Technical Note—Some Very Easy Knapsack/Partition Problems

James B. Orlin
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James B. Orlin: Massachusetts Institute of Technology, Cambridge, Massachusetts

Operations Research, 1985, vol. 33, issue 5, 1154-1160

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.

Keywords: 702; some; very; easy; knapsack/partition; problems (search for similar items in EconPapers)
Date: 1985
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