Generating bounded solutions for multi-demand multidimensional knapsack problems: a guide for operations research practitioners

A generalization of the 0-1 knapsack problem that is hard-to-solve both theoretically (NP-hard) and in practice multi-demand multidimensional (MDMKP). Solving an MDMKP can be difficult because its conflicting demand constraints. Approximate solution approaches provide no guarantees on quality. Recently, with use classification trees, MDMKPs were partitioned into three general categories based their expected performance using integer programming option CPLEX® software package a standard PC: Category A—relatively easy to solve, B—somewhat C—difficult solve. However, methods associated these categories. The primary contribution this article it demonstrates, customized each category, how general-purpose (CPLEX case) iteratively used efficiently generate bounded solutions for MDMKPs. Specifically, simple sequential increasing tolerance (SSIT) methodology will CPLEX loosening tolerances solutions. real strength approach SSIT particular category (A, B, or C) instance being solved. This practitioners requires time-consuming effort coding specific-algorithms. Statistical analyses compare results single-pass execution terms time