Optimal dynamic pricing of perishable products with demand substitution

This paper addresses the problem of optimal dynamic pricing of perishable products when demand is substitutable. Namely, when a firm sells homogeneous products with different qualities or packages at the same time, demands according to different classes are spilling, based on the prices, inventory on hand and the customers' willing-to-pay. We consider one firm sell two kinds of product at the same time, of which one is old and the other is newly into the market. We show that the marginal value of the old product is decreasing in both inventory and the selling period left. Furthermore, we find that old product's marginal value will decrease with the entrance of new products into the market. We also apply the theory of maximal concave envelope into simplifying the computation process. A numerical example is provided.