Assortment Optimization under the Decision Forest Model

Abstract

The decision forest model is a recently proposed nonparametric choice model that is capable of representing any discrete choice model and in particular, can be used to represent non-rational customer behavior. In this paper, we study the problem of finding the assortment that maximizes expected revenue under the decision forest model. This problem is of practical importance because it allows a firm to tailor its product offerings to profitably exploit deviations from rational customer behavior, but at the same time is challenging due to the extremely general nature of the decision forest model. We approach this problem from a mixed-integer optimization perspective and propose three different formulations. We theoretically compare these formulations in strength, and analyze when these formulations are integral in the special case of a single tree. We propose a methodology for solving these problems at a large-scale based on Benders decomposition, and show that the Benders subproblem can be solved efficiently by primal-dual greedy algorithms when the master solution is fractional for two of our formulations, and in closed form when the master solution is binary for all of our formulations. Using synthetically generated instances, we demonstrate the practical tractability of our formulations and our Benders decomposition approach, and their edge over heuristic approaches.