From share of choice to buyers' welfare maximization: Bridging the gap through distributionally robust optimization

We study the product design problem where a decision maker selects the features of a product from a set of feasible options. We focus on two widely studied objectives in this field, that is, the share of choice (SOC) and buyers' welfare (BW). The two objectives are vulnerable to different types of customer preference misspecification, that is, deviation from the nominal utility distribution and effects of outliers, respectively. We formulate a distributionally robust optimization (DRO) SOC maximization model and a winsorized BW maximization model to obtain robust solutions to the two problems. Interestingly, we show that the two robust models are equivalent in a certain sense—for appropriate choices of robustness parameters, both models return the same solution. This observation has important ramifications. For instance, it indicates that a product designed to yield higher BW is more robust to the deviation from the nominal utility distribution for the SOC problem, while that with higher SOC is less sensitive to the effect of outliers for the BW problem. Last but not least, we use the equivalence to develop a new approach to solve the DRO model for the SOC problem, using a version of the winsorized BW model. Extensive numerical experiments demonstrate the superior performance of the proposed approach.