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An important generalization of the classic 0-1 knapsack problem is the multi-demand multidimensional knapsack problem (MDMKP). In addition to being theoretically difficult to solve (it is NP-hard), it can be in practice difficult to solve because of its conflicting knapsack and demand constraints. Since there are significant large-scale applications of the MDMKP, approximate solution approaches are commonly used to solve these problems. However, using 1620 MDMKPs discussed in the literature, this article demonstrates which types of large MDMKPs can be solved efficiently by operations research practitioners using general purpose integer programming software on a standard personal computer within 0.1% of optimum. Statistical analyses are used to determine which problem parameters significantly impact solution time. Finally, based on these 1620 MDMKP instances, a classification tree is generated. This tree can be used to guide practitioners in solving MDMKPs that arise in business and industry.

When to use Integer Programming Software to solve large multi-demand multidimensional knapsack problems: a guide for operations research practitioners