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We study a single-item, periodic-review inventory system with one or two supply sources and the simultaneous presence of the following major practical complications: (1) bilateral inventory adjustment options, via procurement orders and salvage sales or returns to the supplier; (2) fixed costs associated with procurement orders and salvage sales or returns; (3) capacity limits associated with upward or downward inventory adjustments. In the single sourcing setting, we characterize the optimal adjustment strategy, both for finite and infinite horizon models, by showing that in each period the inventory position line is to be partitioned into (maximally) five regions. In the dual sourcing setting, the regular and expedited suppliers are differentiated by their per-unit cost and lead time, resulting in a trade-off between cost and responsiveness. We obtain a two-stage optimal policy structure under a unit lead time difference. We develop effective heuristics for general lead time combinations. Numerical studies provide insights into the factors impacting on the value of dual sourcing, that of a salvage option and capacity investments in the primary and dual source.
Our results are obtained by identifying a novel generalized convexity property for the value functions, termed as strong (C1K1, C2K2)-convexity. To our knowledge, we recover almost all existing structural results for inventory models with exogenous demands as special cases of a unified analysis.