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The Linear Multiple Choice Knapsack Problem

Author

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  • Eitan Zemel

    (Northwestern University, Evanston, Illinois)

Abstract

A fast algorithm is presented for the linear programming relaxation of the Multiple Choice Knapsack Problem. If N is the total number of variables and J and J max denote the total number of multiple choice variables and the cardinality of the largest multiple choice set, respectively, the running time of the algorithm is then bounded by 0( J log J max ) + 0( N ). Under certain conditions it is possible to reduce this bound to 0( N ) steps on the average. Possible further improvements are also discussed.

Suggested Citation

  • Eitan Zemel, 1980. "The Linear Multiple Choice Knapsack Problem," Operations Research, INFORMS, vol. 28(6), pages 1412-1423, December.
    • Handle: RePEc:inm:oropre:v:28:y:1980:i:6:p:1412-1423
    DOI: 10.1287/opre.28.6.1412
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    Citations

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    Cited by:

    1. 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.
    2. Boysen, Nils & Fliedner, Malte, 2008. "A versatile algorithm for assembly line balancing," European Journal of Operational Research, Elsevier, vol. 184(1), pages 39-56, January.
    3. Tue R. L. Christensen & Kim Allan Andersen & Andreas Klose, 2013. "Solving the Single-Sink, Fixed-Charge, Multiple-Choice Transportation Problem by Dynamic Programming," Transportation Science, INFORMS, vol. 47(3), pages 428-438, August.
    4. Bagchi, Ansuman & Bhattacharyya, Nalinaksha & Chakravarti, Nilotpal, 1996. "LP relaxation of the two dimensional knapsack problem with box and GUB constraints," European Journal of Operational Research, Elsevier, vol. 89(3), pages 609-617, March.
    5. Schulze, Philipp & Scholl, Armin & Walter, Rico, 2024. "R-SALSA: A branch, bound, and remember algorithm for the workload smoothing problem on simple assembly lines," European Journal of Operational Research, Elsevier, vol. 312(1), pages 38-55.
    6. Walter, Rico & Schulze, Philipp & Scholl, Armin, 2021. "SALSA: Combining branch-and-bound with dynamic programming to smoothen workloads in simple assembly line balancing," European Journal of Operational Research, Elsevier, vol. 295(3), pages 857-873.
    7. 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.
    8. Wilbaut, Christophe & Todosijevic, Raca & Hanafi, Saïd & Fréville, Arnaud, 2023. "Heuristic and exact reduction procedures to solve the discounted 0–1 knapsack problem," European Journal of Operational Research, Elsevier, vol. 304(3), pages 901-911.
    9. Nikolaos Argyris & José Figueira & Alec Morton, 2011. "Identifying preferred solutions to Multi-Objective Binary Optimisation problems, with an application to the Multi-Objective Knapsack Problem," Journal of Global Optimization, Springer, vol. 49(2), pages 213-235, February.
    10. Endre Boros & Noam Goldberg & Paul Kantor & Jonathan Word, 2011. "Optimal sequential inspection policies," Annals of Operations Research, Springer, vol. 187(1), pages 89-119, July.

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