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The knapsack problem with disjoint multiple‐choice constraints

Author

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  • Vijay Aggarwal
  • Narsingh Deo
  • Dilip Sarkar

Abstract

In this article we consider the binary knapsack problem under disjoint multiple‐choice constraints. We propose a two‐stage algorithm based on Lagrangian relaxation. The first stage determines in polynomial time an optimal Lagrange multiplier value, which is then used within a branch‐and‐bound scheme to rank‐order the solutions, leading to an optimal solution in a relatively low depth of search. The validity of the algorithm is established, a numerical example is included, and computational experience is described.

Suggested Citation

  • Vijay Aggarwal & Narsingh Deo & Dilip Sarkar, 1992. "The knapsack problem with disjoint multiple‐choice constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(2), pages 213-227, March.
    • Handle: RePEc:wly:navres:v:39:y:1992:i:2:p:213-227
    DOI: 10.1002/nav.3220390206
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    References listed on IDEAS

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    1. Eitan Zemel, 1980. "The Linear Multiple Choice Knapsack Problem," Operations Research, INFORMS, vol. 28(6), pages 1412-1423, December.
    2. Marshall L. Fisher, 1981. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 27(1), pages 1-18, January.
    3. Prabhakant Sinha & Andris A. Zoltners, 1979. "The Multiple-Choice Knapsack Problem," Operations Research, INFORMS, vol. 27(3), pages 503-515, June.
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