Part-machine grouping using weighted similarity coefficients
Introduction
Cellular manufacturing requires the identification of groups of similar parts (part families) and the corresponding manufacturing resources they require (machine cells) in order to partition the shop into several, as self-contained as possible, manufacturing cells. The similarity of parts facilitates set-up time reductions, which translate into smaller lot sizes, reduced in-process inventories, shorter lead times, higher throughput and improved product quality. In addition, the small number of machines in each cell simplifies and reduces material handling. Wemmerlöv and Johnson (1997) presents a survey of users' experiences.
The first step in the transition to cellular manufacturing is part-machine grouping, i.e. determining the part families and associated machine cells. A machine-part incidence matrix [air] whose components take a binary value to indicate whether or not machine i is required to process part r, may be used. More detailed data include part demands, sequence and duration of operations, alternative process plans, machine capacities, intercell transportation costs, machine acquisition costs, part subcontracting costs, etc. The simplest criterium used for cell formation is the minimization of intercellular moves. Other criteria may be maximization of a weighted grouping measure, cost minimization, within-cell load balancing, intercell load balancing, etc. As for constraints, simpler approaches consider none, while other approaches impose limits on cell sizes or on the number of cells, machine capacity constraints, budget constraints, etc. Part families and machine cells can be formed simultaneously or machine cells can be formed first and then parts assigned to them or part families formed first and then machines assigned.
As can be deducted from the above considerations, many different approaches have been proposed for part-machine grouping. There are a number of interesting review papers (Reisman et al., 1997, Selim et al., 1998, Singh, 1993, Venugopal, 1998). Many researchers have used the concept of similarity coefficient (or, equivalently, a distance/dissimilarity measure) between machines or between parts. In Table 1, those approaches have been classified according to the definition of similarity coefficient used and the solution technique proposed. The main classification of similarity coefficients is whether or not they use information on the sequence of operations. As it can be seen in the table, most of the proposed approaches are not sequence based. Although a variety of similarity measures have been proposed, the two most common are Jaccard (McAuley, 1972) and Hamming distance (Kusiak, 1987).
In this paper, after illustrating the problem with a simple example, we present a two-phase approach involving a quadratic integer program in Phase One and a linear minimum cost network flow program in Phase Two. A Tabu search (TS) algorithm is proposed for Phase One. Finally, computational experiences with the proposed approach are reported and conclusions are drawn.
Section snippets
A simple example
Consider the binary part-machine incidence matrix shown in Table 2.
For this simple problem, the well known SLCA approach (McAuley, 1972) would first compute the Jaccard similarity coefficients (SC) between any two machines i and j aswhere nij is the number of parts requiring processing on both machines i and j, while ñij is the number of parts requiring processing on machine i but not on machine j. Table 3 shows the Jaccard SC matrix for this problem.
The corresponding
A two-phase approach
The following notation will be used.
Input data
- i, j
machine indexes
- r
part type index
- k
cell/family index
- M
number of machines
- P
number of part types
- Mmin
minimum number of machines per cell
- Mmax
maximum number of machines per cell
- Pmin
minimum number of part types per family
- Pmax
maximum number of part types per family
- A=[air]
M×P binary part-machine incidence matrix
Decision variables for Phase One
Decision variables for Phase Two
Tabu search algorithm
TS is a metaheuristic procedure that has proven itself to be a useful optimization technique for solving a wide variety of combinatorial problems. For a thorough description of TS, we refer to books (Glover & Laguna, 1996) and tutorials (Glover, 1990, Glover and Laguna, 1995) that cover this technique.
In TS, the crucial implementation decisions include the definition of the neighborhood structure, and the way the current solution is modified according to the history of the search. For the
Computational experiences
To show the flexibility of the two-phase approach and to compare the performance of the TS algorithm, a maximum spanning tree (MST) heuristic (Lozano, Adenso-Díaz, Eguia, & Onieva, 1999) has been used. Table 8 shows a list of 22 problems from the literature, with their sizes and references. In a first set of experiments, the two methods were used to solve the part-machine grouping problem assuming no cell size limits exist. Initially, a value of q=0.1 was used. Such a low value means
Conclusions
This paper presents a two-phase approach for part-machine grouping with limits on both machine cells and part families sizes. A weighted sum of intracell voids and exceptional elements is used to evaluate the quality of the solution obtained. For Phase One and in order to be in line with that objective function, weighted SC are proposed. To solve the resulting quadratic integer programming a TS algorithm has been implemented and compared with three heuristics. Computational experiences show
Acknowledgement
This paper was partially funded by the Asturian government, contract number PC-04-08.
References (60)
- et al.
A Tabu search approach to the cell formation problems
Computers and Industrial Engineering
(1997) - et al.
An extendison to the p-median group technology algorithm
Computers and Operations Research
(1994) - et al.
Simulated annealing procedures for forming machine cells in group technology
European Journal of Operational Research
(1994) - et al.
A novel machine grouping and knowledge-based approach for cellular manufacturing
European Journal of Operational Research
(1993) - et al.
Application of fuzzy decision making in part-machine grouping
International Journal of Production Economics
(2000) - et al.
Weighted similarity measure heuristics for the group technology machine clustering problem
Omega
(1985) - et al.
Cell formation in group technology: Review, evaluation and directions for future research
Computers and Industrial Engineering
(1998) Design of cellular manufacturing systems: An invited review
European Journal of Operational Research
(1993)- et al.
Multiple criteria clustering algorithm for solving the group technology problem with multiple process routings
Computers and Industrial Engineering
(1997) - et al.
Concurrent formation of part families and machine cells based on the fuzzy set theory
Journal of Manufacturing Systems
(1992)
A hard clustering approach to the part family formation problem
Production Planning and Control
A genetic algorithm for the part family formation problem
Production Planning and Control
A Hamiltonian path approach to reordering the part-machine matrix for cellular manufacturing
International Journal of Production Research
Manufacturing cell formation using similarity coefficients and pair-wise interchange: Formulation and comparison
Production Planning and Control
Relaxation methods for minimum cost for ordinary and generalized network flow problems
Operations Research
Grouping PCBs for set-up reduction: A maximum spanning tree approach
International Journal of Production Research
A linear formulation of the machine-part cell formation problem
International Journal of Production Research
ZODIAC—an algorithm for concurrent formation of part-families and machine-cells
International Journal of Production Research
Groupability: An analysis of the properties of binary data matrices for group technology
International Journal of Production Research
A framework for the design of cellular manufacturing systems
International Journal of Production Research
The use of similarity coefficients in production flow analysis
International Journal of Production Research
Tabu search: A tutorial
Interfaces
Tabu search
Tabu search
Production data based similarity coefficient for machine-component grouping decisions in the design of a cellular manufacturing system
International Journal of Production Research
A similarity coefficient measure and machine-parts grouping in cellular manufacturing sytems
International Journal of Production Research
Cell formation using genetic algorithms
International Journal of Flexible Automation and Integrated Manufacturing
Machine-component group formation in group technology: Review and extension
International Journal of Production Research
The generalized group technology concept
International Journal of Production Research
Designing cellular manufacturing systems: Branch- and bound and A* approaches
IIE Transactions
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