A model-based approximation of opportunity cost for dynamic pricing in attended home delivery

For online retailers with attended home delivery business models, the decisive factor for promising dynamic time slot pricing decisions is the quality of the opportunity cost approximation concerning incoming customer requests. For this purpose, we present a novel approximation approach based on mixed-integer linear programming that we integrate into the de facto standard dynamic pricing framework prevalent in the academic literature. Our approximation combines the most current information regarding the customers accepted to date with a forecast of expected customers to come that is adapted during the progress of the booking horizon. Thus, future customer requests demand management, i.e. the consequences of future pricing decisions, is anticipated. We approximate the retailer's vehicle routes and thus delivery costs of expected customers by a dynamic seed-based scheme in which potential seeds' locations as well as related distance approximations are dynamically adjusted under consideration of the locations of already accepted customers. In a computational study, we compare the approach to established pricing approaches in practice and to the state-of-the-art dynamic pricing policy. We show that our approach constantly yields the highest profit, specifically given a tight capacity level. We further provide implications for practical use. We show that, even for large-scale implementations in a real-time environment, our approach is applicable by using parallel computing and by only periodically recalculating opportunity cost. Even then, our approach leads to very good results.