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A tutorial on column generation and branch-and-price for vehicle routing problems

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Abstract

This paper provides a tutorial on column generation and branch-and-price for vehicle routing problems. The main principles and the basic theory of the methods are first outlined. Some additional issues, including reinforcement of the relaxation or stabilization, complete the paper. For the sake of simplicity, this material is illustrated with the case of the vehicle routing problem with time windows.

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References

  • Baldacci R, Toth P, Vigo D (2007) Recent advances in vehicle routing exact algorithms. 4OR 5(4): 269–298

    Article  Google Scholar 

  • Bard JF, Kontoravdis G, Yu G (2002) A branch-and-cut procedure for the vehicle routing problem with time windows. Transport Sci 36(2): 250–269

    Article  Google Scholar 

  • Boland N, Dethridge J, Dumitrescu I (2006) Accelerated label setting algorithms for the elementary resource constrained shortest path problem. Oper Res Lett 34(1): 58–68

    Article  Google Scholar 

  • Boussier S, Feillet D, Gendreau M (2007) An exact algorithm for team orienteering problems. 4OR 5: 211–230

    Article  Google Scholar 

  • Braysy O, Gendreau M (2005a) Vehicle routing problem with time windows, part i: route construction and local search algorithms. Transport Sci 39(1): 104–118

    Article  Google Scholar 

  • Braysy O, Gendreau M (2005b) Vehicle routing problem with time windows, part ii: metaheuristics. Transport Sci 39(1): 119–139

    Article  Google Scholar 

  • Briant O, Lemaréchal C, Meurdesoif P, Michel S, Perrot N, Vanderbeck F (2008) Comparison of bundle and classical column generation. Math Program 113(2): 299–344

    Article  Google Scholar 

  • Chabrier A (2006) Vehicle routing problem with elementary shortest path based column generation. Comput Oper Res 33: 2972–2990

    Article  Google Scholar 

  • Cook W, Rich JL (1999) A parallel cutting-plane algorithm for the vehicle routing problem with time windows. Technical report TR99-04, Department of Computational and Applied Mathematics, Rice University

  • Cordeau J-F, Desaulniers G, Desrosiers J, Solomon MM, Soumis F (2001) The VRP with time windows. In: Toth P, Vigo D (eds) The vehicle routing problem, SIAM monographs on discrete mathematics and applications. pp 157–194

  • Desaulniers G, Desrosiers J, Solomon MM (2001) Accelerating strategies in column generation methods for vehicle routing and crew scheduling problems. In: Ribeiro CC, Hansen P (eds) Essays and surveys in metaheuristics. Kluwer, Boston, pp 309–324

    Google Scholar 

  • Desaulniers G, Desrosiers J, Solomon MM (eds) (2005) Column generation. GERAD 25th Anniversary Series. Springer

  • Desaulniers G, Desrosiers J, Spoorendonk S (2009) Cutting planes for branch-and-price algorithms. Technical report G-2009-52, GERAD, Canada

  • Desaulniers G, Lessard F, Hadjar A (2008) Tabu search, partial elementarity, and generalized k-path inequalities for the vehicle routing problem with time windows. Transport Sci 42(3): 387–404

    Article  Google Scholar 

  • Desrochers M, Desrosiers J, Solomon MM (1992) A new optimization algorithm for the vehicle routing problem with time windows. Oper Res 40(2): 342–354

    Article  Google Scholar 

  • Dror M (1994) Note on the complexity of the shortest path models for column generation in VRPTW. Oper Res 42(5): 977–978

    Article  Google Scholar 

  • du Merle O, Villeneuve D, Desrosiers J, Hansen P (1999) Stabilized column generation. Discrete Math 194(1-3): 229–237

    Article  Google Scholar 

  • Feillet D, Dejax P, Gendreau M, Gueguen C (2004) An exact algorithm for the elementary shortest path problem with resource constraints: application to some vehicle routing problems. Networks 44(3): 216–229

    Article  Google Scholar 

  • Frangioni A (2002) Generalized bundle methods. SIAM J Optim 13(1): 117–156

    Article  Google Scholar 

  • Goffin JL, Vial JP (2002) Convex nondifferentiable optimization: a survey focused on the analytic center cutting plane method. Optim Methods Softw 17(5): 805–867

    Article  Google Scholar 

  • Irnich S, Desaulniers G (2005) Shortest path problems with resource constraints. In: Desaulniers G, Desrosiers J, Solomon MM (eds) Column generation, GERAD 25th anniversary series, chap 2. Springer, pp 33–65

  • Irnich S, Villeneuve D (2006) The shortest path problem with k-cycle elimination for k≥3. Transport Sci 18(3): 391–406

    Google Scholar 

  • Jepsen M, Petersen B, Spoorendonk S, Pisinger D (2008) Subset row inequalities applied to the vehicle routing problem with time windows. Oper Res 56(2): 497–511

    Article  Google Scholar 

  • Kallehauge B, Larsen J, Madsen OBG (2001) Lagrangean duality applied on vehicle routing with time windows—experimental results. Technical report IMM-TR-2001-9, IMM, Technical University of Denmark

  • Kallehauge B, Larsen J, Madsen OBG (2006) Lagrangian duality applied to the vehicle routing problem with time windows. Comput Oper Res 33(5): 1464–1487

    Article  Google Scholar 

  • Kelley JE (1960) The cutting plane method for solving convex programs. J SIAM 8: 703–712

    Google Scholar 

  • Kim S, Chang K-N, Lee J-Y (1995) A descent method with linear programming subproblems for nondifferentiable convex optimization. Math Program 71: 17–28

    Article  Google Scholar 

  • Kohl N, Desrosiers J, Madsen OBG, Solomon MM, Soumis F (1999) 2-path cuts for the vehicle routing problem with time windows. Transport Sci

  • Lemaréchal C, Nemirovskii A, Nesterov Y (1995) New variants of bundle methods. Math Program 69: 111–149

    Article  Google Scholar 

  • Lübbecke ME, Desrosiers J (2005) Selected topics in column generation. Oper Res 53(6):1007–1023

    Article  Google Scholar 

  • Marsten RE, Hogan WW, Blankenship JW (1975) The BOXSTEP method for large-scale optimization. Oper Res 23: 389–405

    Article  Google Scholar 

  • Neame PJ (1999) Nonsmooth dual methods in integer programming. PhD thesis, University of Melbourne

  • Righini G, Salani M (2008) New dynamic programming algorithms for the resource constrained elementary shortest path problem. Networks 51(3): 155–170

    Article  Google Scholar 

  • Rousseau L-M, Gendreau M, Feillet D (2007) Interior point stabilization for column generation. Oper Res Lett 35: 660–668

    Article  Google Scholar 

  • Spoorendonk S (2008) Cut and column generation. PhD thesis, Technical University of Denmark

  • Spoorendonk S, Desaulniers G (2008) Clique inequalities applied to the vehicle routing problem with time windows. Technical report G-2008-72, GERAD, Canada. Forthcoming in INFOR

  • Vanderbeck F (2000) On Dantzig-Wolfe decomposition in integer programming and ways to perform branching in a branch-and-price algorithm. Oper Res 48(1): 111–128

    Article  Google Scholar 

  • Vanderbeck F (2005) Implementing mixed integer column generation. In: Desaulniers G, Desrosiers J, Solomon MM (eds) Column generation, GERAD 25th anniversary series, chap 12. Springer, pp 331–358

  • Vanderbeck F, Savelsbergh MWP (2006) A generic view of Dantzig-Wolfe decomposition in mixed integer programming. Oper Res Lett 34: 296–306

    Article  Google Scholar 

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Authors and Affiliations

  1. Ecole Nationale Supérieure des Mines de Saint-Etienne, CMP Georges Charpak, 13541, Gardanne, France

    Dominique Feillet

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  1. Dominique Feillet
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Correspondence to Dominique Feillet.

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Feillet, D. A tutorial on column generation and branch-and-price for vehicle routing problems. 4OR-Q J Oper Res 8, 407–424 (2010). https://doi.org/10.1007/s10288-010-0130-z

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  • DOI: https://doi.org/10.1007/s10288-010-0130-z

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