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Some branch‐and‐bound procedures for fixed‐cost transportation problems

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  • A. Victor Cabot
  • S. Selcuk Erenguc

Abstract

In this article we present three properties that will improve the performance of branch‐and‐bound algorithms for fixed‐cost transportation problems. By applying Lagrangian relaxation we show that one can develop stronger up and down penalties than those traditionally used and also develop a strengthened penalty for nonbasic variables. We also show that it is possible to “look ahead” of a particular node and determine the solution at the next node without actually calculating it. We present computational evidence by comparing our developments with existing procedures.

Suggested Citation

  • A. Victor Cabot & S. Selcuk Erenguc, 1984. "Some branch‐and‐bound procedures for fixed‐cost transportation problems," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 31(1), pages 145-154, March.
    • Handle: RePEc:wly:navlog:v:31:y:1984:i:1:p:145-154
    DOI: 10.1002/nav.3800310115
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    Cited by:

    1. Kurt M. Bretthauer, 1994. "A penalty for concave minimization derived from the tuy cutting plane," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(3), pages 455-463, April.
    2. Alexey Sorokin & Vladimir Boginski & Artyom Nahapetyan & Panos M. Pardalos, 2013. "Computational risk management techniques for fixed charge network flow problems with uncertain arc failures," Journal of Combinatorial Optimization, Springer, vol. 25(1), pages 99-122, January.
    3. Fred Glover & Hanif Sherali, 2005. "Some Classes of Valid Inequalities and Convex Hull Characterizations for Dynamic Fixed-Charge Problems under Nested Constraints," Annals of Operations Research, Springer, vol. 140(1), pages 215-233, November.

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