Dynamic Joint Assortment and Pricing Optimization with Demand Learning

Problem definition: We consider a joint assortment optimization and pricing problem where customers arrive sequentially and make purchasing decisions following the multinomial logit (MNL) choice model. Not knowing the customer choice parameters a priori and subjecting to a display capacity constraint, we dynamically determine the subset of products for display and the selling prices to maximize the expected total revenue over a selling horizon. Academic/practical relevance: Assortment and pricing are important decisions for firms such as online retailers and have received enormous attention in the operations literature. In this paper, we present the first learning algorithm for the dynamic joint assortment optimization and pricing problem (based on theMNLchoice model) when the firm has limited prior knowledge about customer demand. Methodology: We design a learning algorithm that balances the trade-off between demand learning and revenue extraction, and we evaluate the performance of the algorithm using Bayesian regret. This algorithm uses the method of random sampling to simultaneously learn the demand and maximize the revenue on the fly. Results: An instance-independent upper bound for the Bayesian regret of the algorithm is obtained, and numerical results show that it performs very well. Managerial implications: Our work is the first to develop an effective learning algorithm for the joint assortment and pricing optimization problem when customer demand information is not known a priori. The algorithm concurrently learns customer demand while making adaptive assortment and pricing decisions, and it is an effective approach for revenue maximization.