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A survey on pickup and delivery problems

Part I: Transportation between customers and depot

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Abstract

This paper is the first part of a comprehensive survey on pickup and delivery problems. Basically, two problem classes can be distinguished. The first class, discussed in this paper, deals with the transportation of goods from the depot to linehaul customers and from backhaul customers to the depot. This class is denoted as Vehicle Routing Problems with Backhauls (VRPB). Four subtypes can be considered, namely the Vehicle Routing Problem with Clustered Backhauls (VRPCB – all linehauls before backhauls), the Vehicle Routing Problem with Mixed linehauls and Backhauls (VRPMB – any sequence of linehauls and backhauls permitted), the Vehicle Routing Problem with Divisible Delivery and Pickup (VRPDDP – customers demanding delivery and pickup service can be visited twice), and the Vehicle Routing Problem with Simultaneous Delivery and Pickup (VRPSDP – customers demanding both services have to be visited exactly once). The second class, dealt with in the second part of this survey, refers to all those problems where goods are transported between pickup and delivery locations. These are the Pickup and Delivery Vehicle Routing Problem (PDVRP – unpaired pickup and delivery points), the classical Pickup and Delivery Problem (PDP – paired pickup and delivery points), and the Dial-A-Ride Problem (DARP – passenger transportation between paired pickup and delivery points and user inconvenience taken into consideration). Single as well as multi vehicle versions of the mathematical problem formulations are given for all four VRPB types, the corresponding exact, heuristic, and metaheuristic solution methods are discussed.

Zusammenfassung

Der vorliegende Artikel ist Teil I einer umfassenden Überblicksarbeit in zwei Teilen über pickup and delivery Probleme. Grundsätzlich können zwei Problemklassen unterschieden werden. Die erste Problemklasse, mit der sich dieser Artikel befasst, beinhaltet all jene Probleme, die Auslieferungen von einem Depot zu Auslieferungs-Kunden (linehaul customers) und Abholungen von Rückladungs-Kunden (backhaul customers) zu einem Depot behandeln. Diese Problemklasse wird im Folgenden als Vehicle Routing Problems with Backhauls (VRPB) bezeichnet. Vier verschiedene Problemtypen können weiters unterschieden werden: das Vehicle Routing Problem with Clustered Backhauls (VRPCB), alle Auslieferungen müssen vor den Abholungen durchgeführt werden, das Vehicle Routing Problem with Mixedlinehauls and Backhauls (VRPMB), gemischte Ausliefer- und Abholsequenzen sind gestattet, das Vehicle Routing Problem with Divisible Delivery and Pickup (VRPDDP), Kunden, die Ausliefer- und Abholservice verlangen, können zweimal besucht werden, und das Vehicle Routing Problem with Simultaneous Delivery and Pickup (VRPSDP), Kunden, die beide Services verlangen, können nur genau einmal angefahren werden. Die zweite pickup and delivery Problemklasse wird in Teil II dieser Arbeit behandelt. Sie beinhaltet all jene Problemtypen, die sich mit Transporten zwischen Abhol- und Auslieferungsorten befassen: das Pickup and Delivery Vehicle Routing Problem (PDVRP), ungepaarte Abhol- und Auslieferungsorte, das klassische Pickup and Delivery Problem (PDP), gepaarte Abhol- und Auslieferungsorte, und das Dial-A-Ride Problem (DARP), Personentransport zwischen gepaarten Abhol- und Ablieferungsorten unter Berücksichtigung von serviceorientierten Kriterien. Die jeweiligen Problemtypen werden zuerst anhand von mathematischen Einfahrzeug- und Mehrfahrzeugproblemformulierungen definiert. Im Anschluss werden die in der Literatur beschriebenen Lösungsmethoden diskutiert.

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  1. Institut für Betriebswirtschaftslehre, Universität Wien, Brünnerstr. 72, 1210, Wien, Austria

    Sophie N. Parragh, Karl F. Doerner & Richard F. Hartl

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Parragh, S.N., Doerner, K.F. & Hartl, R.F. A survey on pickup and delivery problems . Journal für Betriebswirtschaft 58, 21–51 (2008). https://doi.org/10.1007/s11301-008-0033-7

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