Locating sets of identical machines in a linear layout

Bhaba Sarker, Wilbert Wilhelm and Gary Hogg

Annals of Operations Research, 1998, vol. 77, issue 0, 183-207

Abstract: The assignment of M unique machines to M locations with the objective of minimizing the total machine-to-machine material transportation cost in a flow line may be formulated as a quadratic assignment problem (QAP). Instead of having M unique machines, if an application involves one or more sets of identical machines, the location problem becomes a tertiary assignment problem (TAP). Solving a large problem of this kind is extremely difficult because of its combinatorial nature. When machine-to-machine flow is fixed, the TAP may be specialized to a QAP for which the unique machine problem is a special case. Obtaining an optimum solution to this problem when M is large is also computationally intractable. However, this problem may be solved by identifying sets of identical machines which may be partitioned into individual, "unique" machines. Properties of a special type of matrix called the amoebic matrix are used in the partitioned problems to provide approximate solutions, which are relabeled to prescribe a solution to the original problem. Results are demonstrated along with suggestions for further research. Copyright Kluwer Academic Publishers 1998

Keywords: machine locations; sets of identical machines; one-dimension; backtracking (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1023/A:1018973327327

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