Assortment Optimization Under the Decision Forest Model

Problem definition: We study the problem of finding the optimal assortment that maximizes expected revenue under the decision forest model, a recently proposed nonparametric choice model that is capable of representing any discrete choice model and in particular, can be used to represent nonrational customer behavior. 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. Methodology/results: We approach this problem from a mixed-integer optimization perspective and present two different formulations. We further propose a methodology for solving the two formulations 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 one of the formulations and in closed form when the master solution is binary for both formulations. Using synthetically generated instances, we demonstrate the practical tractability of our formulations and our Benders decomposition approach and their edge over heuristic approaches. Managerial implications: In a case study based on real-world transaction data, we demonstrate that our proposed approach can factor the behavioral anomalies observed in consumer choice into assortment decision and create higher revenue.

Funding: The authors acknowledge the support provided by the UCL School of Management and the UCLA Anderson School of Management.

Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.0634.