The Value of Robust Assortment Optimization Under Ranking-based Choice Models

The ranking-based choice model is a popular model in revenue management for predicting demand for a firm’s products based on the assortment of products that the firm offers to their customers. Because this model has a huge number of parameters, many different ranking-based choice models can be consistent with the historical sales data generated by a firm’s past assortments. Motivated by the use of ranking-based choice models in assortment planning, we consider the following identification question: Is it possible to identify an assortment with an expected revenue that is strictly greater than the expected revenues of the firm’s past assortments under all ranking-based choice models that are consistent with the firm’s historical sales data? In this work, we provide the first answers to the identification question by using robust optimization. We begin by characterizing the structure of optimal assortments for a class of robust assortment optimization problems proposed by Farias, Jagabathula, and Shah (2013). We then leverage this structure to develop the first algorithms for answering the identification question that run in polynomial time for any fixed number of past assortments. We use our algorithms to prove that it is possible to have affirmative answers to the identification question with as few as two past assortments, and that it is impossible to obtain affirmative answers when the past assortments are revenue-ordered. These findings, coupled with concise numerical experiments, reveal that considering the identification question can be essential for finding high-quality assortments from ranking-based choice models in high-stakes assortment planning problems.

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