Optimal Inventory Control of Obsolete Products with Price-Dependent Demand

Since pricing is recognized as one of the most important tools for profit optimization, price competition is one of the major issues facing companies. Determining the appropriate inventory control policy and optimal selling price of various products is a major subject of scientific and industrial research in recent years. On the other hand, today, some of the products on the market have the potential to become obsolete, which means that their demand is reduced at once with the development of new technology. Therefore, determining the optimal price and inventory policies for these types of products is very crucial. In this research, an inventory control model for a retailer is formulated to optimize the inventory and pricing decisions for profit maximization simultaneously. According to the problem assumptions, demand is price-dependent, the time that product becomes obsolete has an exponential distribution, the type of product obsolescence is also sudden, and the retailer determines the optimum price and order quantity of replenishment. The proposed model has a nonlinear profit function, in which the partial derivatives of the objective function are used to reach the optimal value. Finally, the effects of various parameters such as the speed of obsolescence, the holding cost of each item unit, the cost of selling obsolete items, and the purchasing price were studied on the total profit. For this purpose, a numerical example is solved along with a sensitivity analysis to evaluate the validity of the model and investigate the effect of parameters on the optimal solution. The key achievement of this study was the development of a new model and providing a solution to determine the optimal values of product sales price and retailer order quantity with maximum profit.