Optimal Dynamic Joint Pricing and Inventory Control for Multiplicative Demand with Fixed Order Costs and Lost Sales

In this paper we study the optimal dynamic decision-making problem for a retailer selling a single product and facing price-sensitive, stochastic (multiplicative) demand in each period. Any leftover inventory for a period is carried over and charged a holding cost at the end of the period. Leftovers at the end of the selling horizon earn a non-negative salvage value. On the other hand, any unsatisfied demand, and associated revenue, is lost to the system. The purchasing cost for the retailer includes both variable and fixed components. The objective of the retailer is to maximize its discounted expected profit over the selling horizon by dynamically deciding on the optimal pricing and inventory control policy for each period. Under some mild conditions on the model parameters, we characterize the structure of the retailer’s optimal inventory policy, and specify the optimal price to charge in each period, for both finite and infinite selling horizons.