Robust Assortment Optimization in Revenue Management Under the Multinomial Logit Choice Model

We study robust formulations of assortment optimization problems under the multinomial logit choice model. The novel aspect of our formulations is that the true parameters of the logit model are assumed to be unknown, and we represent the set of likely parameter values by a compact uncertainty set. The objective is to find an assortment that maximizes the worst case expected revenue over all parameter values in the uncertainty set. We consider both static and dynamic settings. The static setting ignores inventory consideration, while in the dynamic setting, there is a limited initial inventory that must be allocated over time. We give a complete characterization of the optimal policy in both settings, show that it can be computed efficiently, and derive operational insights. We also propose a family of uncertainty sets that enables the decision maker to control the tradeoff between increasing the average revenue and protecting against the worst case scenario. Numerical experiments show that our robust approach, combined with our proposed family of uncertainty sets, is especially beneficial when there is significant uncertainty in the parameter values. When compared to other methods, our robust approach yields over 10% improvement in the worst case performance, but it can also maintain comparable average revenue if average revenue is the performance measure of interest.