Networks and Spatial Economics

, Volume 11, Issue 1, pp 101–126

A Dantzig-Wolfe Decomposition Based Heuristic Scheme for Bi-level Dynamic Network Design Problem


    • Department of Civil, Architectural & Environmental EngineeringUniversity of Texas at Austin
  • Ampol Karoonsoontawong
    • School of Transportation Engineering, Institute of Engineering, Suranaree University of Technology
  • S. Travis Waller
    • Department of Civil, Architectural & Environmental EngineeringUniversity of Texas at Austin

DOI: 10.1007/s11067-008-9093-4

Cite this article as:
Lin, D., Karoonsoontawong, A. & Waller, S.T. Netw Spat Econ (2011) 11: 101. doi:10.1007/s11067-008-9093-4


We present a heuristic to solve the NP-hard bi-level network design problem (NDP). The heuristic is developed based on the Dantzig-Wolfe decomposition principle such that it iteratively solves a master problem and a pricing problem. The master problem is the budget allocation linear program solved by CPLEX to determine the budget allocation and construct a modified cell transmission network for the pricing problem. The pricing problem is the user-optimal dynamic traffic assignment (UODTA) solved by an existing combinatorial algorithm. To facilitate the decomposition principle, we propose a backward connectivity algorithm and complementary slackness procedures to efficiently approximate the required dual variables from the UODTA solution. The dual variables are then employed to augment a new column in the master program in each iteration. The iterative process repeats until a stopping criterion is met. Numerical experiments are conducted on two test networks. Encouraging results demonstrate the applicability of the heuristic scheme on solving large-scale NDP. Though a single destination problem is considered in this paper, the proposed scheme can be extended to solve multi-destination problems as well.


Dynamic network designDantzig-Wolfe decompositionDual variables approximationCell transmission model

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© Springer Science+Business Media, LLC 2008