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Cost operator algorithms for the transportation problem

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Abstract

A primal transportation algorithm is devised via post-optimization on the costs of a modified problem. The procedure involves altering the costs corresponding to the basic cells of the initial (primal feasible) solution so that it is dual feasible as well. The altered costs are then successively restored to their true values with appropriate changes in the “optimal” solution by the application of cell or area cost operators discussed elsewhere. The cell cost operator algorithm converges to optimum within (2T − 1) steps for primal nondegenerate transportation problems and [(2T + 1) ⋅ min (m, n)] − 1 steps for primal degenerate transportation problems, whereT is the sum of the (integer) warehouse availabilities (also the sum of the (integer) market requirements) andm andn denote the number of warehouses and markets respectively. For the area cost operator algorithm the corresponding bounds on the number of steps areT and (T + 1) ⋅ min (m, n) respectively.

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This report was prepared as part of the activities of the Management Sciences Research Group, Carnegie—Mellon University, under Contract N00014-67-A-0314-0007 NR 047-048 with the U.S. Office of Naval Research.

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Srinivasan, V., Thompson, G.L. Cost operator algorithms for the transportation problem. Mathematical Programming 12, 372–391 (1977). https://doi.org/10.1007/BF01593805

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  • DOI: https://doi.org/10.1007/BF01593805

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