The One-Dimensional Dynamic Dispatch Waves Problem

We study same-day delivery (SDD) distribution systems by formulating the Dynamic Dispatch Wave Problem (DDWP), which models a depot where delivery requests arrive dynamically throughout a service day. At any dispatch epoch (wave), the information available to the decision maker is (1) a set of known, open requests which remain unfulfilled, and (2) a set of potential requests that may arrive later in the service day. At each wave, the decision maker decides whether or not to dispatch a vehicle, and if so, which subset of open requests to serve, with the objective of minimizing expected vehicle operating costs and penalties for unserved requests. We consider the DDWP with a single delivery vehicle and request destinations on a line, where vehicle operating times and costs depend only on the distance between points. We propose an efficient dynamic programming approach to solve a deterministic variant, where all request arrival times are known. Next, we describe a class of a priori dispatch policies that plan the vehicle’s routes from the depot for each wave in advance, and provide a dynamic programming approach for determining an optimal policy of this kind. Finally, we propose heuristics and dual bounds for the dynamic case.

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H. Milton Stewart School of Industrial and Systems Engineering, March 2015

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