Coordinating Inventory and Pricing Decisions with General Price-Dependent Demands

We consider a periodic review, joint inventory and pricing control problem for a firm that faces general random price-dependent demands. Any unsatisfied demand can be either backordered or lost immediately. The objective is to maximize the expected profit over a finite selling horizon by coordinating the inventory and pricing decisions in each period. For both the backorder model and the lost sales model, we derive some quite general sufficient conditions to ensure the optimality of a base-stock list price (BSLP) policy based on the strict monotonicity of demand functions in the realizations of random noises. We are among the first to utilize the strict monotonicity of demand functions in the realizations of random noises for deriving the sufficient conditions. We derive the sufficient conditions in both the backorder model and the lost-sales model by utilizing the new concept of upper-set and lower-set decreasing properties (USDP/LSDP), which is a generalized version of the first-order stochastic dominance. This study reveals that the optimality of a BSLP policy is robust to more general business environments than what we previously thought. Finally, we also apply the USDP/LSDP in other inventory management problems.