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Multiple subset sum with inclusive assignment set restrictions

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  • Hans Kellerer
  • Joseph Y.‐T. Leung
  • Chung‐Lun Li

Abstract

In a traditional multiple subset sum problem (MSSP), there is a given set of items and a given set of bins (or knapsacks) with identical capacities. The objective is to select a subset of the items and pack them into the bins such that the total weight of the selected items is maximized. However, in many applications of the MSSP, the bins have assignment restrictions. In this article, we study the subset sum problem with inclusive assignment set restrictions, in which the assignment set of one item (i.e., the set of bins that the item may be assigned to) must be either a subset or a superset of the assignment set of another item. We develop an efficient 0.6492‐approximation algorithm and test its effectiveness via computational experiments. We also develop a polynomial time approximation scheme for this problem. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011

Suggested Citation

  • Hans Kellerer & Joseph Y.‐T. Leung & Chung‐Lun Li, 2011. "Multiple subset sum with inclusive assignment set restrictions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(6), pages 546-563, September.
    • Handle: RePEc:wly:navres:v:58:y:2011:i:6:p:546-563
    DOI: 10.1002/nav.20466
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    References listed on IDEAS

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    1. M. Dawande & J. Kalagnanam & P. Keskinocak & F.S. Salman & R. Ravi, 2000. "Approximation Algorithms for the Multiple Knapsack Problem with Assignment Restrictions," Journal of Combinatorial Optimization, Springer, vol. 4(2), pages 171-186, June.
    2. Leung, Joseph Y.-T. & Li, Chung-Lun, 2008. "Scheduling with processing set restrictions: A survey," International Journal of Production Economics, Elsevier, vol. 116(2), pages 251-262, December.
    3. Geir Dahl & Njål Foldnes, 2006. "LP based heuristics for the multiple knapsack problem with assignment restrictions," Annals of Operations Research, Springer, vol. 146(1), pages 91-104, September.
    4. Jinwen Ou & Joseph Y.‐T. Leung & Chung‐Lun Li, 2008. "Scheduling parallel machines with inclusive processing set restrictions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(4), pages 328-338, June.
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    Cited by:

    1. Goldberg, Noam & Karhi, Shlomo, 2019. "Online packing of arbitrary sized items into designated and multipurpose bins," European Journal of Operational Research, Elsevier, vol. 279(1), pages 54-67.
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    3. Huiqiao Su & Michael Pinedo & Guohua Wan, 2017. "Parallel machine scheduling with eligibility constraints: A composite dispatching rule to minimize total weighted tardiness," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(3), pages 249-267, April.
    4. Xueqi Wu & Zhi‐Long Chen, 2022. "Fulfillment scheduling for buy‐online‐pickup‐in‐store orders," Production and Operations Management, Production and Operations Management Society, vol. 31(7), pages 2982-3003, July.

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