Multimodularity and Its Applications in Three Stochastic Dynamic Inventory Problems

Abstract

We apply the concept of multimodularity in three stochastic dynamic inventory problems in which state and decision variables are economic substitutes. The first is clearance sales of perishable goods. The second is sourcing from multiple suppliers with different lead times. The third is transshipment under capacity constraints. In all three problems, we establish monotone optimal polices with bounded sensitivity. Multimodularity proves to be an effective tool for these problems because it implies substitutability, it is preserved under minimization, and it leads directly to monotone optimal policies with bounded sensitivity.