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Fixed‐cost transportation problems

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  • Michel L. Balinski

Abstract

This paper formulates a fixed‐cost transportation problem as an integer program, describes some of its special properties, and suggests an approximate method of solution. Examples are given to demonstrate the approximation technique.

Suggested Citation

  • Michel L. Balinski, 1961. "Fixed‐cost transportation problems," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 8(1), pages 41-54, March.
    • Handle: RePEc:wly:navlog:v:8:y:1961:i:1:p:41-54
    DOI: 10.1002/nav.3800080104
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    Cited by:

    1. A. Karakitsiou & A. Migdalas, 2016. "Convex optimization problems in supply chain planning and their solution by a column generation method based on the Frank Wolfe method," Operational Research, Springer, vol. 16(3), pages 401-421, October.
    2. Aghalari, Amin & Nur, Farjana & Marufuzzaman, Mohammad, 2020. "A Bender’s based nested decomposition algorithm to solve a stochastic inland waterway port management problem considering perishable product," International Journal of Production Economics, Elsevier, vol. 229(C).
    3. Jesús Sáez Aguado, 2009. "Fixed Charge Transportation Problems: a new heuristic approach based on Lagrangean relaxation and the solving of core problems," Annals of Operations Research, Springer, vol. 172(1), pages 45-69, November.
    4. Fernández, Elena & Hinojosa, Yolanda & Puerto, Justo & Saldanha-da-Gama, Francisco, 2019. "New algorithmic framework for conditional value at risk: Application to stochastic fixed-charge transportation," European Journal of Operational Research, Elsevier, vol. 277(1), pages 215-226.
    5. Kurt Spielberg, 2007. "IP over 40+ Years at IBM Scientific Centers and Marketing," Annals of Operations Research, Springer, vol. 149(1), pages 195-208, February.
    6. Yixin Zhao & Torbjörn Larsson & Elina Rönnberg & Panos M. Pardalos, 2018. "The fixed charge transportation problem: a strong formulation based on Lagrangian decomposition and column generation," Journal of Global Optimization, Springer, vol. 72(3), pages 517-538, November.
    7. Ассаул В.Н.* & Погодин И.Е.**, 2019. "О Транспортной Задаче С Экологическим Критерием," Журнал Экономика и математические методы (ЭММ), Центральный Экономико-Математический Институт (ЦЭМИ), vol. 55(2), pages 58-64, апрель.
    8. Monique Guignard & Ellis Johnson & Kurt Spielberg, 2005. "Logical Processing for Integer Programming," Annals of Operations Research, Springer, vol. 140(1), pages 263-304, November.
    9. Lara, Cristiana L. & Koenemann, Jochen & Nie, Yisu & de Souza, Cid C., 2023. "Scalable timing-aware network design via lagrangian decomposition," European Journal of Operational Research, Elsevier, vol. 309(1), pages 152-169.
    10. Haeringer, Guillaume, 2023. "Minimizing settlements," Journal of Mathematical Economics, Elsevier, vol. 106(C).
    11. Nabil Nehme & Bacel Maddah & Isam A. Kaysi, 2021. "An integrated multi-ship crane allocation in Beirut Port container terminal," Operational Research, Springer, vol. 21(3), pages 1743-1761, September.
    12. Gurwinder Singh & Amarinder Singh, 2021. "Solving fixed-charge transportation problem using a modified particle swarm optimization algorithm," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 12(6), pages 1073-1086, December.
    13. Aghalari, Amin & Nur, Farjana & Marufuzzaman, Mohammad, 2021. "Solving a stochastic inland waterway port management problem using a parallelized hybrid decomposition algorithm," Omega, Elsevier, vol. 102(C).
    14. Bala Shetty, 1990. "A relaxation/decomposition algorithm for the fixed charged network problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(2), pages 327-340, April.
    15. Ovidiu Cosma & Petrică C. Pop & Cosmin Sabo, 2020. "An Efficient Hybrid Genetic Approach for Solving the Two-Stage Supply Chain Network Design Problem with Fixed Costs," Mathematics, MDPI, vol. 8(5), pages 1-20, May.
    16. Gaudioso, Manlio & Monaco, Maria Flavia & Sammarra, Marcello, 2021. "A Lagrangian heuristics for the truck scheduling problem in multi-door, multi-product Cross-Docking with constant processing time," Omega, Elsevier, vol. 101(C).

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