Optimal replenishment policy for perishable items with stock-dependent selling rate and capacity constraint

In this paper, a deterministic inventory model is developed for deteriorating items with stock-dependent demand and finite shelf/display space. Furthermore, we allow for shortages and the unsatisfied demand is partially backlogged at the exponential rate with respect to the waiting time. We provide solution procedures for finding the maximum total profit per unit time. In a specific circumstance, the model will reduce to the case with no shortage. Further, we use numerical examples to illustrate the model.