Dynamic Inventory–Pricing Control Under Backorder: Demand Estimation and Policy Optimization

Inventory-based dynamic pricing has become a common operations strategy in practice and has received considerable attention from the research community. From an implementation perspective, it is desirable to design a simple policy like a base-stock list-price (BSLP) policy. The existing research on this problem often imposes restrictive conditions to ensure the optimality of a BSLP policy, which limits its applicability in practice. In this paper, we analyze the dynamic inventory and pricing control problem in which the demand follows a generalized additive model (GAM). The GAM overcomes the limitations of several demand models commonly used in the literature, but introduces analytical challenges in analyzing the dynamic program. Via a variable transformation approach, we identify a new set of technical conditions under which a BSLP policy is optimal. These conditions are easy to verify because they depend only on the location and scale parameters of demand as functions of price and are independent of the cost parameters or the distribution of the random demand component. Moreover, although a BSLP policy is optimal under these conditions, the optimal price may not be monotone decreasing in the inventory level. We further demonstrate our results by applying a constrained maximum likelihood estimation procedure to simultaneously estimate the demand function and verify the optimality of a BSLP policy on a retail data set.