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Locating sets of identical machines in a linear layout

Author

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  • Bhaba Sarker
  • Wilbert Wilhelm
  • Gary Hogg

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

Suggested Citation

  • Bhaba Sarker & Wilbert Wilhelm & Gary Hogg, 1998. "Locating sets of identical machines in a linear layout," Annals of Operations Research, Springer, vol. 77(0), pages 183-207, January.
    • Handle: RePEc:spr:annopr:v:77:y:1998:i:0:p:183-207:10.1023/a:1018973327327
    DOI: 10.1023/A:1018973327327
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    Cited by:

    1. Keller, Birgit & Buscher, Udo, 2015. "Single row layout models," European Journal of Operational Research, Elsevier, vol. 245(3), pages 629-644.
    2. Diponegoro, Ahmad & Sarker, Bhaba R., 2003. "Flow distance reduction for a multi-product flowline with sets of identical machines," European Journal of Operational Research, Elsevier, vol. 147(3), pages 591-612, June.

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