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Solving a Practical Pickup and Delivery Problem

Author

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  • Hang Xu

    (Manugistics, Inc., 585 East Swedesford Road, Wayne, Pennsylvania 19087)

  • Zhi-Long Chen

    (Robert H. Smith School of Business, University of Maryland, College Park, Maryland 20742-1815)

  • Srinivas Rajagopal

    (Manugistics, Inc., 585 East Swedesford Road, Wayne, Pennsylvania 19087)

  • Sundar Arunapuram

    (Manugistics, Inc., 585 East Swedesford Road, Wayne, Pennsylvania 19087)

Abstract

We consider a pickup and delivery vehicle routing problem commonly encountered in real-world logistics operations. The problem involves a set of practical complications that have received little attention in the vehicle routing literature. In this problem, there are multiple carriers and multiple vehicle types available to cover a set of pickup and delivery orders, each of which has multiple pickup time windows and multiple delivery time windows. Orders and carrier/vehicle types must satisfy a set of compatibility constraints that specify which orders cannot be covered by which carrier/vehicle types and which orders cannot be shipped together. Order loading and unloading sequence must satisfy the nested precedence constraint that requires that an order cannot be unloaded until all the orders loaded into the truck later than this order are unloaded. Each vehicle trip must satisfy the driver's work rules prescribed by the Department of Transportation which specify legal working hours of a driver. The cost of a trip is determined by several factors including a fixed charge, total mileage, total waiting time, and total layover time of the driver. We propose column generation based solution approaches to this complex problem. The problem is formulated as a set partitioning type formulation containing an exponential number of columns. We apply the standard column generation procedure to solve the linear relaxation of this set partitioning type formulation in which the resulting master problem is a linear program and solved very efficiently by an LP solver, while the resulting subproblems are computationally intractable and solved by fast heuristics. An integer solution is obtained by using an IP solver to solve a restricted version of the original set partitioning type formulation that only contains the columns generated in solving the linear relaxation. The approaches are evaluated based on lower bounds obtained by solving the linear relaxation to optimality by using an exact dynamic programming algorithm to solve the subproblems exactly. It is shown that the approaches are capable of generating near-optimal solutions quickly for randomly generated instances with up to 200 orders. For larger randomly generated instances with up to 500 orders, it is shown that computational times required by these approaches are acceptable.

Suggested Citation

  • Hang Xu & Zhi-Long Chen & Srinivas Rajagopal & Sundar Arunapuram, 2003. "Solving a Practical Pickup and Delivery Problem," Transportation Science, INFORMS, vol. 37(3), pages 347-364, August.
    • Handle: RePEc:inm:ortrsc:v:37:y:2003:i:3:p:347-364
    DOI: 10.1287/trsc.37.3.347.16044
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    References listed on IDEAS

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    Cited by:

    1. Männel, Dirk & Bortfeldt, Andreas, 2018. "Solving the pickup and delivery problem with three-dimensional loading constraints and reloading ban," European Journal of Operational Research, Elsevier, vol. 264(1), pages 119-137.
    2. Ostermeier, Manuel, 2024. "The supply of convenience stores: Challenges of short-distance routing within the constraints of working time regulations," European Journal of Operational Research, Elsevier, vol. 314(3), pages 997-1012.
    3. Eskandarzadeh, Saman & Fahimnia, Behnam, 2022. "Rest break policy comparison for heavy vehicle drivers in Australia," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 159(C).
    4. Tilk, Christian & Goel, Asvin, 2020. "Bidirectional labeling for solving vehicle routing and truck driver scheduling problems," European Journal of Operational Research, Elsevier, vol. 283(1), pages 108-124.
    5. Kok, A.L. & Hans, E.W. & Schutten, J.M.J., 2011. "Optimizing departure times in vehicle routes," European Journal of Operational Research, Elsevier, vol. 210(3), pages 579-587, May.
    6. Zhang, Zizhen & Che, Oscar & Cheang, Brenda & Lim, Andrew & Qin, Hu, 2013. "A memetic algorithm for the multiperiod vehicle routing problem with profit," European Journal of Operational Research, Elsevier, vol. 229(3), pages 573-584.
    7. Cortés, Cristián E. & Matamala, Martín & Contardo, Claudio, 2010. "The pickup and delivery problem with transfers: Formulation and a branch-and-cut solution method," European Journal of Operational Research, Elsevier, vol. 200(3), pages 711-724, February.
    8. Sun, Yanshuo & Kirtonia, Sajeeb & Chen, Zhi-Long, 2021. "A survey of finished vehicle distribution and related problems from an optimization perspective," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 149(C).
    9. Farshad Majzoubi & Lihui Bai & Sunderesh S. Heragu, 2021. "The EMS vehicle patient transportation problem during a demand surge," Journal of Global Optimization, Springer, vol. 79(4), pages 989-1006, April.
    10. Männel, Dirk & Bortfeldt, Andreas, 2016. "A hybrid algorithm for the vehicle routing problem with pickup and delivery and three-dimensional loading constraints," European Journal of Operational Research, Elsevier, vol. 254(3), pages 840-858.
    11. Koç, Çağrı & Bektaş, Tolga & Jabali, Ola & Laporte, Gilbert, 2016. "A comparison of three idling options in long-haul truck scheduling," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 631-647.
    12. Wang, Yu & Chen, Feng & Chen, Zhi-Long, 2018. "Pickup and delivery of automobiles from warehouses to dealers," Transportation Research Part B: Methodological, Elsevier, vol. 117(PA), pages 412-430.
    13. Regnier-Coudert, Olivier & McCall, John & Ayodele, Mayowa & Anderson, Steven, 2016. "Truck and trailer scheduling in a real world, dynamic and heterogeneous context," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 93(C), pages 389-408.
    14. Xiang, Zhihai & Chu, Chengbin & Chen, Haoxun, 2006. "A fast heuristic for solving a large-scale static dial-a-ride problem under complex constraints," European Journal of Operational Research, Elsevier, vol. 174(2), pages 1117-1139, October.
    15. Mayerle, Sérgio Fernando & De Genaro Chiroli, Daiane Maria & Neiva de Figueiredo, João & Rodrigues, Hidelbrando Ferreira, 2020. "The long-haul full-load vehicle routing and truck driver scheduling problem with intermediate stops: An economic impact evaluation of Brazilian policy," Transportation Research Part A: Policy and Practice, Elsevier, vol. 140(C), pages 36-51.
    16. Xu Cheng & Lixin Tang & Panos Pardalos, 2015. "A Branch-and-Cut algorithm for factory crane scheduling problem," Journal of Global Optimization, Springer, vol. 63(4), pages 729-755, December.
    17. Goel, Asvin, 2018. "Legal aspects in road transport optimization in Europe," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 114(C), pages 144-162.
    18. Wang, Zhongxiang & Haghani, Ali, 2020. "Column generation-based stochastic school bell time and bus scheduling optimization," European Journal of Operational Research, Elsevier, vol. 286(3), pages 1087-1102.
    19. Goel, Asvin, 2014. "Hours of service regulations in the United States and the 2013 rule change," Transport Policy, Elsevier, vol. 33(C), pages 48-55.
    20. Mor, Andrea & Archetti, Claudia & Jabali, Ola & Simonetto, Alberto & Speranza, M. Grazia, 2022. "The Bi-objective Long-haul Transportation Problem on a Road Network," Omega, Elsevier, vol. 106(C).
    21. Daiane Maria Genaro Chiroli & Sérgio Fernando Mayerle & João Neiva Figueiredo, 2022. "Using state-space shortest-path heuristics to solve the long-haul point-to-point vehicle routing and driver scheduling problem subject to hours-of-service regulatory constraints," Journal of Heuristics, Springer, vol. 28(1), pages 23-59, February.
    22. Brønmo, Geir & Nygreen, Bjørn & Lysgaard, Jens, 2010. "Column generation approaches to ship scheduling with flexible cargo sizes," European Journal of Operational Research, Elsevier, vol. 200(1), pages 139-150, January.
    23. Liu, Ran & Xie, Xiaolan & Augusto, Vincent & Rodriguez, Carlos, 2013. "Heuristic algorithms for a vehicle routing problem with simultaneous delivery and pickup and time windows in home health care," European Journal of Operational Research, Elsevier, vol. 230(3), pages 475-486.
    24. Francis, Peter & Zhang, Guangming & Smilowitz, Karen, 2007. "Improved modeling and solution methods for the multi-resource routing problem," European Journal of Operational Research, Elsevier, vol. 180(3), pages 1045-1059, August.
    25. Pang, King-Wah & Xu, Zhou & Li, Chung-Lun, 2011. "Ship routing problem with berthing time clash avoidance constraints," International Journal of Production Economics, Elsevier, vol. 131(2), pages 752-762, June.

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