A perishable inventory model under stock-dependent selling rate and shortage-dependent partial backlogging with capacity constraint

This article develops a deterministic inventory model for perishable items with stock-dependent selling rate. In the model, the unsatisfied demand is partial backlogged and the backlogged demand rate is dependent on the negative inventory level during the stock-out period. Furthermore, a ceiling is imposed on the number of on-display stocks because too much inventory leaves a negative impression on the buyer and the amount of shelf space is limited. Next, the existence and uniqueness of the solution to the problem under two cases are examined, respectively. Then a solution procedure is shown to find the optimal replenishment policy of the considered problem. At last, two numerical examples and a real case study are presented to illustrate the application of the developed model.