Lower bounds for multi-stage vehicle routing

The primary purpose of this paper is to develop a new universal lower bound on performance for multi-stage problems that arise in many applications such as manufacturing, communication, inventory routing and vehicle routing. In this paper, we develop such bounds on average delay in the context of the dynamic pickup and delivery problem (DPDP), where a collection of vehicles are responsible for picking up and delivering requests that arrive at unknown times and locations in a certain geographic area. We show that our bounds are tight (order optimal) for a large class of batching policies.