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

Dung Ying Lin, Ampol Karoonsoontawong, S. Travis Waller

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)101-126
Number of pages26
JournalNetworks and Spatial Economics
Issue number1
Publication statusPublished - 2011 Mar

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Networks and Communications
  • Artificial Intelligence


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