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Pickup and delivery problems with autonomous vehicles on rings

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  • Trotta, Manuel
  • Archetti, Claudia
  • Feillet, Dominique
  • Quilliot, Alain

Abstract

In this paper we introduce a new class of Pickup and Delivery problems on circles (or rings). These problems arise in the field of public transportation systems where autonomous (i.e. driverless) vehicles travel on circular networks. We consider a set of stations arranged in a circle and a set of transportation requests. Each request asks for the transportation of a certain quantity from a pickup station to a delivery station. A fleet of capacitated vehicles is available at the depot. In the first part of the paper we propose a classification scheme for these problems. In the second part, we address the variants in which the vehicles are allowed to move in a single direction of the circle (either clockwise or counterclockwise) and the objective is to minimize the number of tours on the ring while serving all the requests. We provide a complexity analysis for this class of problems. We develop polynomial time algorithms for the variants that are polynomially solvable and proofs of NP-hardness for the variants that are NP-hard. In addition, for the latter, we provide mathematical formulations and perform computational tests that show the effectiveness of these formulations. Finally, we compare optimal solutions with those obtained using a straightforward greedy algorithm.

Suggested Citation

  • Trotta, Manuel & Archetti, Claudia & Feillet, Dominique & Quilliot, Alain, 2022. "Pickup and delivery problems with autonomous vehicles on rings," European Journal of Operational Research, Elsevier, vol. 300(1), pages 221-236.
    • Handle: RePEc:eee:ejores:v:300:y:2022:i:1:p:221-236
    DOI: 10.1016/j.ejor.2021.07.050
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    References listed on IDEAS

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    1. Gerardo Berbeglia & Jean-François Cordeau & Irina Gribkovskaia & Gilbert Laporte, 2007. "Rejoinder on: Static pickup and delivery problems: a classification scheme and survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 45-47, July.
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    3. Gerardo Berbeglia & Jean-François Cordeau & Irina Gribkovskaia & Gilbert Laporte, 2007. "Static pickup and delivery problems: a classification scheme and survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 1-31, July.
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