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Technical Note—Some Very Easy Knapsack/Partition Problems

Author

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  • James B. Orlin

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

Abstract

Consider the problem of partitioning a group of b indistinguishable objects into subgroups, each of size at least l 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 − l + 1) steps. In the case that c (·) is concave, we solve the problem in O (min( l , b / u , ( b / l ) − ( b / u ), u − l )) steps. This problem generalizes a lot-sizing result of Chand and has potential applications in clustering.

Suggested Citation

  • James B. Orlin, 1985. "Technical Note—Some Very Easy Knapsack/Partition Problems," Operations Research, INFORMS, vol. 33(5), pages 1154-1160, October.
    • Handle: RePEc:inm:oropre:v:33:y:1985:i:5:p:1154-1160
    DOI: 10.1287/opre.33.5.1154
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    Cited by:

    1. van den Heuvel, Wilco & Wagelmans, Albert P.M., 2017. "A note on “A multi-period profit maximizing model for retail supply chain management”," European Journal of Operational Research, Elsevier, vol. 260(2), pages 625-630.

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