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Challenges and Advances in A Priori Routing

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

An a priori route is a route which specifies an ordering of all possible customers that a particular driver may need to visit. The driver may then skip those customers on the route who do not receive a delivery. Despite the prevalence of a priori routing, construction of these routes still presents considerable challenges. Exact methods are limited to small problem sizes, and even heuristic methods are intractable in the face of real-world-sized instances. In this chapter, we will review some of the ideas that have emerged in recent years to help solve these larger instances. We focus on the probabilistic traveling salesman problem and the recently introduced probabilistic traveling salesman problem with deadlines and discuss how objective-function approximations can reduce computation time without significantly impacting solution quality. We will also present several open research questions in a priori routing.

Key words

Stochastic routing a priori routing 

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References

  1. 1.
    J.J. Bartholdi, L.K. Platzman, R.L. Collins, and W.H. Warden. A minimal technology routing system for meals on wheels.Interfaces, 13:1–8, 1983.Google Scholar
  2. 2.
    J.J. Bartholdi and L.K. Platzman. An o(n log n) planar traveling salesman heuristic based on spacefilling curves.Operations Research Letters, 1:121–125, 1982.CrossRefGoogle Scholar
  3. 3.
    C. Bastian and A.H.G. Rinnooy Kan. The stochastic vehicle routing problem revisited.European Journal of Operational Research, 56:407–412, 1992.CrossRefGoogle Scholar
  4. 4.
    J.E. Beasley and N.Christofides. Vehicle routing with a sparse feasibility graph.European Journal of Operational Research, 98:499–511, 1997.CrossRefGoogle Scholar
  5. 5.
    W.C. Benton and M.D. Rosetti. The vehicle scheduling problem with intermittent customer demands.Computers and Operations Research, 19:521–531, 1992.CrossRefGoogle Scholar
  6. 6.
    P.Beraldi, G.Ghiani, G.Laporte, and R.Musmanno. Efficient neighborhood search for the probabilistic pickup and delivery travelling salesman problem.Networks, 45 (4):195–198, 2005.Google Scholar
  7. 7.
    D.Simchi-Levi. Finding optimal a priori tour and location of traveling salesman with nonhomogenous customers.Transportation Science, 22:148–154, 1988.Google Scholar
  8. 8.
    D.J. Bertsimas.Probabilistic Combinatorial Optimizations Problems. PhD thesis, Massachusetts Institute of Technology, 1988.Google Scholar
  9. 9.
    D.J. Bertsimas and L.H. Howell. Further results on the probabilistic traveling salesman problem.European Journal of Operational Research, 65:68–95,1993.CrossRefGoogle Scholar
  10. 10.
    D.J. Bertsimas, P.Jaillet, and A.R. Odoni. A priori optimization.Operations Research, 38:1019–1033, 1990.Google Scholar
  11. 11.
    D.J. Bertsimas, P. Chervi, and M. Peterson. Computational approaches to stochastic vehicle routing problems.Transportation Science, 29:342–352, 1995.Google Scholar
  12. 12.
    L. Bianchi and A.M. Campbell. Extension of the 2-p-opt and 1-shift algorithms to the heterogeneous probabilistic traveling salesman problem.European Journal of Operational Research, 176: 131–144, 2007.CrossRefGoogle Scholar
  13. 13.
    L. Bianchi, L.M. Gambardella, and M. Dorigo. Solving the homogeneous probabilistic traveling salesman problem by the aco metaheuristic. In M. Dorigo, G. DiCaro, and M. Sampels, editors,Proceedings of ANTS 2002: Third International Workshop, volume 2463/2002 ofLecture Notes in Computer Science, pages 176–187, Berlin, 2002. Springer.Google Scholar
  14. 14.
    L. Bianchi, L.M. Gambardella, and M. Dorigo. An ant colony optimization approach to the probabilistic traveling salesman problem. In G. Goos, J. Hartmanis, and J. van Leeuwen, editors,Proceedings of the 7th International Conference on Parallel Problem Solving from Nature, volume 2439/2002 ofLecture Notes in Computer Science, pages 883–892, Berlin, 2002. Springer.Google Scholar
  15. 15.
    Leonora Bianchi, Joshua Knowles, and Neil Bowler. Local search for the probabilistic traveling salesman problem: Correction to the 2-p-opt and 1-shift algorithms.European Journal of Operational Research, 162: 206–219, 2005.CrossRefGoogle Scholar
  16. 16.
    J.R. Birge and F.Louveaux.Introduction to Stochastic Programming. Springer-Verlag, New York, 1997.Google Scholar
  17. 17.
    N.E. Bowler, T.M.A. Fink, and R.C. Ball. Characterization of the probabilistic traveling salesman problem.Physical Review E, 68:036703, 2003.CrossRefGoogle Scholar
  18. 18.
    J. Bramel, E.G. Coffman, P.W. Shor, and D.Simchi-Levi. Probabilistic analysis of the capacitated vehicle routing problem with unsplit demands.Operations Research, 340:1095–1106, 1992.Google Scholar
  19. 19.
    J. Branke and M. Guntsch. Solving the probabilistic tsp with ant colony optimization.Journal of Mathematical Modelling and Algorithms, 3 (4):403–425, 2004.Google Scholar
  20. 20.
    M.L. Braun and J.M. Buhmann. The noisy euclidean traveling salesman problem and learning. In T.Dietterich, S.Becker, and Z.Ghahramani, editors,Advances in Neural Information Processing Systems, volume14, pages 251–258. MIT Press, 2002.Google Scholar
  21. 21.
    A.M. Campbell. Aggregation for the probabilistic traveling salesman problem.Computers & Operations Research, 33:2703–2724, 2006.CrossRefGoogle Scholar
  22. 22.
    A.M. Campbell and B.W. Thomas. The probabilistic traveling salesman problem with deadlines. forthcoming inTransportation Science, 2007Google Scholar
  23. 23.
    A.M. Campbell and B.W. Thomas. Runtime reduction techniques for the probabilistic traveling salesman problem with deadlines. Submitted to Computers and Operations Research, 2007Google Scholar
  24. 24.
    A.M. Campbell and B.W. Thomas. The stochastic vehicle routing problem with deadlines. Working Paper, 2007.Google Scholar
  25. 25.
    B.Carey. Expedited grows on the surface.Traffic World, page1, January 2, 2006.Google Scholar
  26. 26.
    A. Charnes and W.W. Cooper. Chance-constrained programming.Management Science, 6:73–79, 1959.Google Scholar
  27. 27.
    A. Charnes and W.W. Cooper. Deterministic equivalents for optimizing and satisficing under chance constraints.Operations Research, 11:18–39, 1963.Google Scholar
  28. 28.
    P.Chervi. A computational approach to probabilistic vehicle routing problems. Master’s thesis, Massachusetts Institute of Technology, 1988.Google Scholar
  29. 29.
    M.S. Daskin, A. Haghani, M. Khanal, and C. Malandraki. Aggregation effects in maximum covering models.Annals of Operations Research, 18:115–139, 1989.CrossRefGoogle Scholar
  30. 30.
    M.deBerg, O.Schwarzkopf, M.van Kreveld, and M.Overmars.Computational Geometry: Algorithms and Applications. Springer-Verlag, 2000.Google Scholar
  31. 31.
    M. Dror. Modeling vehicle routing with uncertain demands as stochastic programs: Properties of the corresponding solution.European Journal of Operational Research, 64: 432–441, 1993.CrossRefGoogle Scholar
  32. 32.
    M. Dror and P. Trudeau. Stochastic vehicle routing with modified savings algorithm.European Journal of Operational Research, 23:228–235, 1986.CrossRefGoogle Scholar
  33. 33.
    M. Dror, G. Laporte, and P. Trudeau. Vehicle routing with stochastic demands: Properties and solution frameworks.Transportation Science, 23:166–176, 1989.Google Scholar
  34. 34.
    R. L. Francis and T. J. Lowe. On worst-case aggregation analysis for network location problems.Annals of Operations Research, 40:229–246, 1992.CrossRefGoogle Scholar
  35. 35.
    M. Gendreau, G. Laporte, and R. Séguin. An exact algorithm for the vehicle routing problem with stochastic demands and customers.Transportation Science, 29:143–155, 1995.Google Scholar
  36. 36.
    M. Gendreau, G. Laporte, and R. Séguin. Stochastic vehicle routing.European Journal of Operational Research, 88:3–12, 1996.CrossRefGoogle Scholar
  37. 37.
    M. Gendreau, G. Laporte, and R. Séguin. A tabu search heuristic for the vehicle routing problem with stochastic demands and customers.Operations Research, 44:469–477, 1996.Google Scholar
  38. 38.
    J. Grefenstette, R. Gopal, B. Rosmaita, , and D. Van Gucht. Genetic algorithms for the traveling salesman problem. In J.Grefenstette, editor,Proceedings of the First International Conference on Genetic Algorithms, Hillsdale, New York, 1985. Lawrence Erlbaum Associates.Google Scholar
  39. 39.
    M. A. Haughton. Quantifying the benefits of route reoptimisation under stochastic customer demand.Journal of the Operational Research Society, 51:320–332, 2000.CrossRefGoogle Scholar
  40. 40.
    M. A. Haughton. Route reoptimization’s impact on delivery efficiency.Transportation Research - Part E, 38:53–63, 2002.CrossRefGoogle Scholar
  41. 41.
    P.Jaillet.Probabilistic Traveling Salesman Problems. PhD thesis, Massachusetts Institute of Technology, 1985.Google Scholar
  42. 42.
    P. Jaillet. A priori solution of the traveling salesman problem in which a random subset of customers are visited.Operations Research, 36:929–936, 1988.CrossRefGoogle Scholar
  43. 43.
    G. Laporte, F.V. Louveaux, and H. Mercure. Models and exact solutions for a class of stochastic location-routing problems.European Journal of Operational Research, 39:71–78, 1989.CrossRefGoogle Scholar
  44. 44.
    G. Laporte, F. V. Louveaux, and H. Mercure. A priori optimization of the probabilistic traveling salesman problem.Operations Research, 42:543–549, 1994.Google Scholar
  45. 45.
    F.Li, B.Golden, and E.Wasil. The noisy euclidean traveling salesman problem: A computational analysis. In F.Alt, M.Fu, and B.Golden, editors,Perspectives in Operations Research: Papers in Honor of Saul Gass’80th Birthday, pages 247–270. Springer, 2006.Google Scholar
  46. 46.
    S. Lin. Computer solution of the traveling salesman problem.Bell System Technical Journal, 44:2245–2269, 1965.Google Scholar
  47. 47.
    Y.-H. Liu. A scatter search based approach with approximate evaluation for the heterogeneous probabilistic traveling salesman problem. InProceedings of the 2006 IEEE Congress on Evolutionary Computation, pages 1603–1609, 2006.Google Scholar
  48. 48.
    J. Mercenier and P. Michel. Discrete-time finite horizon approximation of infinite horizon optimization problems with steady-state variance.Econometrica, 62 (3):635–656, 1994.Google Scholar
  49. 49.
    A. M. Newman and M. Kuchta. Using aggregation to optimize long-term production planning at an underground mine.European Journal of Operational Research, 176: 1205–1218, 2007.Google Scholar
  50. 50.
    M. B. Rayco, R. L. Francis, and A. Tamir. A p-center grid-positioning aggregation procedure.Computers and Operations Research, 26:1113–1124, 1999.CrossRefGoogle Scholar
  51. 51.
    S. Rosenow. A heuristic for the probabilistic TSP. In H.Schwarze, editor,Operations Research Proceedings 1996. Springer Verlag, 1997.Google Scholar
  52. 52.
    S.Rosenow. Comparison of an exact branch-and-bound and an approximative evolutionary algorithm for the probabilistic traveling salesman problem. working paper, available at urlhttp://www2.hsu-hh.de/uebe/paper-engl-SOR98.pdf, 1998.Google Scholar
  53. 53.
    F.Rossi and I.Gavioli. Aspects of heuristic methods in the probabilistic traveling salesman problem. InAdvanced School on Stochastics in Combinatorial Optimization, pages 214–227. World Scientific, 1987.Google Scholar
  54. 54.
    Martin W.P. Savelsbergh and M. Goetschalckx. A comparison of the efficiency of fixed versus variable vehicle routes.Journal of Business Logistics, 46:474–490, 1995.Google Scholar
  55. 55.
    W. R. Stewart and Bruce L. Golden. Stochastic vehicle routing: A comprehensive approach.European Journal of Operational Research, 14: 371–385, 1983.CrossRefGoogle Scholar
  56. 56.
    Hao Tang and Elise Miller-Hooks. Approximate procedures for the probabilistic traveling salesman problem.Transportation Research Record, 1882:27–36, 2004.CrossRefGoogle Scholar
  57. 57.
    S. Y. Teng, H. L. Ong, and H. C. Huang. An integer L-shaped algorithm for the time-constrained traveling salesman problem with stochastic travel times and service times.Asia-Pacific Journal of Operational Research, 21: 241–257, 2004.CrossRefGoogle Scholar
  58. 58.
    F. Tillman. The multiple terminal delivery problem with probabilistic demands.Transportation Science, 3:192–204, 1969.Google Scholar
  59. 59.
    United Parcel Service. About UPS. urlhttp://www.corporate-ir.net/ireye/ir_site.zhtml?ticker=UPS&script=2100& layout=7, 2002. Accessed on November 30, 2006.Google Scholar
  60. 60.
    C. D.J. Waters. Vehicle scheduling problems with uncertainty and omitted customers.Journal of the Operational Research Society, 40: 1099–1108, 1989.CrossRefGoogle Scholar
  61. 61.
    Jacky C.F. Wong, Janny M.Y. Leung, and C.H. Cheng. On a vehicle routing problem with time windows and stochastic travel times: Models, algorithms, and heuristics. Technical Report SEEM2003-03, Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, 2003.Google Scholar
  62. 62.
    Wen-Huei Yang, Kamlesh Mather, and RonaldH. Ballou. Stochastic vehicle routing problem with restocking.Transportation Science, 34:99–112, 2000.CrossRefGoogle Scholar
  63. 63.
    H. Zhong, R. W. Hall, and M. Dessouky. Territory planning and driver learning in vehicle dispatching.Transportation Science, to appear.Google Scholar
  64. 64.
    Hongsheng Zhong.Territory Planning and Vehicle Dispatching with Stochastic Customers and Demand. PhD thesis, University of Southern California, 2001.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Tippie College of Business Department of Management SciencesUniversity of IowaIowa City

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