Locating sets of identical machines in a linear layout
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文摘
The assignment of M unique machines to M locations with the objective of minimizingthe total machine-to-machine material transportation cost in a flow line may be formulatedas a quadratic assignment problem (QAP). Instead of having M unique machines, if anapplication involves one or more sets of identical machines, the location problem becomesa tertiary assignment problem (TAP). Solving a large problem of this kind is extremelydifficult because of its combinatorial nature. When machine-to-machine flow is fixed, theTAP 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 computationallyintractable. However, this problem may be solved by identifying sets of identical machineswhich may be partitioned into individual, ""unique"" machines. Properties of a special type ofmatrix called the amoebic matrix are used in the partitioned problems to provide approximatesolutions, which are relabeled to prescribe a solution to the original problem. Results aredemonstrated along with suggestions for further research.