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The One-Dimensional Dynamic Dispatch Waves Problem

Mathias Klapp (maklapp***at***gatech.edu)
Alan L Erera (aerera***at***isye.gatech.edu)
Alejandro Toriello (atoriello***at***isye.gatech.edu)

Abstract: 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.

Keywords: same-day delivery, dynamic dispatch, approximate dynamic program, approximate linear program

Category 1: Applications -- OR and Management Sciences (Production and Logistics )

Category 2: Applications -- OR and Management Sciences (Transportation )

Category 3: Other Topics (Dynamic Programming )

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

Download: [PDF]

Entry Submitted: 03/18/2015
Entry Accepted: 03/18/2015
Entry Last Modified: 06/30/2015

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