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On a Class of Capacitated Transportation Problems

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  • Harvey M. Wagner

    (Stanford University)

Abstract

Transportation models (ordinary and transhipment) having certain types of capacity constraints on the flows between origins and destinations are studied from the point of view of transforming them into enlarged standardized (non-capacitated) models. Specifically constraints on the flow from disjoint and/or nested sets of origins to all destinations, and from any single origin to disjoint and/or nested sets of destinations are considered. Dual formulations are indicated for constraints on the flow to destinations from origins. In the case of a set of capacity constraints on the flow from each origin to each destination, the models proposed are easily seen to be of minimal dimension for any "standardized" version of such a capacitated problem.

Suggested Citation

  • Harvey M. Wagner, 1959. "On a Class of Capacitated Transportation Problems," Management Science, INFORMS, vol. 5(3), pages 304-318, April.
    • Handle: RePEc:inm:ormnsc:v:5:y:1959:i:3:p:304-318
    DOI: 10.1287/mnsc.5.3.304
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    Cited by:

    1. Sharma, Anuj & Verma, Vanita & Kaur, Prabhjot & Dahiya, Kalpana, 2015. "An iterative algorithm for two level hierarchical time minimization transportation problem," European Journal of Operational Research, Elsevier, vol. 246(3), pages 700-707.
    2. 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.
    3. Fontes, Dalila B.M.M. & Hadjiconstantinou, Eleni & Christofides, Nicos, 2006. "A dynamic programming approach for solving single-source uncapacitated concave minimum cost network flow problems," European Journal of Operational Research, Elsevier, vol. 174(2), pages 1205-1219, October.

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