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An Improved Reduction Method For The Robust Optimization Of The Assignment Problem

Author

Listed:
  • BYUNGJUN YOU

    (Department of Computer Science, The National Defense Academy, Yokosuka, Kanagawa 239-8686, Japan)

  • DAISUKE YOKOYA

    (Department of Computer Science, The National Defense Academy, Yokosuka, Kanagawa 239-8686, Japan;
    Air Self-Defense Force of Japan, Japan)

  • TAKEO YAMADA

    (Department of Computer Science, The National Defense Academy, Yokosuka, Kanagawa 239-8686, Japan)

Abstract

We are concerned with a variation of the assignment problem, where the assignment costs differ under different scenarios. We give a surrogate relaxation approach to derive a lower bound and an upper bound quickly, and show that the pegging test known for zero–one programming problems is also applicable to this problem. Next, we discuss how the computation time for pegging can be shortened by taking the special structure of the assignment problem into account. Finally, through numerical experiments we show that the developed method finds exact solutions for instances with small number of scenarios in relatively small CPU time, and good approximate solutions in case of many scenarios.

Suggested Citation

  • Byungjun You & Daisuke Yokoya & Takeo Yamada, 2012. "An Improved Reduction Method For The Robust Optimization Of The Assignment Problem," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 29(05), pages 1-14.
    • Handle: RePEc:wsi:apjorx:v:29:y:2012:i:05:n:s0217595912500327
    DOI: 10.1142/S0217595912500327
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    Cited by:

    1. Marc Goerigk, 2014. "A note on upper bounds to the robust knapsack problem with discrete scenarios," Annals of Operations Research, Springer, vol. 223(1), pages 461-469, December.

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