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A Dual Approach for Solving the Combined Distribution and Assignment Problem with Link Capacity Constraints

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  • Seungkyu Ryu
  • Anthony Chen
  • Xiangdong Xu
  • Keechoo Choi

Abstract

In this paper, we consider the combined distribution and assignment (CDA) problem with link capacity constraints modeled as a hierarchical logit choice problem based on random utility theory. The destination and route choices are calculated based on the multi-nominal logit probability function, which forms the basis for constructing the side constrained CDA (SC-CDA) problem as an equivalent mathematical programming (MP) formulation. A dual MP formulation of the SC-CDA problem is developed as a solution algorithm, which consists of an iterative balancing scheme and a column generation scheme, for solving the SC-CDA problem. Due to the entropy-type objective function, the dual formulation has a simple nonlinear constrained optimization structure, where the feasible set only consists of nonnegative orthants. The iterative balancing scheme explicitly makes use of the optimality conditions of the dual formulation to analytically adjust the dual variables and update the primal variables, while a column generation scheme is used to iteratively generate routes to the working route set as needed to satisfy the side constraints. Two numerical experiments are conducted to demonstrate the features of the SC-CDA model and the computational performance of the solution algorithm. The results reveal that imposing link capacity constraints can have a significant impact on the network equilibrium flow allocations, and the dual approach is a practical solution algorithm for solving the complex SC-CDA problem. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Seungkyu Ryu & Anthony Chen & Xiangdong Xu & Keechoo Choi, 2014. "A Dual Approach for Solving the Combined Distribution and Assignment Problem with Link Capacity Constraints," Networks and Spatial Economics, Springer, vol. 14(2), pages 245-270, June.
    • Handle: RePEc:kap:netspa:v:14:y:2014:i:2:p:245-270
    DOI: 10.1007/s11067-013-9218-2
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    1. Justin Siegel & Joaquín Cea & José Fernández & Renán Rodriguez & David Boyce, 2006. "Comparisons of Urban Travel Forecasts Prepared with the Sequential Procedure and a Combined Model," Networks and Spatial Economics, Springer, vol. 6(2), pages 135-148, June.
    2. Jen-Jia Lin & Cheng-Min Feng, 2003. "A bi-level programming model for the land use – network design problem," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 37(1), pages 93-105, February.
    3. Wong, K. I. & Wong, S. C. & Yang, Hai, 2001. "Modeling urban taxi services in congested road networks with elastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 35(9), pages 819-842, November.
    4. Bar-Gera, Hillel & Boyce, David, 2003. "Origin-based algorithms for combined travel forecasting models," Transportation Research Part B: Methodological, Elsevier, vol. 37(5), pages 405-422, June.
    5. Chen, Anthony & Pravinvongvuth, Surachet & Xu, Xiangdong & Ryu, Seungkyu & Chootinan, Piya, 2012. "Examining the scaling effect and overlapping problem in logit-based stochastic user equilibrium models," Transportation Research Part A: Policy and Practice, Elsevier, vol. 46(8), pages 1343-1358.
    6. Yan, Hai & Lam, William H. K., 1996. "Optimal road tolls under conditions of queueing and congestion," Transportation Research Part A: Policy and Practice, Elsevier, vol. 30(5), pages 319-332, September.
    7. Larsson, Torbjörn & Patriksson, Michael, 1999. "Side constrained traffic equilibrium models-- analysis, computation and applications," Transportation Research Part B: Methodological, Elsevier, vol. 33(4), pages 233-264, May.
    8. Damberg, Olof & Lundgren, Jan T. & Patriksson, Michael, 1996. "An algorithm for the stochastic user equilibrium problem," Transportation Research Part B: Methodological, Elsevier, vol. 30(2), pages 115-131, April.
    9. Yang, Hai & Bell, Michael G. H., 1997. "Traffic restraint, road pricing and network equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 31(4), pages 303-314, August.
    10. Nie, Yu & Zhang, H. M. & Lee, Der-Horng, 2004. "Models and algorithms for the traffic assignment problem with link capacity constraints," Transportation Research Part B: Methodological, Elsevier, vol. 38(4), pages 285-312, May.
    11. Yang, Hai & Bell, Michael G. H. & Meng, Qiang, 2000. "Modeling the capacity and level of service of urban transportation networks," Transportation Research Part B: Methodological, Elsevier, vol. 34(4), pages 255-275, May.
    12. Bell, Michael G. H., 1995. "Stochastic user equilibrium assignment in networks with queues," Transportation Research Part B: Methodological, Elsevier, vol. 29(2), pages 125-137, April.
    13. Tam, M. L. & Lam, William H. K., 2000. "Maximum car ownership under constraints of road capacity and parking space," Transportation Research Part A: Policy and Practice, Elsevier, vol. 34(3), pages 145-170, April.
    14. Mohamad Hasan & Hussain Dashti, 2007. "A Multiclass Simultaneous Transportation Equilibrium Model," Networks and Spatial Economics, Springer, vol. 7(3), pages 197-211, September.
    15. Zhou, Zhong & Chen, Anthony & Wong, S.C., 2009. "Alternative formulations of a combined trip generation, trip distribution, modal split, and trip assignment model," European Journal of Operational Research, Elsevier, vol. 198(1), pages 129-138, October.
    16. Torbjörn Larsson & Michael Patriksson, 1992. "Simplicial Decomposition with Disaggregated Representation for the Traffic Assignment Problem," Transportation Science, INFORMS, vol. 26(1), pages 4-17, February.
    17. Larsson, Torbjörn & Patriksson, Michael & Rydergren, Clas, 2004. "A column generation procedure for the side constrained traffic equilibrium problem," Transportation Research Part B: Methodological, Elsevier, vol. 38(1), pages 17-38, January.
    18. Chen, Anthony & Kasikitwiwat, Panatda, 2011. "Modeling capacity flexibility of transportation networks," Transportation Research Part A: Policy and Practice, Elsevier, vol. 45(2), pages 105-117, February.
    19. David Boyce, 2007. "Forecasting Travel on Congested Urban Transportation Networks: Review and Prospects for Network Equilibrium Models," Networks and Spatial Economics, Springer, vol. 7(2), pages 99-128, June.
    20. Ferrari, Paolo, 1995. "Road pricing and network equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 29(5), pages 357-372, October.
    21. Anthony Chen & Chao Yang & Sirisak Kongsomsaksakul & Ming Lee, 2007. "Network-based Accessibility Measures for Vulnerability Analysis of Degradable Transportation Networks," Networks and Spatial Economics, Springer, vol. 7(3), pages 241-256, September.
    22. Wong, K.I. & Wong, S.C. & Yang, Hai & Wu, J.H., 2008. "Modeling urban taxi services with multiple user classes and vehicle modes," Transportation Research Part B: Methodological, Elsevier, vol. 42(10), pages 985-1007, December.
    23. Larsson, Torbjörn & Patriksson, Michael, 1995. "An augmented lagrangean dual algorithm for link capacity side constrained traffic assignment problems," Transportation Research Part B: Methodological, Elsevier, vol. 29(6), pages 433-455, December.
    24. Louis Grange & Enrique Fernández & Joaquín Cea & Magdalena Irrazábal, 2010. "Combined Model Calibration and Spatial Aggregation," Networks and Spatial Economics, Springer, vol. 10(4), pages 551-578, December.
    25. Chen, Anthony & Chootinan, Piya & Recker, Will, 2009. "Norm approximation method for handling traffic count inconsistencies in path flow estimator," Transportation Research Part B: Methodological, Elsevier, vol. 43(8-9), pages 852-872, September.
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