A Parallelizable And Approximate Dynamic Programming-Based Dynamic Fleet Management Model With Random Travel Times And Multiple Vehicle Types

  • Huseyin Topaloglu
Chapter
Part of the Operations Research/Computer Science Interfaces Series book series (ORCS, volume 38)

Abstract

This chapter presents an approximate dynamic programming-based dynamic fleet management model that can handle random load arrivals, random travel times and multiple vehicle types. Our model decomposes the fleet management problem into a sequence of time-indexed subproblems by formulating it as a dynamic program and uses approximations of the value function. To handle random travel times, the state variable of our dynamic program includes all individual decisions over a relevant portion of the history. We propose a sampling-based strategy to approximate the value function under this high-dimensional state variable in a tractable manner. Under our value function approximation strategy, the fleet management problem decomposes into a sequence of time-indexed min-cost network flow subproblems that naturally yield integer solutions. Moreover, the subproblem for each time period further decomposes by the locations, making our model suitable for parallel computing. Computational experiments show that our model yields high-quality solutions within reasonable runtimes

Keywords

dynamic programming approximate dynamic programming fleet management 
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Reference

  1. Abara, J., 1989, “Applying integer linear programming to the fleet assignment problem”, Interfaces 19(4), 20-28.Google Scholar
  2. Adelman, D., 2004, Price-directed control of a closed logistics queueing network, Technical report, The University of Chicago, Graduate School of Business.Google Scholar
  3. Bourbeau, B., Crainic, T. G. and Gendron, B., 2000, “Branch-and-bound parallelization strategies applied to depot location and container fleet management problem”, Parallel Computing 26(1), 27-46.CrossRefGoogle Scholar
  4. Carvalho, T. A. and Powell, W. B., 2000, “A multiplier adjustment method for dynamic resource allocation problems”, Transportation Science 34, 150-164.CrossRefGoogle Scholar
  5. Chien, T. W., Balakrishnan, A. and Wong, R. T., 1989, “An integrated inventory allocation and vehicle routing problem”, Transportation Science 23(2), 67-76.Google Scholar
  6. Crainic, T. G., Gendreau, M. and Dejax, P., 1993, “Dynamic and stochastic models for the allocation of empty containers”, Operations Research 41, 102-126.Google Scholar
  7. Crainic, T. G. and Laporte, G., eds., 1998, Fleet Management and Logistics, Kluver Academic Publishers.Google Scholar
  8. Dantzig, G. and Fulkerson, D., 1954, “Minimizing the number of tankers to meet a fixed schedule”, Naval Research Logistics Quarterly 1, 217-222.CrossRefGoogle Scholar
  9. Dejax, P. and Crainic, T., 1987, “A review of empty flows and fleet management models in freight transportation”, Transportation Science 21, 227-247.Google Scholar
  10. Ferguson, A. and Dantzig, G. B., 1955, “The problem of routing aircraft - A mathematical solution”, Aeronautical Engineering Review 14, 51-55.Google Scholar
  11. Frantzeskakis, L. and Powell, W. B., 1990, “A successive linear approximation procedure for stochastic dynamic vehicle allocation problems”, Transportation Science 24(1), 40-57.Google Scholar
  12. Fumero, F. and Vercellis, C., 1999, “Synchronized development of production, inventory and distribution schedules”, Transportation Science 33(3), 330-340.Google Scholar
  13. Godfrey, G. A. and Powell, W. B., 2002a, “An adaptive, dynamic programming algorithm for stochastic resource allocation problems I: Single period travel times”, Transportation Science 36(1), 21-39.CrossRefGoogle Scholar
  14. Godfrey, G. A. and Powell, W. B., 2002b, “An adaptive, dynamic programming algorithm for stochastic resource allocation problems II: Multi-period travel times”, Transportation Science 36(1), 40-54.CrossRefGoogle Scholar
  15. Hane, C. A., Barnhart, C., Johnson, E. L., Marsten, R. E., Nemhauser, G. L. and Sigismondi, G., 1995, “The fleet assignment problem: Solving a large scale integer program”, Mathematical Programming 70, 211-232.Google Scholar
  16. Jordan, W. and Turnquist, M., 1983, “A stochastic dynamic network model for railroad car distribution”, Transportation Science 17, 123-145.Google Scholar
  17. Kenyon, A. S. and Morton, D. P., 2003, “Stochastic vehicle routing with random travel times”, Transportation Science 37(1), 69-82.CrossRefGoogle Scholar
  18. Laporte, G., Louveaux, F. and Mercure, H., 1992, “The vehicle routing problem with stochastic travel times”, Transportation Science 26(3), 161-170.Google Scholar
  19. Powell, W. B., 1986, “A stochastic model of the dynamic vehicle allocation problem”, Transportation Science 20, 117-129.CrossRefGoogle Scholar
  20. Powell, W. B., 1988, A comparative review of alternative algorithms for the dynamic vehicle allocation problem, in B. Golden and A. Assad, eds., “Vehicle Routing: Methods and Studies”, North Holland, Amsterdam, 249-292.Google Scholar
  21. Powell, W. B., 1996, “A stochastic formulation of the dynamic assignment problem, with an application to truckload motor carriers”, Transportation Science 30(3), 195-219.Google Scholar
  22. Powell, W. B., Jaillet, P. and Odoni, A., 1995, Stochastic and dynamic networks and routing, in C. Monma, T. Magnanti and M. Ball, eds., “Handbook in Operations Research and Management Science, Volume on Networks”, North Holland, Amsterdam, 141-295.Google Scholar
  23. Powell, W. B., Ruszczynski, A. and Topaloglu, H., 2004, “Learning algorithms for separable approximations of stochastic optimization problems”, Mathematics of Operations Research 29(4), 814-836.CrossRefGoogle Scholar
  24. Puterman, M. L., 1994, Markov Decision Processes, John Wiley and Sons, Inc., New York.Google Scholar
  25. Topaloglu, H., 2005, A parallelizable dynamic fleet management model with random travel times, Technical report, Cornell University, School of Operations Research and Industrial Engineering.Google Scholar
  26. Topaloglu, H. and Powell, W. B., 2006, “Dynamic programming approximations for stochastic, time-staged integer multicommodity flow problems”, INFORMS Journal on Computing 18(1), 31-42.CrossRefGoogle Scholar
  27. White, W., 1972, “Dynamic transshipment networks: An algorithm and its application to the distribution of empty containers”, Networks 2(3), 211-236.CrossRefGoogle Scholar
  28. White, W. and Bomberault, A., 1969, “A network algorithm for empty freight car allocation”, IBM Systems Journal 8(2), 147-171.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Huseyin Topaloglu
    • 1
  1. 1.School of Operations Research and Industrial EngineeringCornell UniversityIthacaUSA

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