Dynamic Assortment Optimization with a Multinomial Logit Choice Model and Capacity Constraint

The paper considers a stylized model of a dynamic assortment optimization problem, where given a limited capacity constraint, we must decide the assortment of products to offer to customers to maximize the profit. Our model is motivated by the problem faced by retailers of stocking products on a shelf with limited capacities and by the problem of placing a limited number of ads on a web page. We assume that each customer chooses to purchase the product (or to click on the ad) that maximizes her utility. We use the multinomial logit choice model to represent demand. However, we do not know the demand for each product. We can learn the demand distribution by offering different product assortments, observing resulting selections, and inferring the demand distribution from past selections and assortment decisions. We present an adaptive policy for joint parameter estimation and assortment optimization. To evaluate our proposed policy, we define a benchmark profit as the maximum expected profit that we can earn if we know the underlying demand distribution in advance. We show that the running average expected profit generated by our policy converges to the benchmark profit and establish its convergence rate. Numerical experiments based on sales data from an online retailer indicate that our policy performs well, generating over 90% of the optimal profit after less than two days of sales. 1. Motivation and Problem Formulation Companies have realized the importance of offering products that are tailored to the demand of customers in each region. For instance, Wal-mart stocks specific lines of clothes targeted exclusively to certain groups of customers (Zimmerman (2006)). Car manufacturers are well-known for ∗School of Operations Research and Information Engineering, Cornell University, Ithaca, NY 14853, USA. E-mail: [email protected] †Department of Industrial Engineering and Operations Research, University of California–Berkeley, 4129 Etcheverry Hall, Berkeley, CA 94720, USA. E-mail: [email protected] ‡School of Operations Research and Information Engineering and Department of Computer Science, Cornell University, Ithaca, NY 14853, USA. E-mail: [email protected]