Advertisement

Routing a Heterogeneous Fleet of Vehicles

Chapter
Part of the Operations Research/Computer Science Interfaces book series (ORCS, volume 43)

Summary

In the well-known Vehicle Routing Problem (VRP) a set of identical vehicles, based 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 fleet of vehicles characterized by different capacities and costs is available for distribution activities. The problem is known as the Mixed Fleet VRP or as the Heterogeneous Fleet VRP.

This chapter gives an overview of approaches from the literature to solve heterogeneous VRPs. In particular, we classify the different variants described in the literature and, as no exact algorithm has been presented for any variants of heterogeneous VRP, we review the lower bounds and the heuristic algorithms proposed. Computational results, comparing the performance of the different heuristic algorithms on benchmark instances, are also discussed.

Key words

Heterogeneous vehicle routing problem 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    K. Altinkemer and B. Gavish. A parallel savings heuristic for the delilvery problem with a log q error guarantees.Operations Research Letters, 6: 149–158, 1987.CrossRefGoogle Scholar
  2. 2.
    M. Balinski and R. Quandt. On an integer program for a delivery problem.Operations Research, 12: 300–304, 1964.Google Scholar
  3. 3.
    J.J. Bartholdi and L.K. Platzman. An O(n log n) travelling salesman heuristic based on spacefilling curves.Operation Research Letters, 1(4): 121–125, 1982.CrossRefGoogle Scholar
  4. 4.
    J.E. Beasley. Route-first cluster-second methods for vehicle routing.Omega, 11: 403–408, 1983.CrossRefGoogle Scholar
  5. 5.
    J. Brandão and A. Mercer. A tabu search algorithm for the multi-trip vehicle routing and scheduling problem.European Journal of Operational Research, 100: 180–191, 1997.CrossRefGoogle Scholar
  6. 6.
    O. Bräysy, M. Gendreau, G. Hasle, and A. Løkketangen. A survey of rich vehicle routing models and heuristic solution techniques. Technical report, SINTEF, 2002.Google Scholar
  7. 7.
    O. Bräysy, W. Dullaert, G. Hasle, D. Mester, and M. Gendreau. An effective multi-restart deterministic annealing methauristic for the fleet size and mix vehicle routing problem with time windows.Transportation Science, to appear, 2006.Google Scholar
  8. 8.
    I.M. Chao, B.L. Golden, and E. Wasil. A computational study of a new heuristic for the site-dependent vehicle routing problem.INFOR, 37:3: 319–336, 1999.Google Scholar
  9. 9.
    E. Choi and D. W. Tcha. A column generation approach to the heterogeneous fleet vehicle routing problem.Computers & Operations Research, 34: 2080–2095, 2007.CrossRefGoogle Scholar
  10. 10.
    N. Christofides, A. Mingozzi, and P. Toth. Exact algorithms for the vehicle routing problem based on spanning tree and shortest path relaxation.Mathematical Programming, 10: 255–280, 1981.CrossRefGoogle Scholar
  11. 11.
    G. Clarke and J. Wright. Scheduling of vehicles from a central depot to a number of delivery points.Operations Research, 12(4): 568–581, 1964.Google Scholar
  12. 12.
    J.-F. Cordeau and G. Laporte. A tabu search algorithm for the site dependent vehicle routing problem with time windows.INFOR, 39: 292–298, 2001.Google Scholar
  13. 13.
    J.-F. Cordeau, M. Gendreau, and G. Laporte. A tabu search heuristic for periodic and multi–depot vehicle routing problems.Networks, 30: 105–119, 1997.CrossRefGoogle Scholar
  14. 14.
    J. F. Cordeau, G. Laporte, M. W. P. Savelsbergh, and D. Vigo. Vehicle routing. In C. Barnhart and G. Laporte, editors,Transportation, Handbooks in Operations Research and Management Science, volume 14, pages 367–428. Elsevier, Amsterdam, 2007.Google Scholar
  15. 15.
    G.B. Dantzig and J.H. Ramser. The truck dispatching problem.Management Science, 6 (1): 80–91, 1959.CrossRefGoogle Scholar
  16. 16.
    M. Dell’Amico, M. Monaci, C. Pagani, and D. Vigo. Heuristic approaches for the fleet size and mix vehicle routing problem with time windows.Transportation Science, 2007. To appear.Google Scholar
  17. 17.
    M. Desrochers and T.W. Verhoog. A new heuristic for the fleet size and mix vehicle-routing problem.Computers & Operations Research, 18 (3): 263–274, 1991.CrossRefGoogle Scholar
  18. 18.
    W. Dullaert, G.K. Janssens, K. Sörensen, and B. Vernimmen. New heuristics for the fleet size and mix vehicle routing problem with time windows.Journal of the Operational Research Society, 53 (11): 1232–1238, 2002.CrossRefGoogle Scholar
  19. 19.
    S. Engevall, M. Gothe-Lundgren, and P. Varbrand. The heterogeneous vehicle-routing game.Transportation Science, 38 (1): 71–85, 2004.CrossRefGoogle Scholar
  20. 20.
    J.A. Ferland and P. Michelon. The vehicle scheduling problem with multiple vehicle types.Journal of the Operational Research Society, 39 (6): 577–583, 1988.CrossRefGoogle Scholar
  21. 21.
    M. Fisher and R. Jaikumar. A generalized assignment heuristic for vehicle routing.Networks, 11: 109–124, 1981.CrossRefGoogle Scholar
  22. 22.
    W.W. Garvin, H.W. Crandall, J.B. John, and R.A. Spellman. Applications of vehicle routing in the oil industry.Management Science, 3: 407–430, 1957.Google Scholar
  23. 23.
    T.J. Gaskell. Bases for vehicle fleet scheduling.Operational Research Quarterly, 18: 281–295, 1967.Google Scholar
  24. 24.
    B. Gavish and S.C. Graves. Scheduling and routing in transportation and distribution systems: formulations and new relaxations. Technical report, Graduate School of Management, University of Rochester, 1982.Google Scholar
  25. 25.
    M. Gendreau, G. Laporte, C. Musaraganyi, and E.D. Taillard. A tabu search heuristic for the heterogeneous fleet vehicle routing problem.Computers & Operations Research, 26 (12): 1153–1173, 1999.CrossRefGoogle Scholar
  26. 26.
    F.G. Gheysens, B.L. Golden, and A.A. Assad. A relaxation heuristic for the fleet size and mix vehicle routing problem. InProceedings of SE AIDS Meeting, Williamsburg, Virginia, 1983.Google Scholar
  27. 27.
    F.G. Gheysens, B.L. Golden, and A.A. Assad. A comparison of techniques for solving the fleet size and mix vehicle routing problem.OR Spectrum, 6 (4): 207–216, 1984.Google Scholar
  28. 28.
    F.G. Gheysens, B.L. Golden, and Assad A.A. A new heuristic for determining fleet size and composition.Mathematical Programming Studies, 26: 233–236, 1986.Google Scholar
  29. 29.
    B. Gillett and L. Miller. A heuristic for the vehicle dispatching problem.Operations Research, 22: 340–349, 1974.Google Scholar
  30. 30.
    B.L. Golden, A.A. Assad, L. Levy, and F.G. Gheysens. The fleet size and mix vehicle routing problem.Computers & OR, 11 (1): 49–66, 1984.CrossRefGoogle Scholar
  31. 31.
    B.L. Golden, E. Wasil, J. Kelly, and I.M. Chao. The impact of metaheuristic on solving the vehicle routing problem: algorithms, problem sets, and computational results. In T. Crainic and G. Laporte, editors,Fleet Management and Logistics, pages 33–56. Kluwer, Boston, MA, 1998.Google Scholar
  32. 32.
    F. Li, B.L. Golden, and E.A. Wasil. A record-to-record travel algorithm for solving the heterogeneous fleet vehicle routing problem.Computers & Operations Research, 34: 2734–2742, 2007.CrossRefGoogle Scholar
  33. 33.
    S. Lin. Computer solutions of the traveling salesman problem.Bell System Technical Journal, 44: 2245–2269, 1965.Google Scholar
  34. 34.
    F.H. Liu and S.Y. Shen. The fleet size and mix vehicle routing problem with time windows.Journal of the Operational Research Society, 50 (7): 721–732, 1999.CrossRefGoogle Scholar
  35. 35.
    C.E. Miller, A.W. Tucker, and R.A. Zemlin. Integer programming formulation of traveling salesman problems.J. ACM, 7 (4): 326–329, 1960.CrossRefGoogle Scholar
  36. 36.
    B. Nag.Vehicle Routing in the Presence of Site/Vehicle Dependency Constraints. PhD thesis, College of Business and Management, University of Maryland, 1986.Google Scholar
  37. 37.
    B. Nag, B.L. Golden, and A. Assad. Vehicle routing with site dependencies. In B.L. Golden and A. Assad, editors,Vehicle Routing: Methods and Studies, pages 149–159. Elsevier, Amsterdam, Holland, 1988.Google Scholar
  38. 38.
    L.S. Ochi, D.S. Vianna, L.M.A. Drummond, and A.O. Victor. An evolutionary hybrid metaheuristic for solving the vehicle routing problem with heterogeneous fleet.Lecture notes in computer science, 1391: 187–195, 1998.CrossRefGoogle Scholar
  39. 39.
    L.S. Ochi, D.S. Vianna, L.M.A. Drummond, and A.O. Victor. A parallel evolutionary algorithm for the vehicle routing problem with heterogeneous fleet.Parallel and Distributed Processing, 1388: 216–224, 1998.Google Scholar
  40. 40.
    I. Or.Traveling Salesman-type Combinatorial Optimization Problems and their Relation to the Logistics of Regional Blood Banking. PhD thesis, Department of Industrial Engineering and Management Sciences. Northwestern University, Evanston, IL, 1976.Google Scholar
  41. 41.
    I.H. Osman and S. Salhi. Local search strategies for the vehicle fleet mix problem. In V.J. Rayward-Smith, I.H. Osman, C.R. Reeves, and G.D. Smith, editors,Modern Heuristic Search Methods, pages 131–153. Wiley: Chichester, 1996.Google Scholar
  42. 42.
    D. Pisinger and S. Ropke. A general heuristic for vehicle routing problems.Comput. Oper. Res., 34 (8): 2403–2435, 2007.CrossRefGoogle Scholar
  43. 43.
    C. Prins. Efficient heuristics for the heterogeneous fleet multitrip VRP with application to a large-scale real case.Journal of Mathematical Modelling and Algorithms, 1 (2): 135–150, 2002.CrossRefGoogle Scholar
  44. 44.
    J. Renaud and F.F. Boctor. A sweep-based algorithm for the fleet size and mix vehicle routing problem.European Journal of Operational Research, 140 (3): 618–628, 2002.CrossRefGoogle Scholar
  45. 45.
    Y. Rochat and F. Semet. A tabu search approach for delivering pet food and flour in Switzerland.Journal of the Operational Research Society, 45: 1233–1246, 1994.CrossRefGoogle Scholar
  46. 46.
    Y. Rochat and E.D. Taillard. Probabilistic diversification and intensification in local search for vehicle routing.Journal of Heuristics, 40: 147–167, 1995.CrossRefGoogle Scholar
  47. 47.
    S. Salhi and G.K. Rand. Incorporating vehicle routing into the vehicle fleet composition problem.European Journal of Operational Research, 66 (3): 313–330, 1993.CrossRefGoogle Scholar
  48. 48.
    F. Semet and E. Taillard. Solving real-life vehicle routing problems efficiently using tabu search.Annals Of Operationals Research, 41: 469–488, 1993.CrossRefGoogle Scholar
  49. 49.
    M. Solomon. Algorithms for the vehicle routing and scheduling problems with the time window constraints.Operations Research, 35: 254–265, 1987.Google Scholar
  50. 50.
    E.D. Taillard. A heuristic column generation method for the heterogeneous fleet vrp.RAIRO Recherche Opérationnelle, 33 (1): 1–14, 1999.CrossRefGoogle Scholar
  51. 51.
    C.D. Tarantilis, C.T. Kiranoudis, and V.S. Vassiliadis. A list based threshold accepting metaheuristic for the heterogeneous fixed fleet vehicle routing problem.Journal of the Operational Research Society, 54 (1): 65–71, 2003.CrossRefGoogle Scholar
  52. 52.
    C.D. Tarantilis, C.T. Kiranoudis, and V.S. Vassiliadis. A threshold accepting metaheuristic for the heterogeneous fixed fleet vehicle routing problem.European Journal of Operational Research, 152 (1): 148–158, 2004.CrossRefGoogle Scholar
  53. 53.
    R. Tavakkoli-Moghaddam, N. Safaei, and Y. Gholipour. A hybrid simulated annealing for capacitated vehicle routing problems with the independent route length.Applied Mathematics and Computation, 176 (2): 445–454, May 2006.CrossRefGoogle Scholar
  54. 54.
    D. Teodorovic, E. Krcmarnozic, and G. Pavkovic. The mixed fleet stochastic vehicle-routing problem.Transportation Planning and Technology, 19 (1): 31–43, 1995.CrossRefGoogle Scholar
  55. 55.
    P. Toth and D. Vigo, editors.The Vehicle Routing Problem. Monographs on Discrete Mathematics and Applications. SIAM, Philadelphia, PA, 2002.Google Scholar
  56. 56.
    N.A. Wassan and I.H. Osman. Tabu search variants for the mix fleet vehicle routing problem.Journal of the Operational Research Society, 53 (7): 768–782, 2002.CrossRefGoogle Scholar
  57. 57.
    P.L. Wu, J.C. Hartman, and G.R. Wilson. An integrated model and solution approach for fleet sizing with heterogeneous assets.Transportation Science, 39 (1): 87–103, 2005.CrossRefGoogle Scholar
  58. 58.
    H.D. Yaman. Formulations and valid inequalities for the heterogeneous vehicle routing problem.Mathematical Programming, 106 (2): 365–390, 2006.CrossRefGoogle Scholar
  59. 59.
    P. Yellow. A computational modification to the savings method of vehicle scheduling.Operational Research Quarterly, 21: 281–283, 1970.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.DEISUniversity of Bolognavia Venezia 52Italy

Personalised recommendations