Application of the cross-entropy method to the dynamic assortment optimization problem

Abstract

This work considers an assortment optimization problem, under capacity constraint and unknown demand, where a retailer offers an assortment and observes the sale of one of the products according to a multinomial logit choice model. In this problem, named as the dynamic assortment optimization problem (DAOP), the retailer must offer different assortments in each period to learn the customer preferences. Therefore, the trade-off between exploration of new assortments and the exploitation of the best known assortment must be balanced. Similarities between sampling and exploration are established in order to apply the cross-entropy method as a policy for the solution of the DAOP. The cross-entropy method finds a probability distribution that samples an optimal solution by minimizing the cross-entropy between a target probability distribution and an arbitrarily selected probability distribution. This requires the DAOP to be formulated as a knapsack problem with a penalty for offering assortments that exceed capacity. The results are compared with adaptive exploration algorithms and, experimentally, the cross-entropy method shows competitive results. These results suggest that the cross-entropy method can be used to solve other sequential decision-making problems.