TY - JOUR
AU1 - Xu, Zhou
AB - 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
TI - The knapsack problem with a minimum filling constraint
JF - Naval Research Logistics: An International Journal
DO - 10.1002/nav.21520
DA - 2013-02-01
UR - https://www.deepdyve.com/lp/wiley/the-knapsack-problem-with-a-minimum-filling-constraint-07ooILtxWI
SP - 56
EP - 63
VL - 60
IS - 1
DP - DeepDyve
ER -