Same-day delivery for online purchases is a recent trend in online retail. We introduce a multi-vehicle dynamic pickup and delivery problem with time constraints that incorporates key features associated with same-day delivery logistics. To make better informed decisions, our solution approach incorporates information about future requests into routing decisions. We also introduce an analytical result that identifies when it is beneficial for vehicles to wait at the depot. We present a wide range of computational experiments that demonstrate the value of our approach. The results show that more requests can be filled when time windows are evenly spread throughout the day compared to when many requests' time windows occur late in the day. However, the anticipation of future requests is most valuable when many requests' time windows occur late in the day. As a result of increased flexibility, experiments also demonstrate that the value of anticipating the future decreases when the number of vehicles or the arrival rate of requests increases. The online appendix is available at https://doi.org/10.1287/trsc.2016.0732 .

In this paper, we analyze how drones can be combined with regular delivery vehicles to improve same‐day delivery performance. To this end, we present a dynamic vehicle routing problem with heterogeneous fleets. Customers order goods over the course of the day. These goods are delivered either by a drone or by a regular transportation vehicle within a delivery deadline. Drones are faster, but have a limited capacity as well as require charging after use. In the same‐day context, vehicle capacity is not a constraint, but vehicles are slow due to urban traffic. To decide whether an order is delivered by a drone or by a vehicle, we present a policy function approximation based on geographical districting. Our computational study reveals two major implications. First, geographical districting is highly effective increasing the expected number of same‐day deliveries. Second, a combination of drone and vehicle fleets may significantly reduce the required delivery resources.

In this paper, we introduce a variant of the orienteering problem in which travel and service times are stochastic. If a delivery commitment is made to a customer and is completed by the end of the day, a reward is received, but if a commitment is made and not completed, a penalty is incurred. This problem reflects the challenges of a company who, on a given day, may have more customers than it can serve. In this paper, we discuss special cases of the problem that we can solve exactly and heuristics for general problem instances. We present computational results for a variety of parameter settings and discuss characteristics of the solution structure.