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A Branch-and-Price-and-Cut Algorithm for Heterogeneous Pickup and Delivery Problems with Configurable Vehicle Capacity

Author

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  • Yuan Qu

    (Graduate Program in Operations Research and Industrial Engineering, University of Texas, Austin, Texas 78712)

  • Jonathan F. Bard

    (Graduate Program in Operations Research and Industrial Engineering, University of Texas, Austin, Texas 78712)

Abstract

This paper presents a mixed-integer programming model for a variant of the pickup and delivery problem with time windows. The fleet is assumed to be heterogeneous with a novel feature that allows the vehicles to be configured before service begins to handle various types of demand. The work was motivated by a daily route planning problem arising at a senior activity center. A fleet of configurable vans is available each day to transport participants to and from the center, as well as to secondary facilities for rehabilitative and medical treatment. The number of participants and support equipment that a van can accommodate depends on how it is configured. An exact method is introduced based on branch and price and cut. At each node in the search tree, the master problem is solved by column generation to find a lower bound. To improve the bound, subset-row inequalities are applied to the variables of the master problem. Columns are generated by solving the pricing subproblems with a labeling algorithm enhanced by new dominance conditions. Local search on the current set of columns is used to quickly find promising additions. Implementation details and ways to improve the performance of the overall procedure are discussed. Testing was done on a set of real instances as well as a set of randomly generated instances with up to 50 customer requests. The results show that optimal solutions are obtained in the majority of cases.

Suggested Citation

  • Yuan Qu & Jonathan F. Bard, 2015. "A Branch-and-Price-and-Cut Algorithm for Heterogeneous Pickup and Delivery Problems with Configurable Vehicle Capacity," Transportation Science, INFORMS, vol. 49(2), pages 254-270, May.
    • Handle: RePEc:inm:ortrsc:v:49:y:2015:i:2:p:254-270
    DOI: 10.1287/trsc.2014.0524
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    References listed on IDEAS

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    8. Xuanjing Fang & Yanan Du & Yuzhuo Qiu, 2017. "Reducing Carbon Emissions in a Closed-Loop Production Routing Problem with Simultaneous Pickups and Deliveries under Carbon Cap-and-Trade," Sustainability, MDPI, vol. 9(12), pages 1-15, November.
    9. Ho, Sin C. & Szeto, W.Y. & Kuo, Yong-Hong & Leung, Janny M.Y. & Petering, Matthew & Tou, Terence W.H., 2018. "A survey of dial-a-ride problems: Literature review and recent developments," Transportation Research Part B: Methodological, Elsevier, vol. 111(C), pages 395-421.
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    11. Qiu, Yuzhuo & Ni, Ming & Wang, Liang & Li, Qinqin & Fang, Xuanjing & Pardalos, Panos M., 2018. "Production routing problems with reverse logistics and remanufacturing," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 111(C), pages 87-100.
    12. Timo Gschwind & Michael Drexl, 2016. "Adaptive Large Neighborhood Search with a Constant-Time Feasibility Test for the Dial-a-Ride Problem," Working Papers 1624, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    13. Gaul, Daniela & Klamroth, Kathrin & Stiglmayr, Michael, 2022. "Event-based MILP models for ridepooling applications," European Journal of Operational Research, Elsevier, vol. 301(3), pages 1048-1063.
    14. Luciano Costa & Claudio Contardo & Guy Desaulniers, 2019. "Exact Branch-Price-and-Cut Algorithms for Vehicle Routing," Transportation Science, INFORMS, vol. 53(4), pages 946-985, July.
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