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Locating sets of identical machines in a linear layout

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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.

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Authors
  1. Bhaba R. Sarker
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  2. Wilbert E. Wilhelm
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  3. Gary L. Hogg
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Sarker, B.R., Wilhelm, W.E. & Hogg, G.L. Locating sets of identical machines in a linear layout. Annals of Operations Research 77, 183–207 (1998). https://doi.org/10.1023/A:1018973327327

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