An EOQ Model for Perishable Items with Supply Uncertainty

This paper aims to develop a continuous inventory model for finding the strategy for a retailer that sells a seasonal perishable item over a finite planning time. The purpose of this retailer is to maximize the expected profit by choosing an optimal ordering quantity before the sales horizon and adopting an optimal pricing policy during the sales horizon. With the help of Pontryagin's maximum principle, we can obtain the optimal ordering quantity and the optimal pricing policy by solving a list of equations. For a special case, we not only characterize the structure of the optimal pricing policy for any given initial inventory level but also obtain the optimal solutions by solving a set of equations. A numerical analysis reveals the influence of some parameters on the optimal ordering quantity.