Preservation of Multimodularity: New Results and Applications

This paper establishes two new preservation results of multimodularity for two classes of resource allocation problems, where multiple resources can be used to satisfy multiple demands. Our results show that if allocation priorities between multiple resources and demands are determined by several marginal cost/value inequalities of the objective function, then the multimodularity and marginal cost/value inequalities are both preserved after optimization. We demonstrate their applications to several stochastic optimization problems, including dynamic capacity management problem with general upgrading, remanufacturing inventory systems with multiple return types under the lost-sales setting, buyer-item matching on resale platforms, and dynamic transshipment across multiple locations.

Funding: T. Wang is partially supported by the National Natural Science Foundation of China [Grants 72222008, 72192833/72192830, 72571231, 72131010, and 72221001], and the Research Grants Council of Hong Kong [Grant GRF 11502225]. L. Xiao is partially supported by the National Natural Science Foundation of China [Grant 72271140], and University of Macau [Grants MYRG-GRG2025-00173-FBA and SRG2025-00013-FBA].