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Optimality Properties of a Special Assignment Problem

Author

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  • S. C. Parikh

    (University of California, Berkeley)

  • Roger Wets

    (University of California, Berkeley)

Abstract

In this paper, it is shown that if the cost matrix of an assignment problem has the following property c ij = | j − i | then any basic feasible solution is optimal if and only if its unit components belong to two well-defined symmetric regions. The matrix with above mentioned property is called the “reordering matrix,” because it arose for the first time in the reordering of nodes of a critical path and other acyclic network problems. One deals with similar matrices in some problems related to order statistics.

Suggested Citation

  • S. C. Parikh & Roger Wets, 1964. "Optimality Properties of a Special Assignment Problem," Operations Research, INFORMS, vol. 12(1), pages 139-142, February.
    • Handle: RePEc:inm:oropre:v:12:y:1964:i:1:p:139-142
    DOI: 10.1287/opre.12.1.139
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