Inverse attribute‐based optimization with an application in assortment optimization

Abstract

AbstractMany applications of inverse optimization (IO) arise in settings where the goal is to predict the future actions of an optimizing agent (e.g., an optimizing customer's future purchases). The majority of papers in this area implicitly assume an alternative‐based modeling approach: The forward model finds an optimal set of actions (decisions) from among a given set of alternatives, while the inverse model imputes objective function coefficients corresponding to these alternatives. Since the imputed weights correspond only to alternatives existing in the training set, alternative‐based modeling is limited to applications where the set of options does not change when a prediction is needed. In this paper, we apply an attribute‐based perspective, which allows IO to impute the weights of attributes that lead to an optimal decision instead of imputing the weight of the decision itself. This perspective expands the range of IO applicability; we demonstrate that it facilitates the application of IO in assortment optimization, where changing product selections is a defining feature and accurate predictions of demand are important. We compare inverse attribute‐based optimization with rank‐based and machine learning methods. We show that since IO encodes the utility optimizing behavior of the consumer into the preference learning process, it results in lower assortment regret for the store and a lower utility gap for the consumers.