A General Algorithm for One-Dimensional Knapsack Problems

Giorgio P. Ingargiola and James F. Korsh
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Giorgio P. Ingargiola: Temple University, Philadelphia, Pennsylvania
James F. Korsh: Temple University, Philadelphia, Pennsylvania

Operations Research, 1977, vol. 25, issue 5, 752-759

Abstract: This paper presents a reduction algorithm and a branch-search algorithm that, in sequence, allow the solution of sizeable problems of the form: maximize ∑ i =1 N c i x i , subject to ∑ i =1 N l i x i ≦ s and 0 ≦ x i ≦ b i and integer, 1 ≦ i ≦ N . The reduction algorithm is proportional to N in space and proportional to N ∑ i =1 N b i in time. The branch-search algorithm's space requirement is linear in N . Computational experience with these algorithms is presented.

Date: 1977
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