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An operator theory of parametric programming for the transportation problem‐I

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  • V. Srinivasan
  • G. L. Thompson

Abstract

This paper investigates the effect on the optimum solution of a (capacitated) transportation problem when the data of the problem (the rim conditions‐i. e., the warehouse supplies and market demands‐the per unit transportation costs and the upper bounds) are continuously varied as a (linear) function of a single parameter. An operator theory is developed and algorithms provided for applying rim and cost operators that effect the transformation of optimum solution associated with changes in rim conditions and unit costs. Bound operators that effect changes in upper bounds are shown to be equivalent to rim operators. The discussion in this paper is limited to basis preserving operators for which the changes in the data are such that the optimum basis structures are preserved.

Suggested Citation

  • V. Srinivasan & G. L. Thompson, 1972. "An operator theory of parametric programming for the transportation problem‐I," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 19(2), pages 205-225, June.
    • Handle: RePEc:wly:navlog:v:19:y:1972:i:2:p:205-225
    DOI: 10.1002/nav.3800190202
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    Cited by:

    1. S. Raghavan & Michael O. Ball & Vinai S. Trichur, 2002. "Bicriteria product design optimization: An efficient solution procedure using AND/OR trees," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(6), pages 574-592, September.

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