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The Multi-Index Problem

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  • K. B. Haley

    (Department of Engineering Production, The University, Birmingham, England)

Abstract

The multi-index transportation problem is defined and a summary of the algorithm described in an earlier paper is given. This paper discusses the theorems justifying the use of the algorithm and gives a necessary condition for the existence of a solution. It also describes the formulation of three special-structure linear-programming problems as examples of multi-index problems. The three problems discussed are the capacitated Hitchcock problem, transportation where there is more than one method of transport available, and the transformation of one type of multi-index problem into another. A final section describes problems that have restrictions in the form of inequalities.

Suggested Citation

  • K. B. Haley, 1963. "The Multi-Index Problem," Operations Research, INFORMS, vol. 11(3), pages 368-379, June.
    • Handle: RePEc:inm:oropre:v:11:y:1963:i:3:p:368-379
    DOI: 10.1287/opre.11.3.368
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    Cited by:

    1. Singh, Bikramjit & Singh, Amarinder, 2023. "Hybrid particle swarm optimization for pure integer linear solid transportation problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 243-266.
    2. Abd Elazeem M. Abd Elazeem & Abd Allah A. Mousa & Mohammed A. El-Shorbagy & Sayed K. Elagan & Yousria Abo-Elnaga, 2021. "Detecting All Non-Dominated Points for Multi-Objective Multi-Index Transportation Problems," Sustainability, MDPI, vol. 13(3), pages 1-18, January.
    3. Khurana, Archana & Adlakha, Veena & Lev, Benjamin, 2018. "Multi-index constrained transportation problem with bounds on availabilities, requirements and commodities," Operations Research Perspectives, Elsevier, vol. 5(C), pages 319-333.
    4. Kravtsov, M.K. & Lukshin, E.V., 2008. "Polyhedral combinatorics of multi-index axial transportation problems," European Journal of Operational Research, Elsevier, vol. 189(3), pages 920-938, September.
    5. Jimenez, F. & Verdegay, J. L., 1999. "Solving fuzzy solid transportation problems by an evolutionary algorithm based parametric approach," European Journal of Operational Research, Elsevier, vol. 117(3), pages 485-510, September.

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