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Capacity improvement, penalties, and the fixed charge transportation problem

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  • Gavin J. Bell
  • Bruce W. Lamar
  • Chris A. Wallace

Abstract

Capacity improvement and conditional penalties are two computational aides for fathoming subproblems in a branch‐and‐bound procedure. In this paper, we apply these techniques to the fixed charge transportation problem (FCTP) and show how relaxations of the FCTP subproblems can be posed as concave minimization problems (rather than LP relaxations). Using the concave relaxations, we propose a new conditional penalty and three new types of capacity improvement techniques for the FCTP. Based on computational experiments using a standard set of FCTP test problems, the new capacity improvement and penalty techniques are responsible for a three‐fold reduction in the CPU time for the branch‐and‐bound algorithm and nearly a tenfold reduction in the number of subproblems that need to be evaluated in the branch‐and‐bound enumeration tree. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 341–355, 1999

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  • Gavin J. Bell & Bruce W. Lamar & Chris A. Wallace, 1999. "Capacity improvement, penalties, and the fixed charge transportation problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(4), pages 341-355, June.
    • Handle: RePEc:wly:navres:v:46:y:1999:i:4:p:341-355
    DOI: 10.1002/(SICI)1520-6750(199906)46:43.0.CO;2-A
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    Cited by:

    1. 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.
    2. 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.
    3. Jeffery L. Kennington & Charles D. Nicholson, 2010. "The Uncapacitated Time-Space Fixed-Charge Network Flow Problem: An Empirical Investigation of Procedures for Arc Capacity Assignment," INFORMS Journal on Computing, INFORMS, vol. 22(2), pages 326-337, May.
    4. Dimitri J. Papageorgiou & Alejandro Toriello & George L. Nemhauser & Martin W. P. Savelsbergh, 2012. "Fixed-Charge Transportation with Product Blending," Transportation Science, INFORMS, vol. 46(2), pages 281-295, May.

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