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.

We consider inventory systems which are governed by an ( r , q ) or ( r , nq ) policy. We derive general conditions for monotonicity of the three optimal policy parameters, i.e., the optimal reorder level, order quantity and order-up-to level, as well as the optimal cost value, as a function of the various model primitives, be it cost parameters or complete cost rate functions or characteristics of the demand and leadtime processes. These results are obtained as corollaries from a few general theorems, with separate treatment given to the case where the policy parameters are continuous variables and that where they need to be restricted to integer values. The results are applied both to standard inventory models and to those with general shelf age and delay dependent inventory costs.