We study the problem of optimizing assortment decisions in the presence of product-specific costs when customers choose according to a multinomial logit model. This problem is NP-hard, and approximate solutions methods have been proposed in the literature to obtain both lower and upper bounds in a tractable manner. We propose the first exact solution method for this problem and show that provably optimal assortments of instances with up to 1,000 products can be found, on average, in about 2/10 of a second. In particular, we propose a bounding procedure to enhance an approximation method originally proposed by Feldman and Topaloglu and provide tight lower and upper bounds at a fraction of a second. We show how these bounds can be used to effectively identify an optimal assortment. We also describe how to adapt our approach to handle cardinality or space/resource capacity constraints on the assortment as well as assortment optimization under a mixed-multinomial logit model. In both cases, our solution method provides significant computational boosts compared with exact methods from the literature.

The random utility maximization model is by far the most adopted framework to estimate consumer choice behavior. However, behavioral economics has provided strong empirical evidence of irrational choice behaviors, such as halo effects, that are incompatible with this framework. Models belonging to the random utility maximization family may therefore not accurately capture such irrational behavior. Hence, more general choice models, overcoming such limitations, have been proposed. However, the flexibility of such models comes at the price of increased risk of overfitting. As such, estimating such models remains a challenge. In this work, we propose an estimation method for the recently proposed generalized stochastic preference choice model, which subsumes the family of random utility maximization models and is capable of capturing halo effects. In particular, we propose a column-generation method to gradually refine the discrete choice model based on partially ranked preference sequences. Extensive computational experiments indicate that our model, explicitly accounting for irrational preferences, can significantly boost the predictive accuracy on both synthetic and real-world data instances. Summary of Contribution: In this work, we propose an estimation method for the recently proposed generalized stochastic preference choice model, which subsumes the family of random utility maximization models and is capable of capturing halo effects. Specifically, we show how to use partially ranked preferences to efficiently model rational and irrational customer types from transaction data. Our estimation procedure is based on column generation, where relevant customer types are efficiently extracted by expanding a treelike data structure containing the customer behaviors. Furthermore, we propose a new dominance rule among customer types whose effect is to prioritize low orders of interactions among products. An extensive set of experiments assesses the predictive accuracy of the proposed approach by comparing it against rank-based methods with only rational preferences and with more general benchmarks from the literature. Our results show that accounting for irrational preferences can boost predictive accuracy by 12.5% on average when tested on a real-world data set from a large chain of grocery and drug stores.