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A Primal Method for Minimal Cost Flows with Applications to the Assignment and Transportation Problems

Author

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  • Morton Klein

    (Columbia University)

Abstract

A simple procedure is given for solving minimal cost flow problems in which feasible flows are maintained throughout. It specializes to give primal algorithms for the assignment and transportation problems. Convex cost problems can also be handled.

Suggested Citation

  • Morton Klein, 1967. "A Primal Method for Minimal Cost Flows with Applications to the Assignment and Transportation Problems," Management Science, INFORMS, vol. 14(3), pages 205-220, November.
    • Handle: RePEc:inm:ormnsc:v:14:y:1967:i:3:p:205-220
    DOI: 10.1287/mnsc.14.3.205
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    Cited by:

    1. Balachandran Vaidyanathan & Ravindra K. Ahuja, 2010. "Fast Algorithms for Specially Structured Minimum Cost Flow Problems with Applications," Operations Research, INFORMS, vol. 58(6), pages 1681-1696, December.
    2. Torben S. D. Johansen, 2024. "Optimal Treatment Allocation under Constraints," Papers 2404.18268, arXiv.org.
    3. Xin Chen & Menglong Li, 2021. "Discrete Convex Analysis and Its Applications in Operations: A Survey," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1904-1926, June.
    4. Castro, Jordi & Nasini, Stefano, 2021. "A specialized interior-point algorithm for huge minimum convex cost flows in bipartite networks," European Journal of Operational Research, Elsevier, vol. 290(3), pages 857-869.
    5. Ayoub Tahiri & David Ladeveze & Pascale Chiron & Bernard Archimede & Ludovic Lhuissier, 2018. "Reservoir Management Using a Network Flow Optimization Model Considering Quadratic Convex Cost Functions on Arcs," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(10), pages 3505-3518, August.
    6. Maiko Shigeno & Satoru Iwata & S. Thomas McCormick, 2000. "Relaxed Most Negative Cycle and Most Positive Cut Canceling Algorithms for Minimum Cost Flow," Mathematics of Operations Research, INFORMS, vol. 25(1), pages 76-104, February.
    7. Mocquillon, Cédric & Lenté, Christophe & T'Kindt, Vincent, 2011. "An efficient heuristic for medium-term planning in shampoo production," International Journal of Production Economics, Elsevier, vol. 129(1), pages 178-185, January.
    8. Wang, Yan & Wang, Junwei, 2019. "Integrated reconfiguration of both supply and demand for evacuation planning," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 130(C), pages 82-94.
    9. Xujin Chen & Xiaodong Hu & Xiaohua Jia & Zhongzheng Tang & Chenhao Wang & Ying Zhang, 0. "Algorithms for the metric ring star problem with fixed edge-cost ratio," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-25.
    10. Kevin D. Wayne, 2002. "A Polynomial Combinatorial Algorithm for Generalized Minimum Cost Flow," Mathematics of Operations Research, INFORMS, vol. 27(3), pages 445-459, August.
    11. Gansterer, Margaretha & Hartl, Richard F., 2018. "Collaborative vehicle routing: A survey," European Journal of Operational Research, Elsevier, vol. 268(1), pages 1-12.
    12. Xujin Chen & Xiaodong Hu & Xiaohua Jia & Zhongzheng Tang & Chenhao Wang & Ying Zhang, 2021. "Algorithms for the metric ring star problem with fixed edge-cost ratio," Journal of Combinatorial Optimization, Springer, vol. 42(3), pages 499-523, October.
    13. Orlin, James B., 1953-., 1989. "A faster strongly polynomial minimum cost flow algorithm," Working papers 3060-89., Massachusetts Institute of Technology (MIT), Sloan School of Management.

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