Inventory and pricing strategies for deteriorating items with limited capacity and time-proportional backlogging rate

In the present study, a two-warehouse deterministic inventory model for deteriorating items with price-sensitive demand is developed. A rented warehouse (RW) is used to store the excess units over the fixed capacity of the own warehouse (OW). In addition, shortages are allowed in the OW and it is assumed that the backlogging demand rate is dependent on the duration of the stock-out. The objective is to find the optimal inventory and pricing strategies maximising the total average profit over the infinite planning horizon. For any given selling price, we first prove that the optimal replenishment schedule not only exists but is unique. Next, we show that the total average profit is a concave function of price when the replenishment schedule is given. The optimal selling price and replenishment schedule is also calculated for the proposed model. Finally, the results have been validated with the help of a numerical example.