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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ahuja RK, Magnanti TL, Orlin JB (1993) Network flows: theory, algorithms, and applications. Prentice-Hall, Upper Saddle River
Bertsekas DS (1998) Network optimization: continuous and discrete models. Athena Scientific, Naples
Brotcorne L, Labbe M, Savard G (2000) A bilevel model and solution algorithm for a freight tariff setting problem. Transp Sci 34(3):289–302
Castelli L, Longo G, Pessenti R, Ukovich W (2004) Two player non-cooperative games over a freight transportation network. Transp Sci 38(2):149–159
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
Drissi-Kaitoni O (1992) A dynamic traffic assignment model and a solution algorithm. Transp Sci 26(2):119–128
Drissi-Kaitoni O (1993) A variational inequality formulation of the dynamic traffic assignment problem. Eur J Oper Res 71(2):188–204
Fisk CS (1986) A conceptual framework for optimal transportation systems planning with integrated supply and demand models. Transp Sci 20:80–91
Ford LR, Fulkerson DR (1962) Flows in networks. Princeton University Press, Princeton
Friesz TL, Viton PA, Tobin RL (1985) Economic and computational aspects of freight network equilbrium models: a synthesis. J Reg Sci 25(2):29–49
Friesz TL, Gottfried JA, Morlok EK (1986) A sequential shipper-carrier network model for predicting freight flows. Transp Sci 20(2):80–91
Friesz TL, Rigdon MA, Mookherjee R (2006) Differential variational inequalities and shipper dynamic oligopolistic network competition. Transp Res Part B 40:480–503
Friesz TL, Mookherjee R, Holguin-Veras J, Rigdon MA (2008) Dynamic pricing in an urban freight environment. Transp Res Part B 42:305–324
Golani H, Waller ST (2004) Combinatorial approach for multiple-destination user optimal dynamic traffic assignment. Transp Res Rec 1882(− 1):70–78
Harker PT (1983) Prediction of intercity freight flows: theory and application of a generalized spatial price equilbrium model. PhD Dissertation, University of Pennylvania, Philadelphia
Harker PT, Friesz TL (1986a) Prediction of intercity freight flows, I: theory. Transp Res Part B 20(1986):80–91
Harker PT, Friesz TL (1986b) Prediction of intercity freight flows, II: mathematical formulations. Transp Res Part B 20B:155–174
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 42:392–413
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):277–295
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):327–354
Hurley W, Petersen ER (1994) Nonlinear tariff and freight network equilbrium. Transp Sci 28:236–245
Jeon K, Lee JS, Ukkusuri S, Waller ST (2003) Selectorecombinative genetic algorithm to relax computational complexity of discrete network design problem. Transp Res Rec 1964:91–103
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 1923:91–102
Karoonsoontawong A, Waller ST (2007) Robust dynamic continuous network design problem. Transp Res Rec 2029:58–71
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):814–821
Lobel A (1996) Solving large-scale real-world minimum-cost flow problems by a network. Technical Report SC 96-7
Ruszczynski A (1995) The regularized decomposition for stochastic programming problems. citeseer.ist.psu.edu/ruszczynski93regularized.html
Slyke RMV, Wets R (1969) L-shaped linear programs with applications to optimal control and stochastic programming. SIAM J Appl Math 17(4):638–663
Valsaraj V (2008) Stochastic and dynamic network design in freight transportation network. MS Thesis, University of Texas Austin
Waller ST, Ziliaskopoulos AK (2001) Stochastic dynamic network design problem. Transp Res Rec 1771(− 1):106–113
Waller ST, Schofer JL, Ziliaskopoulos AK (2001) Evaluation with traffic assignment under demand uncertainty. Transp Res Rec 1771(− 1):69–74
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):247–260
Zhang P, Peeta S, Friesz T (2005) Dynamic game theoretic model of multi-layer infrastructure networks. Netw Spat Econ 5(2):147–178
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Unnikrishnan, A., Valsaraj, V. & Waller, S.T. Stochastic and Dynamic Shipper Carrier Network Design Problem. Netw Spat Econ 9, 525–550 (2009). https://doi.org/10.1007/s11067-008-9094-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11067-008-9094-3