An inventory model for deteriorating items with stock-dependent selling rate and partial backlogging under inflation

This paper presents an inventory model for deteriorating items with stock-dependent selling rate under inflation and time value of money over a finite planning horizon. In the model, shortages are allowed and the unsatisfied demand is partially backlogged at the exponential rate with respect to the waiting time. We establish the theoretical results and provide an efficient solution procedure to find the optimal number of replenishment and the cycle time. Then, the optimal order quantity and the total present value of profits are obtained. A numerical example and sensitivity analysis are presented to illustrate the proposed model and particular cases of the model are also discussed.