Operations Management Society (II.S.A), held at ZIT New DcUIi, December 21-24,

1999.

This chapter reviews the literature on the design of cellular

manufacturing systems.

2.2 METHODS OF QROUPmG MACHINES AllD COMPOIIEmS

2.2.1 Part Characteristics Approach t o Part Family Formation.

This method of group formation uses part characteristics such a s

shape, machining operation, dimension, material, accuracy, and shape

of raw material to identify part families. Known a s part coding and

classification analysis (PCA), the approach uses a coding system to

assign numerical weights to part characteristics and identifies part

families using some classification scheme. Component families and

machine cells are also formed using the same code. In the design office,

the code will be useful in retrieving earlier designs of similar form. The

problem of design retrieval is tackled by allocating a code number

through a classification system which covers the important design

features of the parts. Drawings having similar code numbers are filed

together. Designers, after deciding on the general features of a new

component, can locate parts which are similar. Existing parts can be

used, with minor alterations, if necessary.

Kusiak (1985) developed a p-median formulation, a mathematical

model, applied to parts grouping. Since, this mathematical model can't

be applied to large size problems, he has developed 'Rank Energy

Algorithm" for parts grouping. Also, he h a s conducted a detailed

experiment to test the computational efficiency of the Rank Energy

Algorithm.

Offodile (1991) developed a similarity coefficient method for Part

Coding and Classification Analysis (PCA) which is used a s a tool in

group technology. In the first place, the author uses single linkage

cluster analysis (McAuley 1972) for establishing classification of parts

based on parts' attributes. Apart from grouping resident parts and

materials, the best use for the approach presented by him is in the

classification of new part orders received from customers. Whenever

a n order i s received, it i s conveniently coded from customer

specifications. This code can then be used to recompute the similarity

coefficient between the new part and those already in the data base.

Next, based on the threshold value the new part is added to the

appropriate group.

Tatikonda and Wemmerlov (1992) have reported the results from

an empirical study of classification and coding system usage among

manufac ture rs . The invest igat ions, selection, just i f icat ion,

implementation and operation of classification and coding systems by

six user firms are presented in a case study form. A case history of a

classification and coding system user is also presented. User

characteristics and experiences are compared and analysed across the

seven cases.

These systems of classification and coding lack flexibility and

cannot adjust themselves to the changes in the product profile over the

years. The systems cannot identify parts uniquely. Most coding systems

are proprietary in nature.

2.2.2 Evaluative Methods

2.2.2.1 Production Flow Analysis (PFA)

Production flow analysis (PFA) (Burbidge 1989) is a technique for

finding both GT groups and their associated "families" by analyzing

the information in component process routes which show the operations

needed to make each part and the machines to be used for each

operation.

PFA is a technique for simplifying material flow systems. PFA

consists of five sub-techniques used progressively to simplify that

material flow system in an enterprise.

Company flow analysis (CFA): This analyzes the existing flow of

materials between the different factories in a large company and develops

a new, simpler and therefore more efficient system in which each factory

completes all the parts it makes.

Factory flow analysis (FFA): This analysis studies each factory

in turn. It plans the division of the factory into major groups or

departments each of which completes all the parts it makes, and it

plans a simple unidirectional flow system joining these departments.

Group analysis (GA): This analysis uses matrix resolution to divide

each department in turn into groups, each of which completes all the

parts it makes. Providing that one starts with departments which

complete parts, GA can, inside certain limits of group size, and with

very few exceptional parts, always find groups which complete parts,

with no backflow, no crossflow (between groups) and no need to buy

any additional equipment.

Line analysis (LA): This analyses the flow of materials between

the machines in each group to find the information needed for plant

layout.

Tooling analysis (TA): The final technique returns to matrix

resolution - in this case matrices of parts and the tools they use. It

studies each machine in each group in turn, in order to find 'tooling

families" of parts which can all be made on the machine with the same

set of tools a t the same setup and also to find the sequence of loading

which will minimize setup times.

PFA is descriptive in nature involving the use ofjudgement at almost

every stage and suffers from a lack of a clear-cut methodology.

2.2.2.2 Component Flow Analysis

El-Essawy and Torrance (1972) developed component flow

analysis a s a method to form part families by analyzing component

details and their flows. It consists of the following steps to form cells:

1. Find all the combinations of a machine type used for making

components and list the components using each

combination.

2. Group these combinations using similar machines to

form rough groups.

3. Analyze the sequence of machine-type usage for all the

components in each group and determine the load imposed

by each sequence on every machine.

4. Determine the number of machines to be installed in each

group.

The authors did not give any meaningful details of how the analysis

was to be done. Many production engineers find no difference

between component flow analysis and Burbidge's production flow

analysis.

2.2.3 Array Sorting or Analytical Method

The array-based methods concentrate on rearranging the rows and

columns of the machine-component incidence matrix such that the

'1's are brought together. Each block of '1's constitutes a part family

and a machine cell.

McCormick et al. (1972) described a cluster-analysis method, the

bond energy algorithm (McCormick et al. 1969). The bond energy

algorithm (BEA) operates upon a raw input object-object or object-

attribute data array by permuting its rows and columns in order to

find informative variable groups and their interrelations. The authors

described the BEA and illustrated it's use through several examples for

both problem decomposition and data reorganization. The groups are

arrived at by permuting the rows and columns of a n input data array

in such a way a s to push the numerically larger array elements

together. The measure of effectiveness used in the bond energy

algorithm was devised so that an array that possesses dense clumps of

numerically large elements will have a large measure of effectivene~s

when compared to the same array whose rows and columns have been

permuted so that its numerically large elements are more uniformly

distributed throughout the array. The only requirement is that the

array elements be nonnegative. In the case of a zero-one machine-

component incidence matrix, the maximization of the measure of

effectiveness will lead to block-diagonal form. The BEA, a sequential-

selection suboptimal algorithm, which exploits the nearest neighbour

feature, and is believed to be much faster and just a s satisfactory (in

the sense of achieving near optimal arrangements) a s the published

approximate QAP (quadratic assignment problem) algorithms, has been

developed and used successfully to determine array orderings

corresponding to local optima of the measure of effectiveness. The

clustering technique requires no prejudices about the number or size

of the groups. For BEA, the input variables can be listed in any order.

The BEA may be applied to any similarity array where swift

decomposition of blocks consisting of interacting variables is desired.

King (1980) proposed an algorithm known a s rank order clustering

(ROC) algorithm for the formation of machine-component groups. A

relaxation and regrouping procedure (decomposition and recomposition

procedure) was developed whereby the basic rank order clustering

method may be extended to the case where there are bottleneck

machines which process relatively large number of components. The

detailed group analysis, described by Burbidge (1973) is the focus of

attention of his research work. The author reviews in detail the single

linkage cluster analysis (McAuley 1972) and also the bond energy

algorithm (McCormick et al. 1972). The ROC algorithm rearranges rows

and columns in an iterative manner that will ultimately and in a finite

number of steps, produce a matrix in which both columns and rows

are arranged in order of decreasing value when read a s binary words.

The ROC procedure is iterative and it is possible to start with any

rearranged form of matrix. The ROC algorithm requires much less

computer time than the McCormick et al. technique (McCormick et al.

1972) and has a particular facility that can be exploited, to deal with

the practical problems of exceptional elements and/or bottleneck

machines. The single linkage cluster analysis which after, machine

grouping requires a secondary process of component allocation to the

machine groups but the ROC algorithm performs both together. The

author showed that the bond energy method is computationaly less

efficient when compared to the ROC algorithm.

King and Nakornchai (1982) provided a comprehensive review of

the various approaches that have been adopted to design machine-

component cells in Group Technology. The authors proposed a n

algorithm by name ROC2 together with a new relaxation procedure for

bottleneck machines which is an improved version of the ROC algorithm

(King 1980) and implemented the algorithm iteratively. The ROC2

algorithm performs row reordering and column reordering and quickly

arrives a t the final block diagonal form. The results of the ROC2

algorithm compares favourably with King's (1980) solution and

Burbidge's (1973) solution. The ROC2 approach does, however, require

human skill and judgement in its interactive operation. It is this

flexibility to experiment with alternatives that i s the essential

characteristic of the ROC2 approach and where it differs from most of

the other methods, which are rigidly geared to the generation of a

single definitive result.

Chandrasekharan and Rajagopalan (1986b) did extension work

on the well known rank order clustering (ROC) algorithm which was

developed by King (1980). The authors analysed the ROC method and

identified its main drawbacks. They proposed a method by name

MODROC (modified rank order clustering) which uses the ROC algorithm

in conjunction with a block and slice method for obtaining a set of

intersecting machine cells (which are called a s primary cells) and non-

intersecting part families. Then a hierarchical clustering method is

applied based on a measure of association (S..) among pairs of primary 'J

machine cells. Clustering is terminated when all the surviving cells are

non-intersecting or when a single group is formed. In the latter case,

the number of cells is determined on the basis of a suitable decision

criterion. I f the MODROC algorithm generates a hierarchy of solutions,

then it is left to the analyst to choose the level of hierarchy a t which the

grouping has to be implemented. The authors suggested that this could

be done by choosing one of the following a s the decision criterion:

(1) maximum and minimum number of machines in a cell, (2) number

of cells, and (3) a threshold value of Slj (a measure of association between

primary cells) a t which the clustering is terminated. The bottleneck

machines are those which appear in more than one cell a t the final

stage of choice. The authors demonstrated that the composition of the

primary cells remains more or less independent of the initial disposition

of the machine-component incidence matrix.

The disadvantage with the array-based methods is that they do

not give the best solution for problems which have exceptional elements

('1's lying outside the blocks). Even a few exceptions an enough to

completely misdirect the array-based procedures. However, array-based

methods are the fastest and the best when problems not involving

intercell movements are considered.

2.2.4 Gmph Theoretic Approach

Graph theoretical methods treat the machines and components

a s nodes and the processing of components as arcs connecting these

nodes. These models aim at obtaining disconnected subgraphs from

the machine-component graph to identify part families and machine

cells.

Rajagopalan and Batra (1975) proposed a graph partitioning

approach for finding machine-component cells, Information derived from

the route cards of the components is analysed and the situation is

represented in the form of a graph (machine graph) whose vertices

correspond to the machines and whose edges represent the relationships

created between the machines by the components using them. The total

number of different machine types in a cell is a constraint. For designing

a cellular system using graph theory, graph theory h a s been

conveniently divided into three phases. In the phase I, the authors use

the input data to derive a machine graph. The authors obtain the

machine-graph by including an edge i-j (i and j are pair of machines)

only if the Jaccard's similarity coefficient for the machine pair is greater

than a specified threshold value, T. The authors then use graph theory

for recognizing in this machine graph certain groups of vertices strongly

related to each other (ie cliques are identified). The Bron Kerboseh

algorithm (Mulligan 1971) has been used in this research work for

finding the cliques. In phase 11, the authors start with these p u p s ,

draw a move graph taking into consideration of intercell moves and

proceed to form the cells using a graph partitioning approach. In this

research work, the Kernighan-Lin approach (Kemighan and Lin 1970)

( a heuristic graph partitioning approach) h a s been used (with

modifications to take care of the upper bound on cell size) to partition

the move graph. In the final phase, phase 111, the authors allocate the

components to the cells, calculate the intercell moves, find the machine

loads and hence the number of machines of a particular type required

in a cell. In this work, the authors have assumed that any movement

within a cell (intracell move) costs little or nothing by way of time and

effort. This assumption is not a practically valid assumption in a large

company.

De Witte (1980) proposed a method for designing cell systems,

which is based on the use of similarity coefficients, taking into account

that some machine types can be allocated to several cells. Three

similarity coefficients are introduced: one based on the absolute

interdependence between machines types, the second based on relative

m u t u a l interdependence, and the third on relative single

interdependence. Clustering of machine types is done based on the

similarity coefficients or combinations, using the 'graph-theoretic

approach' introduced by Rajagopalan and Batra (1975). The proposed

methodology contains four steps: (1) gathering information, (2) analysis

of relations between machine types and allocation of machine types to

cells, (3) allocation of components to cells, and (4) counting the workload

for each machine type in each cell, and allocation of the requisite

number of machines to cells. Using the method proposed above it is

possible to analyse a great number of routeings and machine types.

The proposed method can be used, even if the relations between

machine types are fuzzy.

Vohra et al. (1990) presented a non-heuristic network approach

to form manufacturing cells with minimum intercellular interactions.

The machines and part types are represented a s the nodes and the

machining operations by the arcs. The network will have every machine

node connected to only part nodes, and vice versa. The weight of an

arc connecting a part node to a machine node represents the machining

time of tha t part type which i s required to be operated on the

corresponding machine. The partitioning which aims a t minimizing

intercellular movements is equivalent to the partitioning of the network

with a minimum cut. The network is subsequently partitioned by using

a modified Gomory-Hu algorithm (Gomory and Hu 1971) to find a

minimum intercellular interaction. The modified algorithm improves

the computational efficiency when compared to the Gomory-Hu

algorithm. The degrees of interaction between cells (or the noise level)

can be quantified by evaluating the amount or percentage of the total

available machining time that is performed in the non-host cells (or

outside the parent cells). The authors claim that minimization of the

noise level in the proposed algorithm gives it a decisive advantage over

all the existing heuristic algorithms available till the publication of this

paper which do not always satisfy the optimality condition. The

sequential formation of cells facilitates the possibility of controlling the

number of cells to be formed or the degrees of intercellular movement.

Vannelli and Hall (1993) developed a new Eigenvector approach

for generating disconnected part families and machine cells.

Disconnected part families are generated while minimizing the extra

cost of purchasing new equipment; disconnected machine cells are 68

produced by subcontracting parts to reliable vendors. In both cases, a

new bounding procedure is utilized to find the lower bounds on these

costs.

Srinivasan (1994) has introduced the concept of minimum spanning

tree for Group Technology applications. The minimum spanning tree

for machines is constructed from which seeds to cluster components

are generated. The process of alternate seed generation and clustering

is continued until feasible solutions are obtained. Edges are removed

from the minimum spanning tree to identify alternate starting seeds

for clustering.

Hadley (1996) developed a new technique for finding economically

attractive disconnected part-machine families in cellular manufacturing

environments. This technique is based on modelling the problem a s a

graph partitioning problem and it exploits the recent advances in the

area of graph approximations. This work is an extension of the earlier

work done by Vannelli and Hall (1993).

2.2.5 Mathematical Prognmming

The mathematical programming approaches optimize the cell-

design problem in cellular manufacturing systems. These approaches

state the cell-design problem mathematically using an objective function

and constraints. The objective may be to maximize or minimize the

variables. (The variables may be sum of the similarities between

machines or components, cost of intercell moves etc).

Purcheck (1975) developed a mathematical classification a s an

essential tool for the systematic analysis of process routes or

engineering drawings and the combinatorial synthesis of their

information and also tested the mathematical classification which

overcomes the shortcomings of conventional methods of workpiece

classification and workflow analysis. The Cranfield method facilitates

the construction of a combinatorial programming model. A hand-

method of solution has been developed which may be used to program

a computer.

Kusiak (1987) presented a generalized approach to GT. In this

approach for one part a number of process plans are generated. This

approach results in an improved quality of process (part) families and

machine cells. The two integer programming models developed by him

provide more convenient representation of the clustering problem than

the matrix model. This is of particular significance for models with

large numbers of rows and columns.

Choobineh (1988) proposed a two-stage design procedure for finding

the part families and cells. The stage one attempts to uncover the natural

part families by using a clustering algorithm which utilizes a special

proximity measure proposed by him. This proximity measure uses the

parts' operations and the operations' sequences. The second stage of

the proposed procedure is a linear integer programming model which

considers the economics of production in cell formation. It identifies

the type and the number of machines in each cell and the assignment

of the part families to the cells. The optimization model takes into

account the facts that some operations could be done on more than

one machine, the demand of the parts, the capacity on each machine,

and the amount of money available for investment.

Co and Araar (1988) presented a three-stage procedure for BO

configuring machines into manufacturing cells, and assigning the cells

to process specific sets of jobs. First, operations are assigned to

machines, with the objective of maximizing the utilization of the

machines by minimizing the deviation between assigned workload and

available capacity. Then, they extended King's algorithm (The rank

order cluster (ROC) algorithm developed by King (1979)) for cluster

analysis. The extended algorithm is used to arrange machines according

to similarities of operations. Finally, they applied a direct-search

algorithm for finding the size and composition of the cells, from the

results of the extended King's algorithm.

Gunasingh and Lashkari (1989a) formulated a 0-1 integer

programming model to solve the problem of machine group formation.

The model takes into account the physical constraints of the system

such a s the restriction on the number of machine groups and the

number of available machines of each type. The objective function of

the model is formulated in order to maximize the sum of the similarity

indices of all the machines in all machine groups with their respective

group medians. The problem of allocating parts to machine groups is

formulated a s a special case of the generalized assignment model. The

principal assumption here is that, in cellular manufacturing systems,

each operation of a part may not be restricted to only one machine,

and may in fact be performed on alternate machines. The objective

function of the model is formulated in order to maximize the sum of the

compatibility indices of all the parts allocated to all the machine groups.

Gunasingh and Lashkari (1989b) proposed a grouping method

which groups the machines on the basis of their capabilities to process

the parts under consideration. The machine capabilities are expressed

in terms of the tool availabilities on each machine. Two compatibility

indices are developed to define the 'compatjbility" of a machine with a

part. The first compatibility index is based on the tooling requirements

of the parts and the second compatibility index is based on the tooling

needs and the processing times. Then, two 0-1 integer programming

formulations of the machine grouping problems are developed. The

formulations assume that the part families are known. The first

formulation groups the parts and machines in such a way that the

sum of the compatibility indices of the machines and the parts in all

the groups is maximized. The second formulation seeks a trade-off

between the cost of duplicating the machines and the cost of intercell

movement. The number of machines in a cell and the number of

machines available of a particular type are considered a s constraints.

Shtub (1989) has shown that the simple cell-formation problem is

equivalent to the Generalized Assignment Problem. He has also shown

that the general case of cell formation, in which several process plans

are considered for each part type, is also equivalent to the Generalized

Assignment Problem

Srinivasan et al. (1990) proposed an assignment model to solve

the grouping problem. A similarity coefficient matrix is used a s the

input to the assignment problem and solve it for the objective of

maximization. Closed loops in the form of subtours are identified after

solving the problem and are used a s the basis for grouping machines.

Then part families are identified. The proposed procedure finally results

in machine cells and the corresponding part families.

Al-Qattan (1990) proposed a method which employs network

analysis to form the machine cells and family of parts. The method is

based on branching from seed machine and bounding on a completed

part. The seed machine represents the starting node for the network

system. Selecting the seed machine with the smallest number of jobs

will help to reduce the size of the network tree and obtain more

alternative solutions. The machines which have twice or more jobs

than the average number of jobs per machine will be considered a s

candidates for duplication. This method creates a number of alternative

solutions and provides an opportunity to evaluate different options

and to select the one which is economical.

Logendran (1990) proposed a model for machine-component cell

formation which is based primarily on machine workload. The total

moves determined a s a weighted sum of both total intercell moves and

total intracell moves is used a s a suitable parameter/measure in the

model. He refers a machine type a s a workstation. All the algorithmic

steps associated with the model has been grouped into four phases. In

the first phase namely the cell representation phase, the workstation

that has the highest total workload per machine is chosen a s the first

key workstation. In this phase a partial set cover model a s proposed by

Francis and White (1974) is used to select the next representative

workstation. In the second phase namely the clustering phase, a

workstation is permanently admitted to the cell that resulted in the

minimum total moves. In the third phase namely the improvement

phase, he has shown that the total moves evaluated at the end of the

clustering phase can further be improved/reduced by admitting each

workstation to other cells in the presence of all of the other

workstations. In the last phase namely the assignment phase, a part

is assigned to a cell that contributes to the highest cumulative

processing time. 63

Ventura et al. (1990) presented an algorithm for grouping parts

and tools in flexible manufacturing systems. This problem is first

formulated a s a 0-1 linear integer program. This 0-1 linear integer

program formulation maximizes the total processing time in all the

groups which is equivalent to minimizing the interdependences among

the groups. The weighted sum of the off-block elements is minimized.

The formulation considers processing time, total number of groups

that need to be formed, the lower and upper bounds on the total

number of elements (both parts and tools) in each group. A Lagrangian

dual formulation is then developed to obtain an upper bound on the

optimal objective function value. The Lagrangian dual program is

further decomposed into a linear network subproblem and a set of

knapsack subproblems. A subgradient algorithm with several

enhancement strategies is employed to minimize the upper bound

obtained from the Lagrangian dual problem.

Nagi et al. (1990) proposed a cell formation algorithm which

considers multiple part routeings, multiple functionally similar

workcentres and projected production. They have suggested part

routeings which favour the division of the manufacturing system into

manufacturing cells in a way that minimizes part traffic, along with

satisfying the part demand and workcentre capacity constraints. They

have developed an algorithm which solves the two problems namely

routeing selection and cell formation. The objective function has been

formulated in order to minimize the total intercell traffic. They proposed

an iterative heuristic algorithm which consists of three main steps. In

the first step workcentres are divided into initial partitions randomly

and given a s input to the second step. In the second step a linear

programming problem is solved using the simplex method. The second

step results in the selection of routeings. The result of the second step

is given a s input to the third step which results in new manufacturing

cells. Second and third steps are repeated until convergence is achieved

and the final manufacturing cells are found out.

Rajamani et al. (1990) developed three integer programming models

to study successively the effect of alternative process plans and

simultaneous formation of part families and machine groups. Model I

assigns machines to parts and gives the part machine incidence matrix

which can be used for cell formation using one of the currently available

techniques. Model I1 assigns machines to known part families to form

cells. The part families so known are generally formed based on part

attributes. Model Ill identifies part families and machine groups

simultaneously. Additional information on number of cells to be formed

and maximum number of machines in a cell is needed for developing

the Model 111. All the models specify the process plan for each part,

machine type to perform each operation in the process plan selected

and the total number of machines required to process all the parts by

considering demand, time and resource constraints. The objective

function of the models is to minimize capital investment.

Wei and Gaither (1990) developed and evaluated a multiobjective

heuristic model to solve cell formation problems. The heuristic is an

extension of Kumar and Vannelli's (1987) work. Also, a n optimal

procedure (a 0-1 linear integer programming enumeration scheme)

has been developed to serve a s a standard against which the heuristic

is measured. Both the heuristic and the optimal procedures require

these inputs: the part-machine matrix with machine standards,

demand forecasts, machine capacities, the number of desired cells,

and the maximum number of machines in a cell. The four objective

functions are a s follows: (1) minimize the bottleneck cost, (2) maximize

the average cell utilization, (3) minimize intracell load imbalances,

and (4) minimize intercell load imbalances. Both the heuristic and the

optimal procedures in this study seek to maximize a weighted additive

utility function comprised of the above four objectives. Unlike the

optimal model which searches all possible solutions, the heuristic forces

a part to be produced outside a cell once the inclusion of the part

causes an overloading in a machine. This practice assigns the parts to

the cells on a first-come-first-serve basis until a machine is overloaded.

I t is this approach that causes the heuristic to be suboptimal. A full

factorial experimental design has been used to evaluate the effects of

environmental factors on the performance of the ht-uristic model.

Boctor (1991) proposed a linear zero-one formulation to design

machine-part groups. The author also presented a simulated annealing

approach to solve large-scale machine-part cell formation problems.

The linear zero-one formulation allows the designer to control cell sizes.

It h a s been shown that most of the integrality conditions of this

formulation can be relaxed. This significantly improves the linear zero-

one formulation's computational efficiency and feasibility. The author

also proposed a heuristic to solve the cell formation problem in the

case of an N-cell partition where no exceptional elements exists. The

objective function of the zero-one linear formulation h a s been

formulated in order to minimize the number of exceptional elements

in the solution. The number of manufacturing cells is predefined. The

author solved the linear zero-one formulation and the simulated

annealing algorithm using 90 problems and found that the simulated

annealing algorithm results in optimal solution for 58 (64.4%) out of

the 90 solved problems. The author also concludes that the percentage

of optimal solutions can be increased by solving the test problems

several times with different sets of parameters.

Logendran (1991) proposed a model that includes two important

factors for determining optimal/near-optimal machine-part clusters

in cellular manufacturing. First, the model takes into consideration

the sequence of operations in evaluating the intercell and intracell

moves; and second, it includes the impact of the layout of cells in

evaluating the intercell moves. Two different layout patterns namely

the linear single row cellular layout and the linear double-row cellular

layout, were considered. The total move is computed a s a weighted

sum of both intercell and intracell moves, and is used a s a suitable

measure to evaluate the performance of the model. Another measure

incorporated in the model is the utilization of a workstation and a

targeted minimum value of 50% utilization was used for each machine

in a workstation. An efficient solution algorithm for this model was

developed and implemented. The algorithm consists of four phases:

( I ) key workstations identification phase, (2) initial clustering phase,

(3) improvement phase, and (4) parts assignment phase. The solution

algorithm considers number of workstations, number of parts, capacity

of each machine, minimum and maximum no of cells, number of

operations on each part, processing time, number of machines in each

work station.

Gunasingh and Lashkari (1991) proposed two non-linear 0-1

integer programming formulations to design machine-part groups. The

methodology presented by them forms machine-part groups based on

the processing requirements of the parts and machine capabilities.

The processing requirements of the parts are related to their tooling

needs, and the machine capabilities are expressed in terms of the tool

availabilities on each machine. Indices have been developed to define

the compatibility of a machine with a part in terms of the tooling

requirements of the parts, toolings available on the machine, and the

processing times. The objective of the first model is to group the parts

and machines in such a way that the sum of the compatibility indices

of machines and parts in all groups is maximized. The objective of the

second model is to form the groups while seeking a trade-off between

the cost of duplicating machines and the cost of intercell movements.

These formulations take into account the physical constraints on the

system such as , limitations on the number of machines and parts in a

group, the number of groups, and the available number of machines of

each type.

Shafer and Rogers (199 1) proposed three goal programming models

corresponding to three unique situations: (1) setting up an entirely

new system and purchasing all new equipment, (2) reorganizing the

system using only existing equipment, and (3) reorganizing the system

using existing equipment and some new equipment. However, because

of the large number of O/ 1 variables contained in the goal programming

formulations they are very difficult to solve for large-sized problems.

Hence, the authors have developed a heuristic solution procedure. The

heuristic solution procedure involved partitioning the goal programming

formulations to two subproblems and solving them in successive stages.

The goal programming formulations have been developed such a way

to minimize setup times, intercellular movements, investments in new

equipment and maintain acceptable utilization levels. In the Model 2,

since only existing equipment is used, the goal associated with funds

available to purchase new equipments is not needed. The formulations

identifies part families and machine cells. The formulations consider

machine capacity, available funds, cell size limits and sequence

dependent setups. The objective function of stage 1 of the heuristic

procedure has been formulated in order to minimize machine costs.

This stage identifies part families and machine cells. In this stage

machine cost and capacity are considered. In stage 2, a model proposed

by Foo and Wager (1983) is solved for each part family defined in stagel.

The objective function is for minimizing the total setup time associated

with processing all parts in the family. This stage 2 considers sequence

dependent setups. The limitation of the heuristic procedure is that

machine capacity being determined on an aggregate basis and not on a

cell by cell basis.

Shafer et al. (1992) presented a mathematical programming model

that deals with exceptional elements. An initial solution is developed

using any of the numerous cell formation procedures. Any exceptional

element that can be eliminated by changing the design or the process

plans of the parts are eliminated. Then, the mathematical programming

model is solved to determine how best to deal with the remaining

exceptional elements. The mathematical programming model considers

three important costs: (1) intercellular transfer costs, (2) machine

duplication costs, and (3) subcontracting costs. The mathematical

programming model has been formulated in order to minimize the

above three types of costs associated with exceptional elements. The

model considers annual forecasted demand, machine capacity and

processing time. The model presented is compatible with all cell

formation procedures. The model is an optimizing model that can

recognize possibly advantageous mixed strategies ignored by previous

approaches.

Rajamani et al. (1992) developed a mixed integer programming

model to solve the cell formation problem. The authors consider the

trade-off between saving on sequence dependent setup costs and

additional investment on new machines for determining the economic

number of cells. The model results in the optimal number of cells to

be formed and the optimal sequence in which the parts are to be

produced in each cell. If the manufacturing environment is not suited

for forming cells, then the model recommends a job shop or flow line,

whichever is best suited. The objective of the proposed mixed integer

programming model is to minimize the sum of total discounted cost of

machines assigned to all the cells, and setup costs incurred due to

sequence dependence of parts in each cell. The model considers

processing time, demand per period, discounted investment cost per

period of a particular machine type, the setup cost, the setup time

and the time available on each machine of a type per period. When

the problem size gets large with increase in part types, the proposed

model can be effectively used by aggregating the part types having

similar setups into fewer families.

Min and Shin (1993) addressed the issues relating to the

simultaneous formation of both machine and compatible human cells.

The au thors developed a multiple objective mixed-integer goal

programming model that enabled them to analyse the trade-off between

economic and behavioural benefits. The model has been formulated in

order to: (1) maximize the sum of similarities among machine and 70

human cells, (2) minimize the total machine processing times, (3)

match each operator's skill to parts a s closely a s possible, and (4)

minimize the total labour costs for cell operators. Considering the

computational difficulty, the authors proposed a sequential heuristic

(a two-stage heuristic procedure) which decomposes the problem into

two smaller subproblems. Stage 1 of the heuristic primarily allocates

parts to machines and then forms part families. After forming the cells

in stagel, stage 2 of the heuristic is run to assign operators (or Jobs)

to the given cells. The authors conclude that the proposed sequential

heuristic performs nearly a s well a s the full multiple objective mixed

integer goal programming model. The merits of the proposed mixed-

integer Archimedian goal programming model are a s follows: (1)

concurrent formation of machine and human cells, (2) multiple objective

nature, and (3) unlike the p-median model developed by Kusiak (1987),

this formulation specifies the optimal number of cells a s model output,

not a s model input (parameter).

Arvindh and Irani (1994) illustrated the need for a cell design

strategy that seeks to solve subproblems in cell design in a non-

sequential manner. They proposed a solution methodology, based on

an MIP formulation, for integrating machine grouping, part family

formation and machine duplication with layout design.

Liang and Taboun (1995) formulated a bicriterion nonlinear-integer

programming model in cellular manufacturing in order to achieve a

preferred compromise between flow-line efficiency and job-shop

flexibility. The number of part types accomodated into the focused

cells (No intercell movements are allowed between focused cells) is

employed a s a measure of system flexibility and the average system

similarity level is used a s a measure of system efficiency. Several

machines of the same type and machine cell size are considered. The

part types that are squeezed out of the focused cellular manufacturing

system are subcontracted. Dice similarity coefficient is employed in

this work. Number of cells is a natural output of the model. The authors

also proposed a heuristic algorithm, consisting of seeding, grouping,

and inserting modules, to solve the model.

Rajamani et a l . (1996) have developed a mixed integer

programming model for the design of cellular manufacturing systems.

The model identifies the part families and machine groups concurrently.

It also specifies the plans selected for each part, quantity to be produced

through the plans selected, machine type to perform each operation

and the total number of machines required. The production features

such a s time and costs, capacity of machines and cell sizes are

considered in the design process. A column generation scheme is

proposed to solve the relaxed linear programming model efficiently. The

branch and bound procedure with depth first strategy is used to solve

the integer programming model. It is well known that the depth first

strategy of the branch and bound procedure has the limitation of

exponential time complexity function, sometimes the technique may

take too much time to solve a large problem.

Though mathematical programming techniques can be used to

accurately formulate the cell-design problem, large combinatorial

problems can't be solved using the mathematical programming

techniques within a reasonable amount of time. Hence, heuristics

become necessary to solve such large combinatorial problems.

Assume that there are n parts and p machines to be grouped

into c part families and corresponding machine cells. Conventional

clustering methods implicitly assume that disjoint part families exist

in the data set; therefore, a part can only belong to one part family.

The classification results, thus, can be expressed a s a binary matrix.

But in many cases, part families are not completely disjoint; rather

the separation of part families is fuzzy. Consequently, the concept

of fuzzy subsets could offer an advantage over conventional clustering

and could allow a representation of the degree or grade of membership

of a part associated with each part family. In fuzzy clustering the

classification results can be expressed a s a matrix: the matrix elements

(x .) are not restricted to values of 0 or 1, ie., they can be fractional V

(between 0 and 1). Therefore, a part can belong to several part families

with different degrees of membership.

Xu and Wang (1989) have developed two different approaches of

fuzzy clustering analysis namely fuzzy classification and fuzzy

equivalence for part family formation. In addition, a dynamic part family

assignment procedure is presented using the methodology of fuzzy

pattern recognition to assign new parts to existing part families. In this

work the part family formation process is controlled by selecting either

a similarity parameter ( I ) or the desired number of part families. The

user can describe the features of the sample parts to be classified directly

from engineering drawings.

Chu and Hayya (1991) argued that in practice, it is clear that some

parts definitely belong to certain part families, whereas there exist parts

that may belong to more than one family. The authors proposed a f u q

C-means clustering algorithm to formulate the cell formation problem.

The proposed fuzzy approach offers a special advantage over

conventional clustering. It not only reveals the specific part family that

a part belongs to, but also provides the degree of membership of a part

associated with each part family. This information would allow users

flexibility in determining to which part family a part should be assigned

so that the workload balance among machine cells can be taken into

consideration. The authors have studied the impact of the model's

parameters on the clustering results. The proposed algorithm performed

quite well a s compared to an optimal integer programming procedure

(Chu and Lee 1990). The proposed fuzzy clustering procedure provides

information for parts or machines reallocation decisions. Also, the fuzzy

solution procedure seems insensitive to the existence of exceptional

elements, which resolves the problem of identifying and removing those

elements from a data set before reaching a final solution. While studying

the impact of the model parameters, the results indicated that the

desired number of part families or machine cells was the most sensitive

factor with respect to clustering effectiveness. If one under-represents

that number, the clustering results would always be inferior. Also, it is

necessary that a reasonable value of stopping criterion should be chosen

for better results. Furthermore, the selection of the degree of fuzziness

should be made with care, a s a large value may confound the analysis.

The authors concluded that they did experience the classification

problems when the desired number of part families was relatively large

(for example, 5), ie some parts were not classified into their appropriate

part families.

Gindy e t a l . (1995) proposed a new component grouping

methodology for cells formation. It is an extended version of the fuzzy

C-means clustering algorithm for component grouping with cluster

validation procedure for selection of optimum component partitions.

The validity measure (R) proposed by them is aimed a t component

grouping for cellular manufacturing applications where maximum

diversity between manufacturing cells i s considered of prime

importance. The validity measure has proved very useful in optimizing

component partitioning by forming component groups with the

maximum compactness of the components within groups and of

machining cells with a minimum number of repeated machines.

The degree of fuzziness has to be chosen with extreme care a s a

large value may confound the analysis. This is an inherent limitation of

fuzzy clustering methods.

2.2.7 Pattern Recognition Methods, Knowledge-band and AX-band

Techniques

Few researchers have shown the applicability of pattern recognition

methods based on artificial neural networks ( A N N ) for solving the part-

machine grouping problem. Neural network, a recent development in

artificial intelligence, is a distributed information processing system

composed of many simple computational elements (nodes) interacting

across weighted connections. Neural networks are analogous to the

working of the brain and the nervous system of human beings. These

networks can learn and adapt themselves to inputs from the actual

processes. They achieve good performance with high computation rate

using their massive parallel processing feature and their ability to

learn. Knowledge is internally represented by the values of the weights

and the topology of the connections. Learning involves modifying the

connection weights (Wasserman 1989). Neural networks have proved

effective a t solving problems in a wide variety of areas, such a s image

processing and speech recognition. It is also applied to group

technology problems.

Kusiak (1988) formulated the problem of grouping machines and

parts in automated manufacturing systems. The formulation is based

on the matrix of processing times. It involves four constraints which

consider availability of processing time at each machine, requirement

for material handling carriers and machines for each cell and

technological constraints. The author has developed a knowledge based

system (EXGT-S) to solve this problem. The EXGT-S comprises of a

heuristic algorithm and an expert system. The system exploits the

expertise of the problem solver.

Kaparthi and Suresh ( 1 992) developed a neural network clustering

method for the part-machine grouping problem in group technology.

The Carpenter-Grossberg neural network was selected because the

clustering method utilises binary valued inputs and it can be trained

without supervision. The algorithm was tested on three data sets from

prior literature and the solutions obtained were found to result in block

diagonal forms. This algorithm gives inferior result in the case of

imperfect data.

Venugopal and Narendran (1994) demonstrated the suitability of

neural network theory for solving the machine cell formation problem.

They have considered a competitive learning model, adaptive resonance

theory (ART) model and self-organizing feature map (SOFM) model.

Applications on trial problems showed the viability for solving the

machine cell formations problem. Also, they compared ART network

model and SOFM model with ZODIAC (Chandrasekharan and

Rajagopalan 1987) and showed that the competitive learning model

fares the best and is on par with ZODIAC. ART model comes a close

second while the SOFM model fares poorly in comparison with the

rest.

Suresh et 81. (1995) developed a hierarchical methodology for the

design of manufacturing cells which synthesizes the capabilities of

new pattern recognition methods for rapid clustering of large part-

machine data sets, with multi-objective optimization capabilities of

mathematical programming. This procedure includes three phases. In

phase 1, part families and associated machine types are identified

through neural network methods for pattern recognition. Phase 2 is a

cell formation phase that involves the assignment of part families and

individual machines to create independent cells. Phase 3 attempts to

minimize intercell traffic further for families that may still have to be

processed in more than one cell.

Kamal and Burke (1996) have developed a neural network based

clustering algorithm for group technology. This paper introduces the

FACT (Fuzzy Art with Add Clustering Technique) algorithm which is a

new neural network-based clustering technique. The FACT algorithm

can accept binary and continuous features of a part a s attributes of

the input data. This important feature enables FACT to cluster parts

based on their design and manufac tur ing character is t ics

simultaneously. FACT has five built-in performance measures which

provide required information for choosing the proper number of

clusters. Parts and machines are clustered simultaneously.

Artificial Neural Networks (ANN) a n primarily suited for and best

utilized in applications that are repetitive in nature. Since each cellular

manufacturing system problem is unique in its configuration, ANN

may require long training sessions and retraining for every new

machine-component incidence matrix and/or the setting of various

parameters by the analyst.

2.2.8 Cluster Analysis - Hierarchical Clustering

The identification of machines and part groups is similar to the

identification of 'clusters" in a scatter of data-points. Researchers have

applied cluster analysis in its varied form to the problem of forming

machine cells and component families.

Cluster analysis seeks to group data into clusters such that the

elements within a cluster are closely related while the clusters

themselves have little or no relationship amongst them. The major

c lasses of c lus te r ana lys i s a r e hierarchical c lus te r ing a n d

nonhierarchical clustering.

A hierarchical clustering method first computes the similarity or

dissimilarity between each pair of parts or machines. Some methods

used agglomerate philosophy while others use divisive philosophy for

clustering hierarchically. The hierarchical clustering algorithms generate

a hierarchy of feasible solutions each with a particular value of a

performance measure. The analyst chooses the best feasible solution

corresponding to the best value of the performance measure.

McAuley (1972) used the similarity coefficient proposed by Jaccard

(Sokal and Sneath 1968) in his work to group machines. The clustering

technique used in this work is called single linkage cluster analysis

and was developed by Sneath (Sokal and Sneath 1968). This method

first clusters together those machines mutually related with the highest

possible similarity coefficient, then it successively lowers the level of

admission by steps of predetermined equal magnitude. The main

disadvantage of this method is that while two clusters may be linked

by this technique on the basis of a single bond, many of the members

of the two clusters may be quite far removed from each other in terms

of similarity. The results of the cluster analysis is represented by a

dendogram. The data used was the machinelpart matrix. Two criteria

were used namely the number of inter-group journeys and intra-group

journey (the total distance moved by a component when it visits a

number of machines within one group). The best solution corresponds

to the solution which gives the minimum cost considering both intercell

movement cost and intracell movement cost.

Carrie (1973) describes the technique of numerical taxonomy and

shows how it may be applied to both cellular layout design and

functional layout design. The production flow analysis, a s presented

by Burbidge (1969b) is shown to be of limited value in practical cases

and an improved method is proposed. Effectiveness of minimal spanning

tree in functional layout design is explained. Numerical taxonomy

involves three stages:

(1) Prepare a data matrix. This indicates which characteristics

are either present or absent.

(2) Compute a similarity coefficient matrix. From the

information contained in the data matrix the similarity

between each pair of objects (machines or components) can

be evaluated. Similarity coefficient matrices are generated

for both components and machines separately. 79

(3) Perform cluster analysis. Cluster analysis examines the

similarity between each pair of objects and forms groups

of objects (machines or components) so that within each

group, the objects (machines or components) are highly

similar to each other.

In this research work done by the author, cluster analysis is carried

out using Ross's algorithm (Ross 1969) after slightly modifying it. The

author also applied an algorithm developed by Wishart (1969) to part

family formation by successive analysis of similarity. Numerical

taxonomy provides algorithms for the study of similarities between

objects in a quantitative manner, contrasting with the classification

techniques of group technology which tend to be descriptive.

Stanfel (1985) proposed a heuristic procedure to group machines

or parts. The proposed clustering technique uses part-machine matrix

a s input. Maximum and minimum cell sizes are considered. The

proposed clustering algorithm is divisive in nature; that is, the machines

are construed a s beginning in a single, parent cell. At each iteration, a

machine is selected to leave the parent cell. Subject to the constraints

on cell size, the machine is tentatively assigned to each existing cell a s

well a s to a new cell, where it would be first. The assignment which

produces the best objective function value is made permanent. The

author introduces the concept of an extraneous machine transition.

The objective function of interest is taken to be

f(P) = z (intercell transitions) + a z (extraneous machine

transitions) where P indicates a partition of machine types and 0 5 a 5

1 is a parameter: the user decides the relative weight to be ascribed to

the extraneous machine transitions. Thus, clusters are formed so a s

to attempt to optimize the objective function. When the parent cell

size lies within the minimum and maximum size, it is also considered

a s a feasible cell. The author highlights that there could be a number

of cells in progress, each with fewer than minimum number of machines

allowed a t a time when the parent set lacks sufficient machines to

bring them all to a feasible level. Therefore, simple numerical

calculations determine whether all subsequent assignments must be

made to 'lightw cells, whether the birth of a new cell must be prohibited,

etc., and these conditions limit the tentative assignments during

iterations when they arise.

Mosier and Taube (1985b) proposed two types of similarity

coefficients to measure the relationship between any two machines

namely Additive Similarity Coefficient and Multiplicative Similarity

Coefficient. Both the similarity coefficients use the machine-part matrix

weighted with the production volume associated with each part. For

clustering with Additive Similarity Coefficient and Multiplicative

Similarity Coefficient, a single linkage clustering algorithm (SLCA) was

used a s in McAuley's (1972) original work. The performance measure

used was the parts transported between cells. Two factors were examined

during experimentation. The first factor was the density of the matrix.

A second factor was introduced to allow for variation in how well defined

were the machine cells. The vector of weights (representing production

volume of parts) was randomly generated from a normal distribution

with a mean of 100 and a standard deviation of 12. The number of cells

formed was forced to be a fmed number. It was shown that the two

methodologies proposed in this work have potential benefits when

compared to King's (1980) and McAuley's (1972) works.

Tam (1990) proposed a similarity coefficient that takes into account

both the commonality of operations and similarity in operation

sequences. The author illustrates that such a similarity coefficient,

augmented with a clustering algorithm namely kNN clustering method

(Wong 1982, Wong a n d Lane 1983) c a n improve production

effectiveness by identifying part families that allow machines to

interleave between identical operations of different parts. The k-

Nearest-Neighbor (kNN) method developed by Wong (Wong 1982, Wong

and Lane 1983) is a density linkage clustering technique that is based

on nonparametric probability density estimates. Machine assignment,

on the other hand, should be determined a s a by-product of the

scheduling task. The main difference between the similarity coefficient

presented in this paper and those already existing is that the one

proposed in th i s paper draws on similar patterns of operation

sequences, instead of on machine requirements. The author shows

that the kNN method generates better groupings than the single linkage

method (McAuley 1972) using the same sets of similarity coefficient

matrices. The author also discusses the classification of new parts and

presents a Nearest Neighbor Classification procedure.

Though hierarchical clustering methods exploit similarity, they

require an arbitrary choice of the threshold value and are hampered by

irreversibility.

2.2.9 Cluster Analysis - Bonhierarchical Clustering

Nonhierarchical clustering algorithms start with an initial set of

machine seeds and results in a set of machine-component cells with

optimum or near optimum value of performance measure.

Chandrasekharan and Rajagopalan (1986a) developed a non-

heuristic algorithm for GT problems and demonstrated by formulating

the problem a s a bipartite graph, adapting the widely used MacQueen's

(1967) K-means method on binary data. An expression for the upper

limit to the number of groups i s derived. Using this limit, a

nonhierarchical clustering method is adopted for grouping components

into families and machines into cells. After diagonally correlating the

groups, an ideal-seed method is used to improve the initial grouping. A

new concept of grouping efficiency is introduced a s a quantitative

measure for comparing different grouping alternatives. The ideal-seed

algorithm was found to be free from the defects of some earlier methods

which depend heavily on the initial disposition of the matrix. The ideal-

seed algorithm is also robust against deviations from optimal solutions

at the previous stage and weeds out 'unnatural groups' formed a s a

result of defective choice of initial seed points. The weighting factor in

the expression for grouping efficiency enables the analyst to shift the

emphasis between utilization and intercell movement according to the

specific nature of the problem.

Chandrasekharan and Rajagopalan (1987) developed a n algorithm

(ZODIAC) for concurrent formation of part families and machine cells

in group technology. The acronym ZODIAC stands for zero-one data:

ideal seed algorithm for clustering. ZODIAC is an expanded and

improved version of the earlier ideal seed method (Chandrasekharan

and Rajagopalan 1986a). The formation of part families and machine

cells has been treated a s a problem of block diagonalization of the

zero-one matrix. The approach followed in developing ZODIAC is to

treat the components and machines (column vectors and row vectors)

independently a s points in an m-dimensional and a n n-dimensional

space respectively and to perform clustering of the da ta se t s

alternatively until a natural structure emerges. Different methods of

choosing seeds have been developed and tested. The 'ideal-seed' stage

of the proposed algorithm (ZODIAC) is robust against suboptimal

solutions in the previous stages. The use of 'natural seeds' brings out

the best block diagonal structure even without the use of ideal seeds.

The concept of grouping efficiency enables the comparison of solutions

on an absolute scale. The concept of relative efficiency developed in

this research work enables the termination of the algorithm at the

best possible solution.

Srinivasan and Narendran (1991) proposed a nonhierarchical

clustering algorithm, based on initial seeds obtained from the

assignment method, for finding part families and machine cells for group

technology. Similarity between two machines a s defined by Kusiak

(1987) is used in this work. Machine similarity matrix for machines

computed using the above mentioned formula is used a s the input to

an assignment problem for machines with an objective of maximization.

Subtours (Bellmore and Nemhauser 1968) are identified from the

assignments and are used to determine machine cells a s well a s initial

seeds to cluster columns. By a process of alternate clustering and

generating seeds from rows and columns, the zero-one machine-

component incidence matrix is block-diagonalized with the aim of

minimizing exceptional elements (intercell movements) and blanks

(machine idling). When compared to another nonhierarchical clustering

method, ZODIAC (Chandrasekharan and Rajagopalan 1987), the

proposed algorithm is found to fare better in terms of grouping efficiency

and grouping efficacy particularly for illstructured matrices.

In the case of the nonhierarchical clustering methods the final

solution is dependent on the initial set of seeds. Also, the algorithm's

significance depends on the objective function.

2.2.9.1 Advantage of IIonhierarchical Clustering Methods over

Hierarchical Clustering Methods

The main drawback of hierarchical methods (Anderberg 1973) is

that when two points (row vectors or column vectors) are grouped

together a t some stage of the algorithm there is no way to retrace the

step even if it leads to suboptimal (or unnatural) clustering a t the end.

At every stage of clustering those points which have formed some sort

of groups face the rest of the data with a fait accompli that severely

limits further possibilities. In nonhierarchical clustering, the choice is

rather free, and the natural clusters emerge from the given data without

permanently binding any data unit due to the linking done in the initial

stages of execution.

2.2.10 Search Methodr

Since the machine-component cell design problem is known to be

NP-complete, search methods such a s Tabu search, simulated annealing

and genetic algorithm have been used in the area of cellular

manufacturing systems. Because of the inbuilt features, the search

methods result in optimum or near optimum solution even for very

large size problems.

Harhalakis et al. (1990) proposed a simulated annealing procedure

to design manufacturing cells of limited size in order to minimize

intercell traffic. They have shown that how the simulated annealing

procedure helps in obtaining a good solution if not optimum. Finally,

they have applied the simulated annealing procedure to an industrial

problem and compared the results with that of the so called twofold

heuristic algorithm (Harhalakis et al. 1990). This particular algorithm

uses an initial feasible solution which is generated randomly. Since,

the initial feasible solution is obtained randomly there is always a

scope to improve the same which will in turn help to result in global

optimum solution.

Logendran et al. (1994) have developed an approach to the selection

of machines and a unique process plan for each part in the design of

cellular manufacturing systems. As the problem is proven NP-hard in

the strong sense, two higher-level heuristic algorithms, based upon a

concept known a s tabu search is developed. Each algorithm is further

extended into two methods, namely method 1 and method 2 .

Murthy and Srinivasan (1995) proposed a simulated annealing

algorithm for machine-component cell formation. The authors propose

fractional cell formation using remainder cells. Here, machines are

grouped into GT cells and a remainder cell, which functions like a job

shop. Component families are formed such that the components mostly

visit the assigned cell and the remainder cell and do not visit other cells.

The objective of the algorithm is to minimize intercell moves. The movement

between machine cells and remainder cells is not counted a s intercell

moves but movement of components among GT cells is considered a s

intercell movement. The input data is a zero-one machine-component

incidence matrix. Machine groups and part families are identified

concurrently by the grouping algorithm. Machine cell size is prefuted.

Each part is assigned to only one part family. Similarly each machine is

assigned to only one machine cell. Number of machine cells is prefxed.

The components are allotted to GT cells only. The authors also proposed

a linear integer programming formulation and another heuristic algorithm.

Large sized problems are solved using simulated annealing algorithm

and the other heuristic algorithm. It is observed that simulated annealing

algorithm performs better than the heuristic algorithm. The authors report

that the linear integer programming formulation for fractional cell

formation can be solved using available integer programming software for

small sized matrices but larger matrices have to be solved using heuristics

(like the simulated annealing algorithm proposed in this work) since

there exists no algorithm to solve this problem optimally in polynomial

time.

Chen et al. (1995) have developed a simulated annealing based

heuristic for cell formation problems. They also applied the algorithm

to many popular examples of cell formation problems and found that

the simulated annealing algorithm performs well in all these examples.

The proposed algorithm has the following three advantages: (1 ) flexibility

in the maximum number of machines allowed in one cell, (2) ability to

solve non-binary problems, and (3) ability to solve large size problems.

Gupta et al. (1996) have developed a genetic algorithm based

approach to cell composition and layout design problems. This

algorithm uses three different objective functions: (1) minimize total

moves (intercell as well a s intracell moves), (2) minimize cell load

variation, and (3) minimize both t h e above objective functions

simultaneously. The utilization of the workstations in a cell is evaluated

and used in determining the best machine cell-part grouping.

Furthermore, the sequence of operations and the impact of the layout

of cells are also considered.

Sofianopoulou (1997) has modelled the cell formation problem a s

a linear programming problem with the objective of minimizing the

number of intercellular moves subject to cell-size constraints and taking

into account the machine operation sequence of each part. A random

search heuristic algorithm based on the simulated annealing method

is adopted for its solution.

Vakharia and Chang (1997) have developed two heuristic methods

for generating solutions to the cell formation problem. These methods

are based on two powerfull combinatorial search methods (Simulated

annealing and Tabu Search). The performance of the heuristics is

examined using randomly generated, published and industry data.

Search methods require lot of experimentation to fix various

parameters. They also take more computational time.

However, to compensate the above drawbacks search methods don't

result in local optimum solution like conventional heuristic algorithms.

Search methods always yield good solution (global optimum solution

or near global optimum solution) for even very large size problems. It

may not be possible to solve such large size problems using optimization

techniques in reasonable amount of time.

2.2.11 Heuristics and Other Methods

Since the machine-component cell design problem is NP-complete,

it is difficult to solve large size problems using optimization techniques

in a reasonable amount of time. Hence, heuristic becomes necessary

to solve such cell design problems. Heuristics are designed to the

specific problem on hand.

Many approaches reported in the area of machine-component cell

formation, after Burbidge's pioneering work in production flow analysis,

make use of the similarity coefficient of the additive type. Waghodekar

and Sahu (1984) presented a heuristic approach based on the similarity

coefficient of the product type. The proposed method, called MACE

(MAchine-component CEll formation), has also been tested by using

the similarity coefficient of additive type. For a large number of problems

tested, the method yields a minimum number of exceptional elements.

The method is computationaly straightforward. The proposed solution

procedure consists of three phases: (1) determination of groups of

machines based on similarity coefficient, (2) determination of intercell-

flows and grouping of cells based on intercell-flow similarity coefficient,

and (3) component placement a s per the sequence of machines

computed. MACE in combination with human skill and judgment, helps

yield favourably acceptable results for number and size of cells. MACE

does not use arbitrary selection of the threshold value for the similarity

coefficient. It provides three outputs based on three different definitions

of similarity coefficient, which provides a good cross-check for consistent

results. The total flow type similarity coefficient, in combination with

material-flow-cost data, can be used for cell formation based on a

minimum material-flow-cost criterion. However MACE, simply a s a tool,

has its own limitations. It cannot alone give fool-pmf solutions for all

the problems associated with machine-component cell formation. A

system approach, in combination with human skill and judgement, is

advocated for making MACE more effective and dependable.

Purcheck (1985) proposed an heuristic for the planning and study

of machine-component groups in flexible production cells and flexible

manufacturing systems. The problem of group formation defined on

master-component process routes is undertaken in terms of minimum

differences between masters and maximum combinations of masters.

The heuristic is designed to search the solution space of the problem in

monotone-increasing order of solution costs so a s to avoid the

enumeration of solutions for cost minimization.

Panneerselvam and Balasubramanian (1985) proposed a new

method for computing similarity coefficient between components. They

proposed a covering technique based heuristic to form machine-

component cells by considering operation sequences, production

volume, processing times, machine hour rates and material handling

costs. The objective of this paper is to determine the desirable number

of machine-component cells such that the total cost comprising of

material handling cost and idle time cost of machines is minimized.

They have introduced a concept of main line which is nothing but the

processing sequence of a component.

Askin and Subramanian (1987) proposed a heuristic approach to

the economic determination of machine groups and their corresponding

component families for group technology. The procedure considers

costs of work-in-process and cycle inventory, intra-group material

handling, set-up, variable processing and r i e d machine costs. The

three stage procedure initially reorders part types based on routeing

similarity using the clustering algorithm proposed by King (1979). An

attempt is then made to combine adjacent part types to reduce machine

requirements. Finally groups are combined where economic benefits

of utilization offset those of set-up, work-in-process and material

handling. The output of the heuristic algorithm can be used to

construct from-to charts for both inter- and intra-group movement,

which is then input to a quadratic assignment problem based, facilities

layout routine for determining placement of each machine on the shop

floor.

Ballakur and Steudel (1987) proposed a new heuristic for the part

family /machine group formation (PFIMGF) problem. The distinguishing

feature of this heuristic is its consideration of several practical criteria

such a s within-cell machine utilization, workload fractions, maximum

number of machines that are assigned to a cell, and the percentage of

operations of parts completed within a single cell. Computational results,

based on several examples from the literature, show that this heuristic

performs well with respect to more than one criterion. The heuristic

also identifies if additional machines are needed due to overloads. The

heuristic is flexible in the sense that the designer can choose different

parameters and evaluate alternatives. The heuristic also clarifies the

source of various arguments in the literature concerning the 'goodness'

of the solutions obtained by other researchers. An application of the

heuristic to a large sample of industrial data showed that it can be a

valuable tool for trading-off several objectives of the PF/MGF problem.

Sule (1991) developed a procedure in group technology

environment to determine the number of machines, their groupings

and the amount of material transfer between the groups, so that all

components can be processed within the plant with minimum total

cost . The factors used in the analysis a r e machine capacity

requirements and between group material handling transfer cost, for

each component, a s well a s the machine cost for each machine.

Sequential or non-sequential processing of the components plays an

important role in the final grouping and cost. Minimizing intercellular

movement is not necessarily the same a s minimizing cost. In fact it

may be more economical to have certain intercellular transfers to reduce

the total cost. This paper presents further analysis that should be

performed to make group technology truly economical.

Frazier and Gaither (1991) have developed Best of Random Seeds

(BRS) approach for generating initial seeds. The outcome of this

approach is given a s input for the Objective Driven Capacity Constrained

(ODCC) cell formation heuristic to design machine-component cells.

They have also compared the results of the BRS approach with that of

several seed generation rules and showed that the BRS approach can

often yield better solutions.

Venugopal and Narendran (1993) tackled the design of cellular

manufacturing systems using the concept of asymptotic forms of a

boolean matrix. A method to identify bottlenecks and an algorithm to

form machine cells and part families are provided, based on the

asymptotic developments of the boolean matrix.

Balasubramanian and Panneeraelvam (1993) have improved their

earlier work (Panneerselvam and Balasubramanian 1985) by refining

the computation of similarity coefficient between components. Also,

they have proposed additional cell arrangements using rank order

clustering algorithm (King 1980). The covering technique-based

heuristic (Panneerselvam and Balasubramanian 1985) h a s been

modified to determine a n economical number of manufacturing cells

and cell arrangements so that each cell is identified to process specific

component(s). The design process considered minimizing the total cost

which includes handling, machine idle time and overtime. They have

applied their algorithm to a practical case problem and also presented

a sensitivity analysis based on production volume.

Lin et al. (1996) developed a model and a heuristic solution

procedure for weighted production-cell formation problem. An automatic

grouping of machines into machine cells and parts into part families is

provided. This heuristic procedure uses processing times and demand

rates to form the production cells. The procedure considers the cell

imbalance costs a s well a s the costs associated with the intercell part

movements and intracell processing. A disadvantage of this procedure

is that it develops the production-cells on the basis of a static

representation of the factory.

If the heuristics are not very efficient, then they will yield local

optimum a s the solution in most of the times. Sometimes, heuristics

may also yield global optimum solution. Usually a heuristic's efficiency

is judged by comparing it to a n optimization technique.

2.3 OBSERVATIONS AND THE PRESENT RESEARCH WORK

The key publications from the GT literature are reviewed and reported

in section 2.2. The outcome of the above review are reported in this section.

A classification of machine-component cell design methods is presented

in Table 2.1.

In general, the machine-component cell design models /

algorithms studied in this chapter possess the characteristics a s

reported in Table 2.2 (for subsequent reference, each characteristic

is assigned a characteristic identification code a s given in Table 2.2).

The characteristics of the machine-component cell design models /

algorithms, which were reviewed in this chapter, are reported in

Table 2.3. The classification of the machine-component cell design

models / algorithms is pictorially represented in Figure 2.1.

A careful analysis of l i terature on the design of cellular

manufacturing system reveals the following:

1. Forty three out of the seventy two research papers

reviewed in this chapter seek to block-diagonalise the

0-1 machine-component incidence matrix.

2. The cell design problem can be solved to varying extents

depending on the input data representation. If the input

da ta i s highly sparsed, only very efficient grouping

algorithms yield optimal or near optimal solutions.

Table 2.1 Classification of machine-component cell formation methods

Senal Methods of grouping machmes Key research publications rrvlrved

number and components

-~ - -

1 Part characterist~cs approach to 1. Kusuk (1985)

p.rt family tonnabon 2 . Ollodlle (1991)

3. Tahkonda m d Wcmmerlov (19921

Remarkrr:

T h n e systerns or classificabon and coding lack na~bility and cannot adjust themselves to the

changes In the pmduct profile over the y e m . The syslems cannot ~dentify pana un~quely. Mort

coding systems are proprietary in nature.

..................................................................................................................................

2 Evaluahve methods I . Durbtdge (1989)

a. Roductlon now analysis (PFA!

Remarks:

PFA rr descriptive In nature lnvolvrng the use of judgement at almost every 8tage and

sullen from a lack of a clrar.cut methdologv.

b. Component now analys~s I . E I - Easauy and Torrance (1Q72]

Remarks:

The authon d ~ d not gve any meaningful detalla of how the analysis was to h done. Many

productlon enginrers find no dlllerencr brtween component flow analysis and Rurbldge's

product~on now analys18.

.................................................................................................................................

3 Array somng 1 . McComick et al. (19721

or 2. King (1980)

Analyt~cal methods 3 . Klng and Nakorncha~ (1982)

4. Chandraaekhann and Ralngopnlan

(1986bl

Remarks:

The dlaadvnnuge wlh the m y - b a s e d methods rs that they do not eve the test solullon for

problems whlch have exccpt~onal elements I'l'a lying outslde the blocksl. Even a In , exceptions

are enough to completely misdlrcct the ar raybased prmedurea. However, anay-based

methods are the fastest and the beat when problems not ~nvolvlng ~ntercell movements

are considered.

Table 2.1 Classification of machine-component cell fonnation methods

(continued]

- - -- -

Serial Methods of grouping machines Key research publications reviewed

number and components

4 Graph theoretic approach 1. Rajagopalan and Batra (1975)

2. De Witte (1980)

3. Vohra et al. (1990)

4. Vannelli and Ha11 (1993)

5. Srinivasan (1994)

6. Madley (1996)

Remarks:

A certain amount ofjudgement is needcd while selecting the threshold value

for the similarity cocflicient to construct the machine graph. If the machinr

graph is too dense, then usually too many cliques will be therr. Since the

number of cliques varies exponentially with the number of vertices of the

machine graph, this approach is diflicult to apply for large size problems.

5 Mathematical programming 1 .

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

Purcheck (1975)

Kusiak (1987)

Choobineh (1988)

Co and Araar (1988)

Gunasingh and Lashkari (1989a)

Gunasingh and Lashkari (1989b)

Shtub (1989)

Srinivasan et al. (1990)

Al - Qattan (1990)

Logendran (1990)

Ventura et al. (1990)

Nqi et al. (1990)

Rajamani et al. (1990)

Wei and Gaither (1990)

Boctor (1991)

Logcndran (1991)

Gunasingh and Lashkari (1991)

Shafer and Rogers (1991)

Table 2.1 Classification of machine-component cell formation methods

(continued)

Send Methods of groupng machmes K e y research pubbcatlons mnd

n u m k r and components

19. Shdcr el d.(1992)

20 Rajamanl el al. (19921

21. Min and Shin (1993)

22. Awindh and Iran1 (1994)

23. Llmg and Taboun (19951

24. Rajaman> el al, (1996)

Remarks:

Though mathematical progammlng techniques csn br uard la arruntely formulate the cell

den~gn problem, large combinator~al problems can't be solved using the mathrrnat~cal

pragramming t s h n l q u a vnthn a reaaonablr amount of tmc Hence, hcuriahcs become necessary

to aolve such largr cnmbinator~al probicma.

.................................................................................................

6 Furry cluatcring approach 1. Xu and Wang (19891

2. Chu and Hayyn (19911

3 Glndy n al. 119951

Remarks

The degree of furuneas has to bc chorrn with extrcmc care as a large value may confound the

analysis. Thin 18 an Inherent l~mltation nf fuzzy cluatcring mcthcds.

................................................................................................................

7 Pattern mognttion mcthoda, knowledge-ha.4 and Al-based techniques

1. Kuriak ll9BB)

2 . Kapanhi and Suremh 11992)

3. Venugopal and Narcndran 119941

4 . Surcsh el al. (19951

5. Kamal and Burke (1996)

Remarks

Art~ficial Ncural Networka (ANN) arc primarily su~ted for and best utd~zed In applications

that are repetsttvc In nature Since each cellular rnanubctur~ng system problem I8 unique

m tta configurat~on, ANN may require long tralnlng sesslons and retraining b r every new

machxne-component rnctdcnce matru and / or the settmg of vnrlous parameters by the

analyst

Table 2.1 Classification of machine-component cell formation methods

(continued)

Serial Methods of grouping machines Key research publications reviewed number and components

8 Cluster analysis - hierarchical 1. McAuley (1972) clustering 2. Came (1973)

3. Stank1 (1985) 4. Mosier and Taube (1985b) 5. Tam (1990)

Remarks: Though hierarchical clustering methods exploit similarity, they require an arbitrary choice of the threshold value and are hampered by irreversibility.

9 Cluster analysis - nonhierarchical 1. Chandrasekharan and clustering Rajagopalan ( 1986a)

2. Chandrasekharan and Rajagopalan (1987)

3. Srinivasan and Narendran (1991)

Remarks: In the case of nonhierarchical clustering methods the final solution is dependent on the initial set of seeds.

10 Search methods 1. Harhalakis et al. (1990) 2. Logendran et al. (1994) 3. Chen et al. (1995) 4. Gupta et al. (1996) 5. Sofianopoulou (1997) 6. Vakharia and Chang (1997)

Remarks: Search methods require lot of experimentation to fvr various parameters. They also take more computational time. However, to compensate the above drawbacks search methods don't result in local optimum solution like conventional heuristic algorithms. Search methods always yield good solution (global optimum solution or near global optimum solution) for even very large size problems. It may not be possible to solve such large size problems using optimization techniques in reasonable amount of

time.

Table 2.1 Classification of machine-component cell formation methods

(continued)

- -- --

Serial Methods of grouping mach~nes Key research publ~cations rcviewed

number and components

11 Heuristics and other methods 1. Waghodekarand Sahu (1984)

2. Purcheck (1985)

3. Panneerselvarn and

Ralasubramanian (1985)

4 . Askin and Subramanian (1987)

5. Ballakur and Steudel(1987)

6. Sule (1991)

7. Frazier and Caithcr (1991)

8. Venugopal Narendran (1993)

9 . Balasubramanian and

Panneerselvarn (1993)

10. Munhy and Srinivasan (1995)

11. Lin et al. (1996)

Remarks:

I f the heuristics are not very efficient, then they will yield local optimum as the

solution in most oi the times. Sometimes, hruristics may also yield global

optimum solution.

Table 2.2 Characteristics of machinecomponent cell design models/

algorithms

Characteristics identification

code

1

la

1 l b I I

I 1

1 c

1 d

I ! .................................................................

2

2a , i

Description

Problem data structure

Data is binary (zero or one) machine-component incidence matrix

Input data is weighted machine-component incidence matrix (zero-one machine-component incidence matrix can be weighted by volume of components produced)

Input data can be either binary or weighted machine-component incidence matrix

Input data is fractional incidence matrix (example: application using fuzzy mathematics)

~ ....... ......................................... ~

Clustering problem

Initially parts are clustered by the grouping algorithm and part families are generated. Subsequently machines are assigned to the generated part family

Initially machine cells are formed by the grouping algorithm. Subsequently parts are assigned to the machine cells

Table 2.2 Characteristics of machine-component cell design models/

algorithms (continued)

Characteristics identification

code Description

Machine groups and part families are identified concurrently by the grouping algorithm I Initially parts are clustered by a grouping algorithm and part families are generated. Subsequently, another algorithm fonns machine cells and then assigns the already generated part families to these machine cells

Only part families are identified II Solution methodology I Part characteristics approach to part family formation

Evaluative methods II Array sorting or analytical methods I I Graph theoretic approach I Mathematical programming I Fuzzy clustering approach 11 Pattern recognition methods, knowledge-based and AI-based techniques I Cluster analysis - hierarchical clustering I Cluster analysis - nonhierarchical clustering I Search methods II Heuristics and other methods 11

Table 2.2 Characteristics of machine-component cell design models/

algorithms (continued)

Characteristics identification

code

i 4a

4b

4c

4d

I 4e /

4f

...

5

I 5a

I 1 5b

1 ! 1 5d I

I i : 5e

Description

Decision variables

Number of machine types that can be assigned to any group (machine group size)

Parts assigned to any group

Machines assigned to any group

Number of parts per family (part family size)

Number of machines of a given type to be assigned to a given cell

Part family assigned to cell k

~ ~ .......... . . . ................... ~~. . .~ .....

Objectives of the models / algorithms used

Minimize intercellular travels

Minimize intracellular travels

Minimize se tup time (or) maximize machine scheduling flexibility

Maximize similarity (or) minimize dissimilarity (or) maximize compatibility measure

Minimize total production cost

Table 2.2 Characteristics of machine-component cell design models /

algorithms (continued)

Characteristics identification

code

5f

5g

5h

5i

s j

5k

51

5m

5n

~... . ..... ............ ~~ ~..

6

6a

6b

Description

Minimize exceptional elements' costs (subcontracting - 5f(a), machine duplication - 5f(b), intercellular transfer costs 5f(c))

Minimize machine idle time

Maximize machine utilization

Maximize an absolute basis performance measure like grouping efficiency and grouping efficacy as a means for evaluating the goodness of the final cell formation solution

Minimize setup cost

Minimize capital investment

Minimize material handling cost

Minimize intracell processing cost

Minimize intercell processing cost

~ ~ ~ . - ~ ~~~- ~-~ ~ ~~~~~ ~ . . ... .. .... ...... . .. - - .

Constraints defined in the models 1 algorithm,

Number of groups (number of cells or number of

part families ] desired

Number of parts per group

Table 2.2 Characteristics of machine-component cell design models / algorithms (continued)

Characteristics identification

code

6c

6d

6e

I 6f I 6g 1

6h

Description

Number of machines per group

Machine capacity

Each part, each machine or both belongs to one part family or one machine group

Annual operating budget

Tool or processing requirement of parts

Number of machines of a particular machine

type

Table 2.3 C h a r a c t e r i s t i c s of t h e m a c h i n e - c o m p o n e n t cell fo rmat ion m o d e l s / a l g o r i t h m s proposed i n key r e s e a r c h p u b l i c a t i o n s of t h e GT l i t e r a t u r e ( c o n t i n u e d )

Serial Research Problem data Clustering Solution Decision Model / Constraints number publication structure problem methodology variable algorithm of the model/

objective algorithm

8 King and l a 2c 3c 517b) Nil Nakornchai (1982) ( Rank order clustering algorithm-2

( ROC2) used ]

9 Chandrasekharan l a 2c 3c 5qb) Nil and Rajagopalan ( Modified rank order clustering algorithm used) (1986b)

Graph Theoretic Appmch:

10 Rajago palan I b 2b 3d 5a ,5h 6c and Batra (19751 I (1) Bron Kerboseh algorithm) and

(2) Kernighan-Lin graph partitioning approach used]

11 De Witte (1980) lb 2b 3d Sa, 5h 6c I (1) Bron Kerboseh algonthm) and

(2) Kernighan-Lin graph partitioning approach used]

Hote: X is used if there are no choices among the characteristics defined in Table 2.2

P a r t characteristics W ~ ~ p u t f . m i l Y formation

Evaluative method8 r+ ,low -*

I 4 Component now analysis

Bond energy algorithm

Analyricd method Rank order clustering algorithm (ROC)

9 = n n k order ciusferiq

Graph thmhc Bmn Kerborh dgonthm

Marhme-Component rrll design models 1 ~lgonthms

Mnthemancal Programming

Kermghan-Lin g n p h pardtiming a p p m c h

E i n v e c t o r approach

Minimum spanning mee

r integer Programming Modrla (IPM) L h e n r l P M i Non-linear IPM i Mixed [PM

i Asaignmmt model

Nrtwork analysis

Partial sct cover model

Lagrnngian d u d formuletion

C o d programming modcls

L-) Branch and bound procedure w t h depth t s t sbategy

Fuzzy c l u l t c r ~ n g Fuzzy p a t t r r n recognltlon approach

Extended-fuzzy C - m e a n s clustering algorithm

Figure 2.1 Classification of machine-component cell design models / algorithms

I '-+ Genetic algorithm

4 Pattern recognition methods, Knowledge-

Expm v-=em appmach

based a n d AI-based Nrural network appmach teehniquca L CarpcnmGroaakgnetamrk

Z CompetitiPc learning model Z Adaptive resonance theory

model (AFT7 b Sell-organising feature map

model [SOFM) P F u y ART neural network B Fuzzy ART with Add

cluaenng technique

C h s t e r analysis-

E Smglc Linkagr clustcr analysis

4 H e u r ~ s t i c s a n d n thrr r' Usrng set theory b ~ s e d boolran methods p r o ~ r a m m w

I--) Based on covering technique

Hlrr~rchlral rludering numerical monomy tcctuuquc

k-Ncarest.Neighbor method [a dens i ty l ~ n k a g c c lus ter ing technique)

~ ~ r h m r - C o m p o n e n t rrll drsrgn models / Q o n d u n s

( b r e d on nnymptotir forms of a boolean matrix

~ ~ u s t r r nnalysss. c McQueen's k-means method N o n h ~ r r a r c h t c a l clustering tlungarinn method used to

generntr in~tial set of machinr c r d n

L~rarch mrthnds S!mulatcd nnnrdmg p r ~ c e d u r r

T ~ b a search mrthod

__)

Figure 2 .1 Classification of machine-component cell design models / algorithms (continued)

3. Nonhierarchical clustering is capable of identifying the

natural groups in a data-set. Only three algorithms are

available for formation of machine groups and part families

using the nonhierarchical clustering technique. The three

nonhierarchical clustering algorithms are given below:

a. Ideal Seed Nonhierarchical Clus te r ing Algorithm

(Chandrasekharan and Rajagopalan 1986a).

b. ZODIAC* (Chandrasekharan and Rajagopalan 1987).

c. GRAFICS (Srinivasan and Narendran 199 1).

Hence, t h e development of a lgor i thms based on

nonhierarchical clustering methods needs to be explored

further.

4. Negligible work has been done regarding seed generation

algorithms. Hence, there is a need for designing new seed

generation algorithms.

5. Since machine-component cell design problem i s

NP-complete, optimization algori thms a r e not able

to yield opt imal solut ions in a reasonable amount

of t i m e w h i l e t h e p r o b l e m s i z e i s large a n d

illstructured. Simple heuristics yield only local optimal

solutions for such problems. But, search algorithm like

simulated annealing algorithm yields optimal or near

optimal solution for large and illstructured problems.

Hence, further research is required to design machine-

component cell design algori thms us ing s imulated

annealing concept which will be useful to industry.

' Kandiller (1994) has reported that ZODIAC is one of the best well-known cell formation algorithms after analyzing six prominent cell formation algorithms

6. From Table 2 .3 (reported under column "Model /

algorithm objective"), it can be observed that only very

few researchers have used an absolute bads performance

measure like grouping efficacy (Kumar and

Chandrasekharan 1990) a n d grouping efficiency

(Chandrasekharan and Rajagopalan 1987) a s a means for

evaluating the goodness of the final cell formation

solution. Hence, it is decided to use such absolute basis

performance measure a s the objective functions of the

algorithms which are to be designed in this research work.

7. From the analysis (reported under "Clustering problem"

in Table 2.3), it is found out that it is desirable to

concurrently design machine groups and part families.

Hence, in this research work, it is decided to design GT

algorithms which will concurrently form machine groups

and part families.

8. From the analysis (reported under "Constraints of the model

/ algorithm" in Table 2.3), it is found out that it is desirable

not to prefvt the number of machine groups and part families

formed as a constraint while designing machine-component

cells. The algorithms which are to be proposed in this

research work are designed keeping the above point in mind.

In general, the literature can be classified into two categories

namely, machine-component cell formation with load consideration

and machine-component cell formation without load consideration. In

the machine-component cell formation with load consideration, capacity

requirements for various machines are computed based on processing

122

times and production volumes of components. These a n used along

with process sequences of the components to obtain the final machine-

component cells. But, in the machine-component cell formation

without load consideration, machine-component cells are formed only

based on the process sequences of the components.

Though the machine-component cell formation problem without

load consideration has been studied in detail by various authors and

attained a stage where many methods are available to get machine-

component cells, still the problem has greater scope for improvement

in terms of grouping efficacy (Kumar and Chandrasekharan 1990) and

grouping efficiency (Chandrasekharan and Rajagopalan 1987).

In the first part of this research, nonhierarchical clustering

approach is considered for further improvement. In nonhierarchical

clustering method, final machine-component cells are formed by a

suitable iterative procedure using some initial set of machine seeds.

The grouping efficacy and grouping efficiency of machine-component

cells obtained using nonhierarchical clustering approach mainly

depend on the initial set of machine seeds.

Frazier and Gaither (1991), Chandrasekharan and Rajagopalan

(1986a1, Chandrasekharan and Rajagopalan (1987) and Srinivasan and

Narendran (1991) have concentrated in this direction. Kandiller (1994)

carried out a n extensive study of six prominent cell formation

algorithms. Kandiller (1994) reported that ZODIAC (Chandrasekharan

and Rajagopalan 1987) is one of the best well-known cell formation

algorithms. Srinivasan and Narendran (1991) have shown that the

performance of GRAFICS (Srinivasan and Narendran 1991) is better

than ZODIAC. Hence, among the three algorithms which are available

under the nonhierarchical clustering approach, GRAFlCS (Srinivasan

and Narendran 1991) i s selected for fur ther improvement and

comparison. In the first part of this research, two algorithms, namely

ALGORITHM1 and ALGORITHM 2 are proposed [along with an Efficient

Seed Generation Algorithm (ESGA) ] and then they are compared with

GRAFICS and ZODIAC. It is found that the ALGORITHM 2 performs

better than the ALGORITHM 1, GRAFICS and ZODIAC. It is also found

that the ALGORITHM 1 performs better than GRAFICS and ZODIAC.

The well known simulated annealing algorithm h a s many

advantages over other algorithms. Mainly, the solution obtained using

the simulated annealing algorithm tends towards the global optimum.

The machine-component cell design problem is combinatorial in

nature. Hence, only efficient heuristics (eg, simulated annealing

algorithm) are able to provide a good solution if not optimum solution.

Hence, in the second part of the research, a Simulated Annealing

Algorithm (SA ALGORITHM) which is based on the ALGORITHM 2 is

proposed. The proposed SA ALGORITHM results in a set of machine-

component cells with the objective of minimizing intercell movement

of components.

The grouping efficacy (Kumar and Chandrasekharan 1990) and

grouping efficiency (Chandrasekharan and Rajagopalan 1987) are used

as quantitative criteria for selecting the best solution amongst the

solutions generated by the proposed SA ALGORITHM. The grouping

efficacy and grouping efficiency of the final solution obtained using

nonhierarchical clustering approach mainly depend on the initial set

of machine seeds. Hence, the set of machine seeds from an efficient

seed generation algorithm (ESGA) (which is also proposed in this work)

are used a s the initial set of machine seeds for the SA ALGORITHM

also.

2.4 SUMMARY

In this chapter, a comprehensive review of literature in the area

of machine-component cell design in cellular manufacturing systems

has been done. The deficiencies in the current state of the art have

been identified and the need for doing research in those areas is

established.