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An all Zero-One Algorithm for a Certain Class of Transportation Problems

Author

Listed:
  • Adriano De Maio

    (Politecnico di Milano, Milan, Italy)

  • Claudio Roveda

    (Politecnico di Milano, Milan, Italy)

Abstract

This paper considers a special class of transportation problems. There is a set of sources producing the same material with a fixed maximum capacity, and a set of users whose demands for the material are known. A cost is associated with the transportation of the material from each source to each user. Each user is to be supplied by one source only. The problem consists of finding the flow of the material from the sources to the users that satisfies their demands and minimizes the total transportation cost. The formulation of the problem is the same as the well-known Hitchcock problem with the further constraint that all the variables are binary. The paper proposes a search method, roughly resembling Balas's filter method, for the solution of the problem, and discusses it from a computational point of view. Finally, it describes an application of the model to a real industrial problem.

Suggested Citation

  • Adriano De Maio & Claudio Roveda, 1971. "An all Zero-One Algorithm for a Certain Class of Transportation Problems," Operations Research, INFORMS, vol. 19(6), pages 1406-1418, October.
    • Handle: RePEc:inm:oropre:v:19:y:1971:i:6:p:1406-1418
    DOI: 10.1287/opre.19.6.1406
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    Cited by:

    1. Narciso, Marcelo G. & Lorena, Luiz Antonio N., 1999. "Lagrangean/surrogate relaxation for generalized assignment problems," European Journal of Operational Research, Elsevier, vol. 114(1), pages 165-177, April.
    2. T Öncan & S N Kabadi & K P K Nair & A P Punnen, 2008. "VLSN search algorithms for partitioning problems using matching neighbourhoods," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(3), pages 388-398, March.
    3. Romeijn, H.E. & Romero Morales, D., 2000. "A Greedy Heuristic for a Three-Level Multi-Period Single-Sourcing Problem," ERIM Report Series Research in Management ERS-2000-04-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    4. June S. Park & Byung Ha Lim & Youngho Lee, 1998. "A Lagrangian Dual-Based Branch-and-Bound Algorithm for the Generalized Multi-Assignment Problem," Management Science, INFORMS, vol. 44(12-Part-2), pages 271-282, December.
    5. H. Edwin Romeijn & Dolores Romero Morales, 2001. "Generating Experimental Data for the Generalized Assignment Problem," Operations Research, INFORMS, vol. 49(6), pages 866-878, December.
    6. Lorena, Luiz Antonio N. & Narciso, Marcelo G., 1996. "Relaxation heuristics for a generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 91(3), pages 600-610, June.
    7. Pisut Pongchairerks, 2023. "A Probabilistic Hill-Climbing Algorithm for the Single-Source Transportation Problem," Sustainability, MDPI, vol. 15(5), pages 1-14, February.

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