Coordinating Dynamic Personalized Pricing and Inventory Decisions

Due to the availability of data-driven customer profiling, many firms (e.g., Amazon) have adopted personalized pricing in practice. We consider a joint dynamic personalized pricing-inventory control problem for a firm that sells a single product to multiple customer segments over a finite selling season. In each period, the demand of each customer segment is stochastic and price-dependent, and any unsatisfied demand is backordered. The firm's objective is to decide on the personalized pricing and ordering policies in order to maximize the expected profit over the planning horizon. We find that, under the mixture of additive and multiplicative demand models, a base-stock personalized price (BSPP) policy is optimal. For the special case with only the additive (resp. multiplicative) demand model, we derive a sequential property that is determined by the (resp. normalized) marginal revenues of different customer segments. Moreover, when the demands are linearly price-dependent under the additive demand model, a uniform adjustment policy for personalized pricing is optimal. Exploiting the BSPP policy, we further provide sufficient conditions (i.e., stationary parameter settings) under which a myopic policy is optimal. Our results provide guidelines for firms on how to coordinate personalized pricing and inventory in practice. We also numerically investigate the benefits of personalized pricing and compare it with uniform pricing. We find that personalized pricing can reap significant benefits (e.g., increasing profit up to 30%). Finally, we show that our results are robust to the settings with correlated demands and limited capacities