Joint pricing and inventory decisions for substitutable and perishable products under demand uncertainty

In this paper, we develop a model for dynamic pricing and inventory decisions for multiple substitutable and perishable products under a multiple-period lifetime. Retailers place orders at the beginning of the first period, and products will be sold at full price during that period. All leftover products will then be carried over to the subsequent periods and sold at discounted prices. Demands for leftover products are assumed to follow a linear stochastic model depending on the discounted prices of the substitutable products. The optimal order quantities and prices are obtained by maximizing the total expected profit over the lifetime, taking into account the revenue, the backorder cost and the holding cost. We provide analytical properties of the optimal policy such as the concavity of the value functions and then utilise these in the numerical scheme for finding the optimal prices and ordering quantities. Experimental results are reported through a case study of a high-street fashion company, demonstrating the benefits of considering pricing and inventory decisions simultaneously for substitutable products.