Optimizing Offline Product Design and Online Assortment Policy: Measuring the Relative Impact of Each Decision

Abstract

Revenue management decisions often involve both offline and online decisions. Offline decisions are made first and establish the broad and long-term operational context in which online decisions are frequently and repeatedly made, often in real time. We consider a joint optimization of offline and online decisions. Specifically, we examine a setting in which the offline decision concerns the selection of product-design characteristics (e.g., price, capacity, return eligibility, and other characteristics) and the online decision concerns the dynamic assortment optimization over a selling season. Our formulation has many applications, including optimizing products' return eligibility and determining product discounts. We formulate an optimization problem that combines the impact of both offline and online decisions on the expected revenue. To determine the product design, we reformulate the choice-based deterministic linear program, solve its continuous relaxation, and round the resulting solution. Using value function approximations enables us to obtain a dynamic assortment policy whose expected revenue is at least a constant fraction of the choice-based deterministic linear program. Combining these two results, we show that our approach provides an approximate solution to the joint optimization problem with performance guarantees. Numerical experiments based on real transaction data from a major U.S. retailer show that our method achieves 95%-97% effectiveness, an advantage of up to 18% over methods that disregard the interplay between offline and online decisions. This framework also yields a systematic quantitative measure of the relative importance of both offline and online decisions. Based on this measure, numerical experiments highlight the crucial role of product design, accounting for 94% and 85% of the observed variation in effectiveness across various methods in applications involving volume discount and return eligibility, respectively.

Keywords: offline decision, online decision, product design, dynamic assortment optimization