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Branch and price for the vehicle routing problem with discrete split deliveries and time windows

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  • Salani, Matteo
  • Vacca, Ilaria

Abstract

The Discrete Split Delivery Vehicle Routing Problem with Time Windows (DSDVRPTW) consists of designing the optimal set of routes to serve, at least cost, a given set of customers while respecting constraints on vehicles' capacity and customer time windows. Each customer can be visited by more than one vehicle since each customer's demand, discretized in items, can be split in orders, i.e., feasible combinations of items. In this work, we model the DSDVRPTW assuming that all feasible orders are known in advance. Remarkably, service time at customer's location depends on the delivered combination of items, which is a modeling feature rarely found in literature. We present a flow-based mixed integer program for the DSDVRPTW, we reformulate it via Dantzig-Wolfe and we apply column generation. The proposed branch-and-price algorithm largely outperforms a commercial solver, as shown by computational experiments on Solomon-based instances. A comparison in terms of complexity between constant service time vs delivery-dependent service time is presented and potential savings are discussed.

Suggested Citation

  • Salani, Matteo & Vacca, Ilaria, 2011. "Branch and price for the vehicle routing problem with discrete split deliveries and time windows," European Journal of Operational Research, Elsevier, vol. 213(3), pages 470-477, September.
    • Handle: RePEc:eee:ejores:v:213:y:2011:i:3:p:470-477
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    References listed on IDEAS

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    1. J. M. Belenguer & M. C. Martinez & E. Mota, 2000. "A Lower Bound for the Split Delivery Vehicle Routing Problem," Operations Research, INFORMS, vol. 48(5), pages 801-810, October.
    2. Guy Desaulniers, 2010. "Branch-and-Price-and-Cut for the Split-Delivery Vehicle Routing Problem with Time Windows," Operations Research, INFORMS, vol. 58(1), pages 179-192, February.
    3. Nowak, Maciek & Ergun, Ozlem & White III, Chelsea C., 2009. "An empirical study on the benefit of split loads with the pickup and delivery problem," European Journal of Operational Research, Elsevier, vol. 198(3), pages 734-740, November.
    4. Gulczynski, Damon & Golden, Bruce & Wasil, Edward, 2010. "The split delivery vehicle routing problem with minimum delivery amounts," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 46(5), pages 612-626, September.
    5. Belfiore, PatrI´cia & Yoshida Yoshizaki, Hugo Tsugunobu, 2009. "Scatter search for a real-life heterogeneous fleet vehicle routing problem with time windows and split deliveries in Brazil," European Journal of Operational Research, Elsevier, vol. 199(3), pages 750-758, December.
    6. Archetti, Claudia & Savelsbergh, Martin W.P. & Grazia Speranza, M., 2008. "To split or not to split: That is the question," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 44(1), pages 114-123, January.
    7. Cynthia Barnhart & Ellis L. Johnson & George L. Nemhauser & Martin W. P. Savelsbergh & Pamela H. Vance, 1998. "Branch-and-Price: Column Generation for Solving Huge Integer Programs," Operations Research, INFORMS, vol. 46(3), pages 316-329, June.
    8. Bolduc, Marie-Claude & Laporte, Gilbert & Renaud, Jacques & Boctor, Fayez F., 2010. "A tabu search heuristic for the split delivery vehicle routing problem with production and demand calendars," European Journal of Operational Research, Elsevier, vol. 202(1), pages 122-130, April.
    9. Martin Desrochers & François Soumis, 1989. "A Column Generation Approach to the Urban Transit Crew Scheduling Problem," Transportation Science, INFORMS, vol. 23(1), pages 1-13, February.
    10. George B. Dantzig & Philip Wolfe, 1960. "Decomposition Principle for Linear Programs," Operations Research, INFORMS, vol. 8(1), pages 101-111, February.
    11. Jin, Mingzhou & Liu, Kai & Bowden, Royce O., 2007. "A two-stage algorithm with valid inequalities for the split delivery vehicle routing problem," International Journal of Production Economics, Elsevier, vol. 105(1), pages 228-242, January.
    12. Claudia Archetti & Martin W. P. Savelsbergh & M. Grazia Speranza, 2006. "Worst-Case Analysis for Split Delivery Vehicle Routing Problems," Transportation Science, INFORMS, vol. 40(2), pages 226-234, May.
    13. C. Archetti & M. G. Speranza & A. Hertz, 2006. "A Tabu Search Algorithm for the Split Delivery Vehicle Routing Problem," Transportation Science, INFORMS, vol. 40(1), pages 64-73, February.
    14. Niklas Kohl & Jacques Desrosiers & Oli B. G. Madsen & Marius M. Solomon & François Soumis, 1999. "2-Path Cuts for the Vehicle Routing Problem with Time Windows," Transportation Science, INFORMS, vol. 33(1), pages 101-116, February.
    15. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    16. Moshe Dror & Pierre Trudeau, 1989. "Savings by Split Delivery Routing," Transportation Science, INFORMS, vol. 23(2), pages 141-145, May.
    17. Giallombardo, Giovanni & Moccia, Luigi & Salani, Matteo & Vacca, Ilaria, 2010. "Modeling and solving the Tactical Berth Allocation Problem," Transportation Research Part B: Methodological, Elsevier, vol. 44(2), pages 232-245, February.
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