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Stochastic and Dynamic Shipper Carrier Network Design Problem

  • Avinash Unnikrishnan
  • Varunraj Valsaraj
  • Steven Travis Waller
Article

Abstract

The focus of this work is to determine the optimal storage capacity to be installed on transhipment nodes by shippers in a dynamic shipper carrier network under stochastic demand. A two stage linear program with recourse formulation is developed where in the first stage, the shipper decides the optimal capacity to be installed on transhipment nodes. In the second stage, the shipper chooses a routing strategy based on the realized demand. The performance of the following solution methods: Stochastic L Shaped Method, Regularized Decomposition and L Shaped Method with preliminary cuts were compared for various network sizes and numerous demand scenarios. A novel capacity shifting heuristic was introduced to generate a feasible implementable solution which significantly improves the performance of Regularized Decomposition and provides the best performance in the cases tested. Various ways of generating analytical bounds on the objective function value was discussed. The new capacity shifting heuristic was found to be efficient in generating tight upper bounds. Even though the formulation considered in this paper is for a single commodity, the model can be easily extended to account for multiple commodities.

Keywords

Stochastic shipper carrier model L shaped method Regularized decomposition Capacity shifting heuristic 

References

  1. Ahuja RK, Magnanti TL, Orlin JB (1993) Network flows: theory, algorithms, and applications. Prentice-Hall, Upper Saddle RiverGoogle Scholar
  2. Bertsekas DS (1998) Network optimization: continuous and discrete models. Athena Scientific, NaplesGoogle Scholar
  3. Brotcorne L, Labbe M, Savard G (2000) A bilevel model and solution algorithm for a freight tariff setting problem. Transp Sci 34(3):289–302CrossRefGoogle Scholar
  4. Castelli L, Longo G, Pessenti R, Ukovich W (2004) Two player non-cooperative games over a freight transportation network. Transp Sci 38(2):149–159CrossRefGoogle Scholar
  5. Chen SH (2008) A heuristic algorithm for hierarchical hub-and-spoke network of time-definite common carrier operation planning problem. Netw Spat Econ (in press). doi: 10.1007/s11067-008-9070-y
  6. Drissi-Kaitoni O (1992) A dynamic traffic assignment model and a solution algorithm. Transp Sci 26(2):119–128CrossRefGoogle Scholar
  7. Drissi-Kaitoni O (1993) A variational inequality formulation of the dynamic traffic assignment problem. Eur J Oper Res 71(2):188–204CrossRefGoogle Scholar
  8. Fisk CS (1986) A conceptual framework for optimal transportation systems planning with integrated supply and demand models. Transp Sci 20:80–91CrossRefGoogle Scholar
  9. Ford LR, Fulkerson DR (1962) Flows in networks. Princeton University Press, PrincetonGoogle Scholar
  10. Friesz TL, Viton PA, Tobin RL (1985) Economic and computational aspects of freight network equilbrium models: a synthesis. J Reg Sci 25(2):29–49CrossRefGoogle Scholar
  11. Friesz TL, Gottfried JA, Morlok EK (1986) A sequential shipper-carrier network model for predicting freight flows. Transp Sci 20(2):80–91CrossRefGoogle Scholar
  12. Friesz TL, Rigdon MA, Mookherjee R (2006) Differential variational inequalities and shipper dynamic oligopolistic network competition. Transp Res Part B 40:480–503CrossRefGoogle Scholar
  13. Friesz TL, Mookherjee R, Holguin-Veras J, Rigdon MA (2008) Dynamic pricing in an urban freight environment. Transp Res Part B 42:305–324CrossRefGoogle Scholar
  14. Golani H, Waller ST (2004) Combinatorial approach for multiple-destination user optimal dynamic traffic assignment. Transp Res Rec 1882(− 1):70–78CrossRefGoogle Scholar
  15. Harker PT (1983) Prediction of intercity freight flows: theory and application of a generalized spatial price equilbrium model. PhD Dissertation, University of Pennylvania, PhiladelphiaGoogle Scholar
  16. Harker PT, Friesz TL (1986a) Prediction of intercity freight flows, I: theory. Transp Res Part B 20(1986):80–91Google Scholar
  17. Harker PT, Friesz TL (1986b) Prediction of intercity freight flows, II: mathematical formulations. Transp Res Part B 20B:155–174CrossRefGoogle Scholar
  18. Holguin-Veras J (2007) Necessary conditions for off-hour deliveries and the effectiveness of urban freight road pricing and alternative financial policies in competitive markets. Transp Res Part A 42:392–413Google Scholar
  19. Holguin-Veras J, Silas M, Polimeni J, Cruz B (2007) An investigation on the effectiveness of joint receiver-carrier policies to increase truck traffic in the off-peak hours part I: the behavior of receivers. Netw Spat Econ 7(3):277–295CrossRefGoogle Scholar
  20. Holguin-Veras J, Silas M, Polimeni J, Cruz B (2008) An investigation on the effectiveness of joint receiver-carrier policies to increase truck traffic in the off-peak hours part II: the behavior of carriers. Netw Spat Econ 8(4):327–354CrossRefGoogle Scholar
  21. Hurley W, Petersen ER (1994) Nonlinear tariff and freight network equilbrium. Transp Sci 28:236–245CrossRefGoogle Scholar
  22. Jeon K, Lee JS, Ukkusuri S, Waller ST (2003) Selectorecombinative genetic algorithm to relax computational complexity of discrete network design problem. Transp Res Rec 1964:91–103CrossRefGoogle Scholar
  23. Karoonsoontawong A, Waller ST (2005) A comparison of system- and user-optimal stochastic dynamic network design models using Monte Carlo bounding techniques. Transp Res Rec 1923:91–102CrossRefGoogle Scholar
  24. Karoonsoontawong A, Waller ST (2007) Robust dynamic continuous network design problem. Transp Res Rec 2029:58–71CrossRefGoogle Scholar
  25. Klingman D, Napier A, Stutz J (1974) NETGEN: a program for generating large scale capacitated assignment, transportation, and minimum cost flow network problems. Manage Sci 20(5):814–821CrossRefGoogle Scholar
  26. Lobel A (1996) Solving large-scale real-world minimum-cost flow problems by a network. Technical Report SC 96-7Google Scholar
  27. Ruszczynski A (1995) The regularized decomposition for stochastic programming problems. citeseer.ist.psu.edu/ruszczynski93regularized.html
  28. Slyke RMV, Wets R (1969) L-shaped linear programs with applications to optimal control and stochastic programming. SIAM J Appl Math 17(4):638–663CrossRefGoogle Scholar
  29. Valsaraj V (2008) Stochastic and dynamic network design in freight transportation network. MS Thesis, University of Texas AustinGoogle Scholar
  30. Waller ST, Ziliaskopoulos AK (2001) Stochastic dynamic network design problem. Transp Res Rec 1771(− 1):106–113CrossRefGoogle Scholar
  31. Waller ST, Schofer JL, Ziliaskopoulos AK (2001) Evaluation with traffic assignment under demand uncertainty. Transp Res Rec 1771(− 1):69–74CrossRefGoogle Scholar
  32. Yang H, Meng Q (1998) Departure time, route choice and congestion toll in a queuing network with elastic demand. Transp Res Part B 32(4):247–260CrossRefGoogle Scholar
  33. Zhang P, Peeta S, Friesz T (2005) Dynamic game theoretic model of multi-layer infrastructure networks. Netw Spat Econ 5(2):147–178CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Avinash Unnikrishnan
    • 1
  • Varunraj Valsaraj
    • 2
  • Steven Travis Waller
    • 3
  1. 1.Department of Civil, Architecture and Environmental EngineeringAustinUSA
  2. 2.Logistics EngineerArrowstreamChicagoUSA
  3. 3.Department of Civil, Architecture and Environmental EngineeringAustinUSA

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