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.

经典0-1背包问题的一个重要推广是多需求多维背包问题（MDMKP）。除了理论上难以解决（它是 NP 难的）之外，由于背包和需求限制相互冲突，在实践中也可能难以解决。由于 MDMKP 有重要的大规模应用，因此通常使用近似解法来解决这些问题。然而，使用文献中讨论的 1620 个 MDMKP，本文演示了运筹学从业者可以在标准个人计算机上使用通用整数编程软件在最优值的 0.1% 内有效地解决哪些类型的大型 MDMKP。统计分析用于确定哪些问题参数显着影响求解时间。最后，基于这 1620 个 MDMKP 实例，生成分类树。该树可用于指导从业者解决商业和工业中出现的 MDMKP。