Joint control of inventory and its pricing for non‐instantaneously deteriorating items under permissible delay in payments and partial backlogging

In this paper we consider a joint pricing and inventory control model for non‐instantaneously deteriorating items with permissible delay in payments. We adopt a demand function which is dependent on the price and time. Shortage is allowed and partially backlogged. The major objective is to determine the optimal selling price, the optimal replenishment schedule and the optimal order quantity simultaneously such that the total profit is maximized. On the basis of the aforementioned assumptions, for any given selling price, we first establish conditions for an optimal replenishment schedule to exist and be unique. Then, we show that the total profit is a concave function of price. Next, we present a simple algorithm for finding the optimal solution. Finally, to illustrate the solution procedure and the algorithm, we solve a numerical example.