On the Approximation of Opportunity Cost for Dynamic Pricing in Attended Home Delivery

Abstract

The decisive factor for promising dynamic time slot pricing decisions in attended home delivery is the quality of the opportunity cost approximation with regard to incoming customer requests. In this paper, we present a novel approximation based on mixed-integer linear programming that we integrate into the dynamic pricing approach recently proposed by [Yang X et al. (2014) Choice-based demand management and vehicle routing in e-fulfillment. Transp Sci. Articles in Advance. 1–16]. In line with these authors’ concluding suggestions, our approximation explicitly combines the most current information regarding the customers accepted to date with a forecast of expected customers to come which is adapted to the progress of the booking horizon. Thereby, future customer requests’ demand management is anticipated. Delivery costs are approximated based on a well-established seed-based scheme [Fisher ML, Jaikumar R (1981) A generalized assignment heuristic for vehicle routing. Netw 11(2):109–124]. In a computational study, we evaluate the proposed approach and compare it to established pricing approaches in practice, e.g. fix prices. We show that our approach constantly yields the highest profit, specifically given a tight capacity level of the service provider. Based on the computational study’s results, we provide implications for the practical use of the approach, especially when real-time pricing decisions are required.