Mitigating choice model ambiguity: A consensus framework and its application to assortment optimization

Discrete choice models have become a popular tool to accurately predict complex choice behavior. Due to a variety of possible error sources, estimated choice models tend to be subject to ambiguity, inducing different optimal decisions of highly varying quality. This study aims at mitigating choice model ambiguity associated with a given set of models in terms of their ability to yield optimal decisions. We propose a framework and a set of performance metrics to assess the reliability of choice models and their induced decisions. The use of this framework is then exemplified in the context of rank-based choice models for assortment optimization. Extensive sets of numerical results suggest that our proposed approaches indeed allow decision-makers to identify choice models that are likely to produce high quality decisions, boosting confidence in using choice models in practice. While robust optimization on the original set of choice models tends to be rather conservative, we then use the proposed metrics to reduce the size of the ambiguity set, allowing us to improve the expected assortment quality and the overall downside risk. Given the practical usefulness of robust optimization in this context, we further propose a decomposition algorithm, solving the optimization problem in a fraction of the original time and revealing that only a few among a large set of choice models are determinant in optimal robust solutions.