  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 non-rational 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. We approach this problem from a
mixed-integer optimization perspective and propose two different formulations.
We theoretically compare the two formulations in strength, and analyze when
they are integral in the special case of a single tree. 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. In a case study based on a
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.
