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The multiple-choice multi-period knapsack problem

Author

Listed:
  • Edward Y H Lin

    (National Taipei University of Technology, Taipei)

  • Chung-Min Wu

    (National Taipei University of Technology, Taipei)

Abstract

This paper introduces the multiple-choice multi-period knapsack problem in the interface of multiple-choice programming and knapsack problems. We first examine the properties of the multiple-choice multi-period knapsack problem. A heuristic approach incorporating both primal and dual gradient methods is then developed to obtain a strong lower bound. Two branch-and-bound procedures for special-ordered-sets type 1 variables that incorporate, respectively, a special algorithm and the multiple-choice programming technique are developed to locate the optimal solution using the above lower bound as the initial solution. A computer program written in IBM's APL2 is developed to assess the quality of this lower bound and to evaluate the performance of these two branch-and-bound procedures.

Suggested Citation

  • Edward Y H Lin & Chung-Min Wu, 2004. "The multiple-choice multi-period knapsack problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(2), pages 187-197, February.
    • Handle: RePEc:pal:jorsoc:v:55:y:2004:i:2:d:10.1057_palgrave.jors.2601661
    DOI: 10.1057/palgrave.jors.2601661
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    References listed on IDEAS

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    1. Yoshiaki Toyoda, 1975. "A Simplified Algorithm for Obtaining Approximate Solutions to Zero-One Programming Problems," Management Science, INFORMS, vol. 21(12), pages 1417-1427, August.
    2. Prabhakant Sinha & Andris A. Zoltners, 1979. "The Multiple-Choice Knapsack Problem," Operations Research, INFORMS, vol. 27(3), pages 503-515, June.
    3. Pisinger, David, 1995. "A minimal algorithm for the multiple-choice knapsack problem," European Journal of Operational Research, Elsevier, vol. 83(2), pages 394-410, June.
    4. Eugene L. Lawler, 1979. "Fast Approximation Algorithms for Knapsack Problems," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 339-356, November.
    5. Lin, Edward Y. H. & Bricker, Dennis L., 1991. "On the calculation of true and pseudo penalties in multiple choice integer programming," European Journal of Operational Research, Elsevier, vol. 55(2), pages 228-236, November.
    6. Bruce H. Faaland, 1981. "Technical Note—The Multiperiod Knapsack Problem," Operations Research, INFORMS, vol. 29(3), pages 612-616, June.
    7. Shizuo Senju & Yoshiaki Toyoda, 1968. "An Approach to Linear Programming with 0-1 Variables," Management Science, INFORMS, vol. 15(4), pages 196-207, December.
    8. Ronald D. Armstrong & Prabhakant Sinha & Andris A. Zoltners, 1982. "The Multiple-Choice Nested Knapsack Model," Management Science, INFORMS, vol. 28(1), pages 34-43, January.
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