The knapsack problem with a minimum filling constraint

Zhou Xu

Naval Research Logistics (NRL), 2013, vol. 60, issue 1, 56-63

Abstract: We study a knapsack problem with an additional minimum filling constraint, such that the total weight of selected items cannot be less than a given threshold. The problem has several applications in shipping, e‐commerce, and transportation service procurement. When the threshold equals the knapsack capacity, even finding a feasible solution to the problem is NP‐hard. Therefore, we consider the case when the ratio α of threshold to capacity is less than 1. For this case, we develop an approximation scheme that returns a feasible solution with a total profit not less than (1 ‐ ε) times the total profit of an optimal solution for any ε > 0, and with a running time polynomial in the number of items, 1/ε, and 1/(1‐α). © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2013

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:wly:navres:v:60:y:2013:i:1:p:56-63

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