Title: The splittable pickup and delivery problem with reloads

Authors: H.L.M. Kerivin, M. Lacroix, A.R. Mahjoub, A. Quilliot

Addresses: LIMOS, CNRS UMR 6158, Universite Blaise Pascal – Clermont-Ferrand II, Complexe Scientifique des Cezeaux, 63177 Aubiere, Cedex, France. ' LIMOS, CNRS UMR 6158, Universite Blaise Pascal – Clermont-Ferrand II, Complexe Scientifique des Cezeaux, 63177 Aubiere, Cedex, France. ' LAMSADE, CNRS UMR 7024, Universite Paris-Dauphine, Place du Marechal de Lattre de Tassigny, 75775 Paris Cedex 16, France. ' LIMOS, CNRS UMR 6158, Universite Blaise Pascal – Clermont-Ferrand II, Complexe Scientifique des Cezeaux, 63177 Aubiere, Cedex, France

Abstract: In this paper, we consider a variant of the Pickup and Delivery Problem (PDP), where any demand may be dropped off elsewhere other than its destination, picked up later by the same or another vehicle, and so on until it has reached its destination. We discuss the complexity of this problem and present two mixed-integer linear programming formulations based on a space-time graph. We describe some valid inequalities for the problem along with separation routines. Based on these results, we develop a branch-and-cut algorithm for the problem, and present some computational results. [Received 31 January 2007; Revised 08 August 2007; Accepted 02 October 2007]

Keywords: transportation problems; mixed-integer linear program; multicommodity flow; metric inequalities; branch-and-cut; pickup and delivery problem; PDP; reloads.

DOI: 10.1504/EJIE.2008.017347

European Journal of Industrial Engineering, 2008 Vol.2 No.2, pp.112 - 133

Published online: 01 Mar 2008 *

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