A branch-and-cut-and-price algorithm for the multi-depot heterogeneous vehicle routing problem with time windows

Abstract We present a branch-and-cut-and-price algorithm for the exact solution of a variation of the vehicle routing problem with time windows in which the transportation fleet is made by vehicles with different capacities and fixed costs, based at different depots. We illustrate different pricing and cutting techniques and we present an experimental evaluation of their combinations. Computational results are reported on the use of the algorithm both for exact optimization and as a heuristic method.

[1]  Richard F. Hartl,et al.  A Variable Neighborhood Search for the Multi Depot Vehicle Routing Problem with Time Windows , 2004, J. Heuristics.

[2]  Marius M. Solomon,et al.  Algorithms for the Vehicle Routing and Scheduling Problems with Time Window Constraints , 1987, Oper. Res..

[3]  Bruce L. Golden,et al.  The vehicle routing problem : latest advances and new challenges , 2008 .

[4]  Giovanni Righini,et al.  A Column Generation Algorithm for a Rich Vehicle-Routing Problem , 2009, Transp. Sci..

[5]  Paolo Toth,et al.  State-space relaxation procedures for the computation of bounds to routing problems , 1981, Networks.

[6]  N. Boland,et al.  Path inequalities for the vehicle routing problem with time windows , 2007 .

[7]  Alain Chabrier,et al.  Vehicle Routing Problem with elementary shortest path based column generation , 2006, Comput. Oper. Res..

[8]  Tobias Achterberg,et al.  Constraint integer programming , 2007 .

[9]  Jaime Cerdá,et al.  A hybrid local improvement algorithm for large-scale multi-depot vehicle routing problems with time windows , 2009, Comput. Chem. Eng..

[10]  Giovanni Righini,et al.  New dynamic programming algorithms for the resource constrained elementary shortest path problem , 2008, Networks.

[11]  Giovanni Righini,et al.  New dynamic programming algorithms for the resource constrained elementary shortest path problem , 2008 .

[12]  Renato F. Werneck,et al.  Robust Branch-and-Cut-and-Price for the Capacitated Vehicle Routing Problem , 2006, Math. Program..

[13]  Brian Kallehauge,et al.  Formulations and exact algorithms for the vehicle routing problem with time windows , 2008, Comput. Oper. Res..

[14]  Gilbert Laporte,et al.  Optimal Routing under Capacity and Distance Restrictions , 1985, Oper. Res..

[15]  Gilbert Laporte,et al.  A unified tabu search heuristic for vehicle routing problems with time windows , 2001, J. Oper. Res. Soc..

[16]  Jacques Desrosiers,et al.  2-Path Cuts for the Vehicle Routing Problem with Time Windows , 1997, Transp. Sci..

[17]  Michel Gendreau,et al.  An exact algorithm for the elementary shortest path problem with resource constraints: Application to some vehicle routing problems , 2004, Networks.

[18]  Jack J. Dongarra,et al.  Performance of various computers using standard linear equations software in a FORTRAN environment , 1988, CARN.

[19]  Giovanni Righini,et al.  Symmetry helps: Bounded bi-directional dynamic programming for the elementary shortest path problem with resource constraints , 2006, Discret. Optim..

[20]  Moshe Dror,et al.  Note on the Complexity of the Shortest Path Models for Column Generation in VRPTW , 1994, Oper. Res..

[21]  Timo Berthold Primal Heuristics for Mixed Integer Programs , 2006 .

[22]  Chris T. Kiranoudis,et al.  An internet-based logistics management system for enterprise chains , 2005 .

[23]  Daniele Vigo,et al.  Heuristic Approaches for the Fleet Size and Mix Vehicle Routing Problem with Time Windows , 2007, Transp. Sci..

[24]  Marshall L. Fisher,et al.  Optimal Solution of Vehicle Routing Problems Using Minimum K-Trees , 1994, Oper. Res..

[25]  Luiz Paulo Lopes Fávero,et al.  Scatter search for the fleet size and mix vehicle routing problem with time windows , 2007, Central Eur. J. Oper. Res..

[26]  Roberto Baldacci,et al.  A unified exact method for solving different classes of vehicle routing problems , 2009, Math. Program..

[27]  Paolo Toth,et al.  Knapsack Problems: Algorithms and Computer Implementations , 1990 .

[28]  Michel Gendreau,et al.  Interior point stabilization for column generation , 2007, Oper. Res. Lett..

[29]  Gerrit K. Janssens,et al.  New heuristics for the Fleet Size and Mix Vehicle Routing Problem with Time Windows , 2002, J. Oper. Res. Soc..

[30]  Matteo Salani,et al.  Branch-and-Price Algorithms for Vehicle Routing Problems , 2006 .

[31]  Nicos Christofides,et al.  An exact algorithm for the vehicle routing problem based on the set partitioning formulation with additional cuts , 2008, Math. Program..

[32]  Jaime Cerdá,et al.  A cluster-based optimization approach for the multi-depot heterogeneous fleet vehicle routing problem with time windows , 2007, Eur. J. Oper. Res..

[33]  Marcus Poggi de Aragão,et al.  A robust branch-cut-and-price algorithm for the heterogeneous fleet vehicle routing problem , 2009 .

[34]  F.-H. Liu,et al.  The fleet size and mix vehicle routing problem with time windows , 1999, J. Oper. Res. Soc..

[35]  Bruce L. Golden,et al.  The fleet size and mix vehicle routing problem , 1984, Comput. Oper. Res..

[36]  John R. Current,et al.  Implementing a multi-vehicle multi-route spatial decision support system for efficient trash collection in Portugal , 2008 .