Dynamic pricing of flexible time slots for attended home delivery

Abstract

In e-commerce, customers are usually offered a menu of home delivery time windows of which they need to select exactly one, even though at least some customers may be more flexible. To exploit the flexibility of such customers, we propose to introduce flexible delivery time slots, defined as any combination of such regular time windows (not necessarily adjacent). In selecting a flexible time slot (out of a set of windows that form the flexible product), the customer agrees to be informed only shortly prior to the dispatching of the delivery vehicle in which regular time window the goods will arrive. In return for providing this flexibility, the company may offer the customer a reduced delivery charge and/or highlight the environmental benefits. Our framework also can accommodate customized flexible slots where customers can self-select a set of regular slots in which a delivery may take place.The vehicle routing problem (VRP) in the presence of flexible time slots bookings corresponds to a VRP with multiple time windows. We build on literature on demand management and vehicle routing for attended home delivery, as well as on flexible products. These two concepts have not yet been combined, and indeed the results from the flexible products literature do not carry over directly because future expected vehicle routing implications need to be taken into account. The main methodological contribution is the development of a tractable linear programming formulation that links demand management decisions and routing cost implications, whilst accounting for customer choice behavior. The output of this linear program provides information on the (approximate) opportunity cost associated with specific orders and informs a tractable dynamic pricing policy for regular and flexible slots. Numerical experiments, based on realistically-sized scenarios, indicate that expected profit may increase significantly depending on demand intensity when adding flexible slots rather than using only regular slots.