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The Transhipment Problem

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  • Alex Orden

    (Burroughs Corporation)

Abstract

The transportation problem has offered two mathematical facets: (1) as a specialized type of linear programming problem, (2) as a method of representation of some combinatorial problems. In this paper a third aspect of the mathematical properties of the transportation problem is developed. It is shown that the same mathematical framework can be extended beyond pair-wise connections, to the determination of optimum linked paths over a series of points. This extension although viewed here as a linear programming problem, takes advantage of the combinatorial aspect of the transportation problem, and applications may arise which, like the assignment problem, appear to be combinatorial problems, but which can be solved by linear programming.

Suggested Citation

  • Alex Orden, 1956. "The Transhipment Problem," Management Science, INFORMS, vol. 2(3), pages 276-285, April.
    • Handle: RePEc:inm:ormnsc:v:2:y:1956:i:3:p:276-285
    DOI: 10.1287/mnsc.2.3.276
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    Cited by:

    1. Osleeb, Jeffrey P. & Ratick, Samuel J., 2010. "An Interperiod Network Storage Location–Allocation (INSLA) model for rail distribution of ethanol biofuels," Journal of Transport Geography, Elsevier, vol. 18(6), pages 729-737.
    2. G. Guastaroba & M. G. Speranza & D. Vigo, 2016. "Intermediate Facilities in Freight Transportation Planning: A Survey," Transportation Science, INFORMS, vol. 50(3), pages 763-789, August.
    3. Stevie Lochran, 2021. "GNOME: A Dynamic Dispatch and Investment Optimisation Model of the European Natural Gas Network and Its Suppliers," SN Operations Research Forum, Springer, vol. 2(4), pages 1-44, December.
    4. Shakeel Javaid & Dr. S.N. Gupta, 2008. "Capacitated Stochastic Fractional Transshipment Problem," Journal of Commerce and Trade, Society for Advanced Management Studies, vol. 3(1), pages 84-93, April.
    5. Cassidy, P.A. & McCarthy, W.O. & Toft, H.I., 1970. "An Application Of Spatial Analysis To Beef Slaughter Plant Location And Size, Queensland," Australian Journal of Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 14(1), pages 1-20, June.
    6. Martin, Alexander & Weibelzahl, Martin, 2014. "Where and when to pray? Optimal mass planning and efficient resource allocation in the church," FAU Discussion Papers in Economics 06/2014, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    7. C. Y. Lam, 2021. "Optimizing logistics routings in a network perspective of supply and demand nodes," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(1), pages 357-377, March.
    8. M T Lucas & D Chhajed, 2004. "Applications of location analysis in agriculture: a survey," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(6), pages 561-578, June.
    9. Vancroonenburg, Wim & Della Croce, Federico & Goossens, Dries & Spieksma, Frits C.R., 2014. "The Red–Blue transportation problem," European Journal of Operational Research, Elsevier, vol. 237(3), pages 814-823.
    10. Paul, Jomon Aliyas & Wang, Xinfang (Jocelyn), 2015. "Robust optimization for United States Department of Agriculture food aid bid allocations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 82(C), pages 129-146.
    11. Weber, Christian E., 2004. "More on complementarity and substitutability in the transshipment problem," European Journal of Operational Research, Elsevier, vol. 156(1), pages 213-222, July.
    12. Ampuero-Ramos, Luis A., 1981. "The Bolivian beef cattle industry: effects of transportation projects upon plant location and product flows in Beni," ISU General Staff Papers 198101010800007868, Iowa State University, Department of Economics.
    13. Brucker, Peter & Qu, Rong & Burke, Edmund, 2011. "Personnel scheduling: Models and complexity," European Journal of Operational Research, Elsevier, vol. 210(3), pages 467-473, May.
    14. Marta Boczoń & Alistair J. Wilson, 2023. "Goals, Constraints, and Transparently Fair Assignments: A Field Study of Randomization Design in the UEFA Champions League," Management Science, INFORMS, vol. 69(6), pages 3474-3491, June.
    15. Kelley, Jason & Kuby, Michael & Sierra, Rodrigo, 2013. "Transportation network optimization for the movement of indigenous goods in Amazonian Ecuador," Journal of Transport Geography, Elsevier, vol. 28(C), pages 89-100.

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