This paper considers a vehicle routing problem with pickup and delivery, time windows and location congestion. Locations provide a number of cumulative resources that are utilized by vehicles either during service (e.g., forklifts) or for the entirety of their visit (e.g., parking bays). Locations can become congested if insufficient resources are available, upon which vehicles must wait until a resource becomes available before proceeding. The problem is challenging from a computational standpoint since it incorporates the vehicle routing problem and the resource-constrained project scheduling problem. The main contribution of this paper is a branch-and-price-and-check model that uses a branch-and-price algorithm that solves the underlying vehicle routing problem, and a constraint programming subproblem that checks the feasibility of the location resource constraints, and then adds combinatorial nogood cuts to the master problem if the resource constraints are violated. Experimental results show the benefits of the branch-and-price-and-check approach.
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An alternative approach would be to transfer only one of these requests to the separation subproblem but this would introduce some random choices in the communication between the master and the subproblem.
Bard, J.F., Kontoravdis, G., & Yu, G. (2002). A branch-and-cut procedure for the vehicle routing problem with time windows. Transportation Science, 36(2), 250–269.
Beck, J. (2010). Checking-up on branch-and-check. In Cohen, D. (Ed.), Principles and practice of constraint programming – cp 2010, lecture notes in computer science (Vol. 6308, pp. 84–98). Berlin Heidelberg: Springer.
Beck, J., Prosser, P., & Selensky, E. (2002). On the reformulation of vehicle routing problems and scheduling problems. In Koenig, S., Holte, R. (Eds.), Abstraction, reformulation, and approximation, lecture notes in computer science (Vol. 2371, pp. 282–289). Berlin Heidelberg: Springer.
Beck, J.C., Prosser, P., & Selensky, E. (2003). Vehicle routing and job shop scheduling: What’s the difference? In ICAPS (pp. 267–276).
Bent, R., & Van Hentenryck, P. (2004). A two-stage hybrid local search for the vehicle routing problem with time windows. Transportation Science, 38(4), 515–530.
Desaulniers, G., Desrosiers, J., & Solomon, M. (2002). Accelerating strategies in column generation methods for vehicle routing and crew scheduling problems. In Essays and surveys in metaheuristics, operations research/computer science interfaces series (Vol. 15, pp. 309–324). US: Springer.
Desaulniers, G., Desrosiers, J., & Solomon, M.M. (2005). Column generation (Vol. 5). Springer.
Drexl, M. (2012). Synchronization in vehicle routing—a survey of VRPs with multiple synchronization constraints. Transportation Science, 46(3), 297–316.
Dumas, Y., Desrosiers, J., & Soumis, F. (1991). The pickup and delivery problem with time windows. European Journal of Operational Research, 54(1), 7–22.
Hachemi, N.E., Gendreau, M., & Rousseau, L.M. (2013). A heuristic to solve the synchronized log-truck scheduling problem. Computers & Operations Research, 40 (3), 666–673. Transport Scheduling.
Hempsch, C., & Irnich, S. (2008). Vehicle routing problems with inter-tour resource constraints. In Golden, B., Raghavan, S., Wasil E. (Eds.), The vehicle routing problem: latest advances and new challenges, operations research/computer science interfaces (Vol. 43, pp. 421–444). US: Springer.
Hooker, J. (1994). Logic-based methods for optimization. In Borning, A. (Ed.) Principles and practice of constraint programming, lecture notes in computer science (Vol. 874, pp. 336–349). Berlin Heidelberg: Springer.
Hooker, J.N., & Mitchell, J.E. (2008). Integrated methods for optimization. SIAM review, 50(1), 183.
Kallehauge, B., Larsen, J., Madsen, O.B., & Solomon, M.M. (2005). Vehicle routing problem with time windows. In Desaulniers, G., Desrosiers, J., Solomon, M.M. (Eds.), Column generation (pp. 67–98). US: Springer.
Lübbecke, M.E., & Desrosiers, J. (2005). Selected topics in column generation. Operations Research, 53(6), 1007–1023.
Rix, G., Rousseau, L.M., & Pesant, G. (2015). A column generation algorithm for tactical timber transportation planning. Journal of the Operational Research Society, 66(2), 278–287.
Ropke, S., & Cordeau, J.F. (2009). Branch and cut and price for the pickup and delivery problem with time windows. Transportation Science, 43(3), 267–286.
Ropke, S., Cordeau, J.F., & Laporte, G. (2007). Models and branch-and-cut algorithms for pickup and delivery problems with time windows. Networks, 49(4), 258–272.
Shaw, P. (1998). Using constraint programming and local search methods to solve vehicle routing problems. In Maher, M., Puget, J.F. (Eds.), Principles and practice of constraint programming — cp98, lecture notes in computer science (Vol. 1520, pp. 417–431), Berlin Heidelberg: Springer.
Thorsteinsson, E. (2001). Branch-and-check: A hybrid framework integrating mixed integer programming and constraint logic programming. In Walsh, T. (Ed.), Principles and practice of constraint programming — cp 2001, lecture notes in computer science (Vol. 2239, pp. 16–30). Berlin Heidelberg: Springer.
Toth, P., & Vigo, D. (2002). The vehicle routing problem. Society for industrial and applied mathematics. Philadelphia.
We would like to thank the reviewers for their constructive comments and suggestions.
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Lam, E., Hentenryck, P.V. A branch-and-price-and-check model for the vehicle routing problem with location congestion. Constraints 21, 394–412 (2016). https://doi.org/10.1007/s10601-016-9241-2
- Vehicle routing problem