Synthesis and Generalization of Structural Results in Inventory Management: A Generalized Convexity Property

We address a general periodic review inventory control model with the simultaneous presence of the following complications: (a) bilateral inventory adjustment options, via procurement orders and salvage sales or returns to the supplier; (b) fixed costs associated with procurement orders and downward inventory adjustments (via salvage sales or returns); and (c) capacity limits associated with upward or downward inventory adjustments. We characterize the optimal adjustment strategy, both for finite and infinite horizon periodic review models, by showing that in each period the inventory position line is to be partitioned into (maximally) five regions. Our results are obtained by identifying a novel generalized convexity property for the value functions, which we refer to as strong (C1K1, C2K2)-convexity. To our knowledge, we recover most existing structural results for models with exogenous demands as special cases of a unified analysis.