L-Convexity and Its Applications in Operations

L-convexity, one of the central concepts in discrete convex analysis, receives significant attentions in the operations literature in recent years as it provides a powerful tool to derive structures of optimal policies and allows for efficient computational procedures. In this paper, we present a survey of key properties of L-convexity and some closely related results in lattice programming, several of which were developed recently and motivated by operations applications. As a new contribution to the literature, we establish the relationship between a notion called μ-differential monotonicity and L-convexity. We then illustrate the techniques of applying L-convexity through a detailed analysis of a perishable inventory model and a joint inventory and transshipment control model with random capacities.