Dynamic service area sizing in urban delivery

We consider an urban instant delivery environment, e.g., meal delivery, in which customers place orders over the course of a day and are promised delivery within a short period of time after an order is placed. Deliveries are made using a fleet of vehicles, each completing one or more trips during the day. To avoid missing delivery time promises as much as possible, the provider manages demand by dynamically adjusting the size of the service area, i.e., the area in which orders can be delivered. The provider seeks to maximize the number of orders served while avoiding missed delivery time promises. We present three techniques to support the dynamic adjusting of the size of the service area which can be embedded in planning and execution tools that help the provider achieve its goal. First, we learn the functional dependency between expected demand and the service area that can be supported with the fleet of vehicles. Second, we use value function approximation to improve an initial service area sizing plan for the day based on expected demand. Finally, we introduce a correction mechanism to dynamically adjust the service area sizing plan in response to observed realized demand. Extensive computational experiments demonstrate the efficacy of the techniques and show that dynamic sizing of the service area can increase the number of orders served significantly without increasing the number of missed delivery time promises.