Inventory Models with Shelf-Age and Delay-Dependent Inventory Costs

In this paper, we show how any model with a general shelf-age-dependent holding cost and delay-dependent backlogging cost structure may be transformed into an equivalent model in which all expected inventory costs are level dependent. We develop our equivalency results, first, for periodic review models with full backlogging of stockouts. These equivalency results permit us to characterize the optimal procurement strategy in various settings and to adopt known algorithms to compute such strategies. For models in which all or part of stockouts are lost, we show that the addition of any shelf-age and delay-dependent cost structure does not complicate the structure of the model beyond what is required under the simplest, i.e., linear, holding and backlogging costs. We proceed to show that our results carry over to continuous review models, with demands generated by compound renewal processes; the continuous review models with shelf-age and delay-dependent carrying and backlogging costs are shown to be equivalent to periodic review models with convex level-dependent inventory cost functions.