Simple strategies that generate bounded solutions for the multiple-choice multi-dimensional knapsack problem: a guide for OR practitioners

The multiple-choice multi-dimensional knapsack problem (MMKP) is an NP-hard generalization of the classic 0-1 knapsack problem. The MMKP has a variety of important industrial and business applications. Approximate solution approaches characteristically give no guarantees on solution quality. Exact solution approaches usually generate solutions that are guaranteed to be close to the optimum but typically take excessive computation times-one to several hours have been recorded in the literature. In this article, we use both simple single-step and multiple step strategies to demonstrate how a commercial software package (Gurobi in this case) can easily be used to generate guaranteed tightly bounded solutions for 293 MMKP instances commonly tested in the literature. These four simple strategies that require no problem-specific algorithms are shown to perform competitively with the five best published algorithms for the MMKP. Since no problem-specific coding is required, these simple strategies are easy for operations research practitioners to use.