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An efficient algorithm for solving supply chain network equilibria and equivalent supernetwork based traffic network equilibria

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Abstract

This paper is concerned with the algorithm of the supply chain network equilibrium model and its equivalent supernetwork based traffic network equilibrium model with elastic demands. Both models are further written as nonlinear complementarity problems. Semismooth least squares reformulations of the complementarity problems are presented and their convergence properties are investigated. Considering the drawbacks of Quasi-Newton method (using the Fischer-Burmeister function), a semi-smooth Levenberg-Marquardt-type method is proposed to solve the problems. Numerical examples show that the Levenberg-Marquardt-type method can solve the supply chain network equilibrium model and its equivalent supernetwork based traffic network equilibrium model significantly, and is more efficient than the Quasi Newton method and the modified projection method. Furthermore, the Levenberg-Marquardt-type method with the equivalent supernetwork based complementarity formulation can be implemented faster than with the supply chain network equilibrium complementarity formulation.

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Authors and Affiliations

  1. MOE Key Laboratory for Urban Transportation Complex Systems Theory and Technology, Beijing Jiaotong University, Beijing, 100044, China

    Meng Xu

  2. Institute of Systems Science, School of Traffic and Transportation, Beijing Jiaotong University, Beijing, 100044, China

    ZiYou Gao

Authors
  1. Meng Xu
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  2. ZiYou Gao
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Correspondence to Meng Xu.

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Xu, M., Gao, Z. An efficient algorithm for solving supply chain network equilibria and equivalent supernetwork based traffic network equilibria. Sci. China Technol. Sci. 53, 3264–3274 (2010). https://doi.org/10.1007/s11431-010-4168-0

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  • DOI: https://doi.org/10.1007/s11431-010-4168-0

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