Optimal pricing policy for stock dependent demand with effective investment in preservation technology

In this paper, we suggested an optimal pricing policy for deteriorating items. To reduce the rate of  deterioration, we apply a preservation technology and calculate the optimal preservation technology  investment. The demand function is dependent on time, stock and selling price. Shortages are allowed in our consideration, and two cases are studied, first complete back-ordering and the second one is partially back-ordering. Our main objective is to find the optimal cycle length, ordering frequency the optimal preservation technology investment and the optimal selling price that maximizes the total profit. This model proves that the total profit is a concave function of the selling price, ordering frequency, preservation technology investment and time cycle. Numerical examples are provided to illustrate the features and advances of the model. A sensitivity analysis is performed in order to assess the stability of the proposed model.