Valid inequalities for the fleet size and mix vehicle routing problem with fixed costs

In the well-known Vehicle Routing Problem (VRP) a set of identical vehicles located at a central depot is to be optimally routed to supply customers with known demands subject to vehicle capacity constraints. An important variant of the VRP arises when a mixed fleet of vehicles, characterized by different capacities and costs, is available for distribution activities. The problem is known as Fleet Size and Mix VRP with Fixed Costs (FSMF) and has several practical applications. In this paper, we present a new mixed integer programming formulation for FSMF based on a two–commodity network flow approach. New valid inequalities are proposed to strengthen the linear programming relaxation of the mathematical formulation. The effectiveness of the proposed cuts is extensively tested on benchmark instances.

[1]  Dong-wan Tcha,et al.  A column generation approach to the heterogeneous fleet vehicle routing problem , 2007, Comput. Oper. Res..

[2]  S. Salhi,et al.  Local Search Strategies for the Vehicle Fleet Mix Problem , 1996 .

[3]  Hande Yaman.  Formulations and Valid Inequalities for the Heterogeneous Vehicle Routing Problem , 2006, Math. Program..

[4]  Michel Gendreau,et al.  A tabu search heuristic for the heterogeneous fleet vehicle routing problem , 1999, Comput. Oper. Res..

[5]  Bruce L. Golden,et al.  A new heuristic for determining fleet size and composition , 1986 .

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

[7]  Maud Göthe-Lundgren,et al.  Mathematical Formulations of the Heterogeneous Fleet Vehicle Routing Problem , 2003 .

[8]  Dalessandro Soares Vianna,et al.  An Evolutionary Hybrid Metaheuristic for Solving the Vehicle Routing Problem with Heterogeneous Fleet , 1998, EuroGP.

[9]  Adam N. Letchford,et al.  Multistars, partial multistars and the capacitated vehicle routing problem , 2002, Math. Program..

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

[11]  Paolo Toth,et al.  Exact algorithms for the vehicle routing problem, based on spanning tree and shortest path relaxations , 1981, Math. Program..

[12]  Marcus Poggi de Aragão,et al.  A robust branch‐cut‐and‐price algorithm for the heterogeneous fleet vehicle routing problem , 2007, WEA.

[13]  Roberto Baldacci,et al.  An Exact Algorithm for the Capacitated Vehicle Routing Problem Based on a Two-Commodity Network Flow Formulation , 2004, Oper. Res..

[14]  Giovanni Rinaldi,et al.  Branch-And-Cut Algorithms for the Capacitated VRP , 2001, The Vehicle Routing Problem.

[15]  Bruce L. Golden,et al.  A comparison of techniques for solving the fleet size and mix vehicle routing problem , 1984 .

[16]  Jacques Renaud,et al.  A sweep-based algorithm for the fleet size and mix vehicle routing problem , 2002, Eur. J. Oper. Res..

[17]  Martin Desrochers,et al.  A new heuristic for the fleet size and mix vehicle routing problem , 1991, Comput. Oper. Res..

[18]  Said Salhi,et al.  Incorporating vehicle routing into the vehicle fleet composition problem , 1993 .

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

[20]  Jean-Yves Potvin,et al.  Vehicle Routing , 2009, Encyclopedia of Optimization.

[21]  Éric D. Taillard,et al.  A heuristic column generation method for the heterogeneous fleet VRP , 1999, RAIRO Oper. Res..

[22]  Dalessandro Soares Vianna,et al.  A parallel evolutionary algorithm for the vehicle routing problem with heterogeneous fleet , 1998, Future Gener. Comput. Syst..

[23]  Renato F. Werneck,et al.  Robust Branch-and-Cut-and-Price for the Capacitated Vehicle Routing Problem , 2004, Math. Program..

[24]  Ibrahim H. Osman,et al.  Tabu search variants for the mix fleet vehicle routing problem , 2002, J. Oper. Res. Soc..

[25]  J. F. Pierce,et al.  ON THE TRUCK DISPATCHING PROBLEM , 1971 .

[26]  Daniele Vigo,et al.  Routing a Heterogeneous Fleet of Vehicles , 2008 .

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

[28]  Adam N. Letchford,et al.  A new branch-and-cut algorithm for the capacitated vehicle routing problem , 2004, Math. Program..