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On the Generalized Transportation Problem

Author

Listed:
  • E. Balas

    (Institute of Mathematics, Rumanian Academy of Science, Bucarest)

  • P. L. Ivanescu

    (Institute of Mathematics, Rumanian Academy of Science, Bucarest)

Abstract

The purpose of the present paper is to extend the loop-technique of the stepping-stone algorithm to the generalized transportation problem. The main result (Theorem and Corollary of §6) is, that passing from a basic feasible solution to another one may always be carried out by constructing a simple symmetrical or a double loop (as defined in §2) and computing new values for the variables only along this path. The amount of computations needed for this turns out to be substantially reduced as compared to the usual way of solving the system of equations relating the new basis to the old one.

Suggested Citation

  • E. Balas & P. L. Ivanescu, 1964. "On the Generalized Transportation Problem," Management Science, INFORMS, vol. 11(1), pages 188-202, September.
    • Handle: RePEc:inm:ormnsc:v:11:y:1964:i:1:p:188-202
    DOI: 10.1287/mnsc.11.1.188
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    Cited by:

    1. Marcin Anholcer, 2013. "Stochastic Generalized Transportation Problem with discrete distribution of demand," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 23(4), pages 9-19.
    2. René Brandenberg & Paul Stursberg, 2021. "Refined cut selection for benders decomposition: applied to network capacity expansion problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(3), pages 383-412, December.
    3. Marcin Anholcer, 2012. "Algorithm for the stochastic generalized transportation problem," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 22(4), pages 9-20.
    4. V. Balachandran & G.L. Thompson, 1974. "A Note on 'Computational Simplifications in Solving Generalized Transportation Problems,' by Glover and Kingman," Discussion Papers 66, Northwestern University, Center for Mathematical Studies in Economics and Management Science.

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