Multiunit dynamic pricing with different types of observable customer information

Abstract

AbstractIn various sectors, such as retail, firms encounter customers with multiunit demand and often implement nonlinear pricing to accommodate this demand structure. While effective, this pricing strategy lacks the adaptability offered by dynamic pricing, a trend gaining significance in the retail landscape due to technological advancements. Neglecting multiunit demand in dynamic pricing, however, can result in suboptimal prices and revenue losses. In response, this paper introduces multiunit dynamic pricing which integrates the strengths of both nonlinear and dynamic pricing strategies. We formulate a stage-wise optimization problem, considering customer preferences for batches of a product through a model based on random willingness-to-pay. The willingness-to-pay is influenced by a combination of the customer’s attraction to and consumption of the product—both private information. The firm, functioning as a monopoly, has the ability to price-discriminate between various order sizes by quoting nonlinear batch prices. Our investigation explores three cases of observable information: attraction to the product, consumption of the product, or both. Optimality conditions are derived for all cases, establishing a closed-form expressions for two of them. Additionally, we demonstrate the preservation of desirable monotonicity in time and capacity. Leveraging this monotonicity, we showcase the dynamics of the optimal pricing policy. A simulation study underscores the potential of our approach, highlighting the value of information in supporting strategic decisions, particularly regarding investments in customer profiling and segmentation. Furthermore, we illustrate how our solutions enable firms to make informed stocking and restocking decisions, providing practical insights for firms in multiunit dynamic pricing environments.