Modeling pricing and inventory control for perishable agricultural items under return to manufacture

In this paper, a joint pricing and inventory control model for perishable agricultural items is developed. The model is studied under a price and time-dependent demand function, also the return to manufacturer are considered as a function of both price and order quantity. The main objective is determining the optimal selling price, the optimal replenishment cycles, and the optimal order quantity simultaneously as it is, the total profit is maximized within a finite time horizon. Firstly, we show that for any selling price, the optimal replenishment cycle exists and is unique. Then, we indicate that the total profit is a concave function of price. Next, a simple algorithm has been presented to find the optimal solution. A numerical example is then taken to illustrate the solution procedure and the algorithm.