The binary knapsack problem with qualitative levels

A variant of the classical knapsack problem is considered in which each item is associated with an integer weight and a qualitative level. We define a dominance relation over the feasible subsets of the given item set and show that this relation defines a preorder. We propose a dynamic programming algorithm to compute the entire set of non-dominated rank cardinality vectors and we state two greedy algorithms, which efficiently compute a single efficient solution. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

This study explores a variant of the knapsack problem and proposes dynamic programming and greedy algorithms to compute non-dominated rank cardinality vectors and efficient solutions.