Determining The Optimal Ordering Policy In A Multi-Period Stochastic Model With The Uncertainty Purchase Price

This paper deals with a two-period inventory planning and control problem with stochastic demand. In this system, a distributor can order the products in a preseason period and sell them in two subsequent selling periods. Demand during the first period is a random variable with a known probability distribution, while the demand for the remaining products at the end of the first period depends on their selling price during the second period. Therefore, the selling price of end-of-period products is very important so that a low price will achieve more sales. It is also assumed that the purchase price of the products in the preseason period is a time-dependent and follows a random process. For the considered problem, a mathematical model is suggested and then using the probabilistic dynamic planning approach, the optimal selling price at the second period, the optimal ordering quantity, and the purchase price of the products are determined to maximize the system profit. Finally, a numerical example is presented to investigate the performance of the model, and the sensitivity analysis of the main parameters.