Preservation of Multimodularity: New Results and Applications

Preserving Multimodular Structure in Substitution Models Substitution is common in operations problems, where one product or resource may be used to satisfy demand intended for another. In models with multiple resources and demand classes, this flexibility makes it harder to establish structural properties of optimal dynamic decisions. In “Preservation of Multimodularity: New Results and Applications,” Tong Wang, Li Xiao, and Fen Xu develop two new preservation results for multimodularity, a key property for deriving monotonicity and bounded sensitivity of optimal decisions. The first applies to one-way substitution, such as upgrading, and the second extends to two-way substitution under suitable cost and priority conditions. A central insight is that when allocation priorities are determined by marginal cost or value inequalities, both multimodularity and these inequalities are preserved after optimization. Applications include dynamic capacity management, remanufacturing inventory systems with lost sales, buyer-item matching on resale platforms, and multilocation transshipment.