Skip to main content

Part of the book series: Operations Research/Computer Science Interfaces ((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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 219.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 279.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 379.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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. 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.

    Article  Google Scholar 

  3. C. Bastian and A.H.G. Rinnooy Kan. The stochastic vehicle routing problem revisited.European Journal of Operational Research, 56:407–412, 1992.

    Article  Google Scholar 

  4. J.E. Beasley and N.Christofides. Vehicle routing with a sparse feasibility graph.European Journal of Operational Research, 98:499–511, 1997.

    Article  Google Scholar 

  5. W.C. Benton and M.D. Rosetti. The vehicle scheduling problem with intermittent customer demands.Computers and Operations Research, 19:521–531, 1992.

    Article  Google Scholar 

  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. 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. D.J. Bertsimas.Probabilistic Combinatorial Optimizations Problems. PhD thesis, Massachusetts Institute of Technology, 1988.

    Google Scholar 

  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.

    Article  Google Scholar 

  10. D.J. Bertsimas, P.Jaillet, and A.R. Odoni. A priori optimization.Operations Research, 38:1019–1033, 1990.

    Google Scholar 

  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. 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.

    Article  Google Scholar 

  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. 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. 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.

    Article  Google Scholar 

  16. J.R. Birge and F.Louveaux.Introduction to Stochastic Programming. Springer-Verlag, New York, 1997.

    Google Scholar 

  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.

    Article  Google Scholar 

  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. 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. 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. A.M. Campbell. Aggregation for the probabilistic traveling salesman problem.Computers & Operations Research, 33:2703–2724, 2006.

    Article  Google Scholar 

  22. A.M. Campbell and B.W. Thomas. The probabilistic traveling salesman problem with deadlines. forthcoming inTransportation Science, 2007

    Google Scholar 

  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, 2007

    Google Scholar 

  24. A.M. Campbell and B.W. Thomas. The stochastic vehicle routing problem with deadlines. Working Paper, 2007.

    Google Scholar 

  25. B.Carey. Expedited grows on the surface.Traffic World, page1, January 2, 2006.

    Google Scholar 

  26. A. Charnes and W.W. Cooper. Chance-constrained programming.Management Science, 6:73–79, 1959.

    Google Scholar 

  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. P.Chervi. A computational approach to probabilistic vehicle routing problems. Master’s thesis, Massachusetts Institute of Technology, 1988.

    Google Scholar 

  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.

    Article  Google Scholar 

  30. M.deBerg, O.Schwarzkopf, M.van Kreveld, and M.Overmars.Computational Geometry: Algorithms and Applications. Springer-Verlag, 2000.

    Google Scholar 

  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.

    Article  Google Scholar 

  32. M. Dror and P. Trudeau. Stochastic vehicle routing with modified savings algorithm.European Journal of Operational Research, 23:228–235, 1986.

    Article  Google Scholar 

  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. R. L. Francis and T. J. Lowe. On worst-case aggregation analysis for network location problems.Annals of Operations Research, 40:229–246, 1992.

    Article  Google Scholar 

  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. M. Gendreau, G. Laporte, and R. Séguin. Stochastic vehicle routing.European Journal of Operational Research, 88:3–12, 1996.

    Article  Google Scholar 

  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. 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. M. A. Haughton. Quantifying the benefits of route reoptimisation under stochastic customer demand.Journal of the Operational Research Society, 51:320–332, 2000.

    Article  Google Scholar 

  40. M. A. Haughton. Route reoptimization’s impact on delivery efficiency.Transportation Research - Part E, 38:53–63, 2002.

    Article  Google Scholar 

  41. P.Jaillet.Probabilistic Traveling Salesman Problems. PhD thesis, Massachusetts Institute of Technology, 1985.

    Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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. 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. S. Lin. Computer solution of the traveling salesman problem.Bell System Technical Journal, 44:2245–2269, 1965.

    Google Scholar 

  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. 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. 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. M. B. Rayco, R. L. Francis, and A. Tamir. A p-center grid-positioning aggregation procedure.Computers and Operations Research, 26:1113–1124, 1999.

    Article  Google Scholar 

  51. S. Rosenow. A heuristic for the probabilistic TSP. In H.Schwarze, editor,Operations Research Proceedings 1996. Springer Verlag, 1997.

    Google Scholar 

  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. 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. 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. W. R. Stewart and Bruce L. Golden. Stochastic vehicle routing: A comprehensive approach.European Journal of Operational Research, 14: 371–385, 1983.

    Article  Google Scholar 

  56. Hao Tang and Elise Miller-Hooks. Approximate procedures for the probabilistic traveling salesman problem.Transportation Research Record, 1882:27–36, 2004.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  58. F. Tillman. The multiple terminal delivery problem with probabilistic demands.Transportation Science, 3:192–204, 1969.

    Google Scholar 

  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. C. D.J. Waters. Vehicle scheduling problems with uncertainty and omitted customers.Journal of the Operational Research Society, 40: 1099–1108, 1989.

    Article  Google Scholar 

  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. Wen-Huei Yang, Kamlesh Mather, and RonaldH. Ballou. Stochastic vehicle routing problem with restocking.Transportation Science, 34:99–112, 2000.

    Article  Google Scholar 

  63. H. Zhong, R. W. Hall, and M. Dessouky. Territory planning and driver learning in vehicle dispatching.Transportation Science, to appear.

    Google Scholar 

  64. Hongsheng Zhong.Territory Planning and Vehicle Dispatching with Stochastic Customers and Demand. PhD thesis, University of Southern California, 2001.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ann Melissa Campbell .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Campbell, A.M., Thomas, B.W. (2008). Challenges and Advances in A Priori Routing. In: Golden, B., Raghavan, S., Wasil, E. (eds) The Vehicle Routing Problem: Latest Advances and New Challenges. Operations Research/Computer Science Interfaces, vol 43. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-77778-8_6

Download citation

Publish with us

Policies and ethics