Differentiated Time Slot Pricing Under Routing Considerations in Attended Home Delivery

In this paper, we study an e-grocer's tactical problem of differentiated time slot pricing in attended home delivery. The purpose of differentiating delivery prices is to influence customers' choice behavior concerning the offered time slots, such that cost-effective delivery schedules on an operational level can be expected and overall profit is maximized. We present a mixed-integer linear programming formulation of the problem, in which delivery costs are anticipated by explicitly incorporating routing constraints, and we model customer behavior by a general nonparametric rank-based choice model. Concerning cost anticipation, we also propose a model-based approximation that enables application to real-world problem sizes. In a setup inspired by an industry partner operating in urban areas, we then perform a comprehensive computational study that reveals the value of the model-based approximation as a supporting instrument for an e-grocer's pricing decisions in practice. In particular, we demonstrate the superiority of the model-based approximation for real-world problem sizes to several benchmark approaches applied in the scientific literature and in practice (e.g., a unit price approach and other standard pricing heuristics).