An Improved Branch - and - Cut Algorithm for the Capacitated Vehicle Routing Problem

The capacitated vehicle routing problem (CVRP) deals with the distribution of a single commodity from a centralized depot to a number of specified customer locations with known demands. The CVRP considered in this paper assumes common vehicle capacity, fixed or variable number of vehicles, and an objective to minimize the total distance traveled by all the vehicles. This paper develops several new cutting planes for this problem, and uses them in an exact branch-and-cut algorithm. Two of the new cutting planes are based on a specified structure of an optimal solution and its existence. Computational results are reported for 1,650 simulated Euclidean problems as well as 24 standard literature test problems; solved problems range in size from 15--100 customers. A comparative analysis demonstrates the significant computational benefit of the proposed method.

[1]  Bernard Fortz,et al.  A Branch-and-Cut Algorithm , 2000 .

[2]  Thomas L. Morin,et al.  A branch-and-cut algorithm for vehicle routing problems , 1994, Ann. Oper. Res..

[3]  J. A. Bondy,et al.  Graph Theory with Applications , 1978 .

[4]  Nicos Christofides,et al.  An Algorithm for the Vehicle-dispatching Problem , 1969 .

[5]  Gilbert Laporte,et al.  The vehicle routing problem: An overview of exact and approximate algorithms , 1992 .

[6]  H. Crowder,et al.  Solving Large-Scale Symmetric Travelling Salesman Problems to Optimality , 1980 .

[7]  Nicos Christofides,et al.  A new exact algorithm for the vehicle routing problem based onq-paths andk-shortest paths relaxations , 1995, Ann. Oper. Res..

[8]  Nicos Christofides,et al.  Distribution management : mathematical modelling and practical analysis , 1971 .

[9]  Louis Caccetta,et al.  Integer linear programming formulation for a vehicle routing problem , 1991 .

[10]  Paolo Toth,et al.  The Vehicle Routing Problem , 2002, SIAM monographs on discrete mathematics and applications.

[11]  Gerhard Reinelt,et al.  TSPLIB - A Traveling Salesman Problem Library , 1991, INFORMS J. Comput..

[12]  Éric D. Taillard,et al.  Parallel iterative search methods for vehicle routing problems , 1993, Networks.

[13]  L. Bodin.  ROUTING AND SCHEDULING OF VEHICLES AND CREWS–THE STATE OF THE ART , 1983 .

[14]  Giovanni Rinaldi,et al.  A Branch-and-Cut Algorithm for the Resolution of Large-Scale Symmetric Traveling Salesman Problems , 1991, SIAM Rev..

[15]  Lawrence Bodin,et al.  Cost models for vehicle routing problems , 2002, Proceedings of the 35th Annual Hawaii International Conference on System Sciences.

[16]  H. Paessens,et al.  The savings algorithm for the vehicle routing problem , 1988 .

[17]  Ángel Corberán,et al.  Polyhedral results for a vehicle routing problem , 1991 .

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

[19]  L. Caccetta,et al.  A new subtour elimination constraint for the vehicle routing problem , 1996 .

[20]  Gérard Cornuéjols,et al.  Polyhedral study of the capacitated vehicle routing problem , 1993, Math. Program..

[21]  Giovanni Rinaldi,et al.  Computational results with a branch and cut code for the capacitated vehicle routing problem , 1998 .

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

[23]  Susan Powell,et al.  Fortran codes for mathematical programming: linear, quadratic and discrete , 1973 .

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