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Some Very Easy Knapsack/Partition Problems

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  • Orlin, J. B.

Abstract

Consider the problem of partitioning a group of b indistinguishable objects into subgroups each of size at least X and at most u. The objective is to minimize the additive separable cost of the partition, where the cost associated with a subgroup of size j is c(j). In the case that c(.) is convex, we show how to solve the problem in O(log u) steps. In the case that c(.) is concave, we solve the problem in 0(min(X, b/u, (b/k)—(b/u), u—X)) steps. This problem generalizes a lot—sizing result of Chand and has potential applications in clustering.

Suggested Citation

  • Orlin, J. B., 1984. "Some Very Easy Knapsack/Partition Problems," Econometric Institute Archives 272288, Erasmus University Rotterdam.
    • Handle: RePEc:ags:eureia:272288
    DOI: 10.22004/ag.econ.272288
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    References listed on IDEAS

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    1. Prabhakant Sinha & Andris A. Zoltners, 1979. "The Multiple-Choice Knapsack Problem," Operations Research, INFORMS, vol. 27(3), pages 503-515, June.
    2. Eric V. Denardo & Bennett L. Fox, 1979. "Shortest-Route Methods: 2. Group Knapsacks, Expanded Networks, and Branch-and-Bound," Operations Research, INFORMS, vol. 27(3), pages 548-566, June.
    3. Chand, Suresh, 1982. "Lot sizing for products with finite demand horizon and periodic review inventory policy," European Journal of Operational Research, Elsevier, vol. 11(2), pages 145-148, October.
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