A new approach to supply chain network equilibrium models

Authors:
Liping Zhang;Yuan Zhou
Affiliations:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China;Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
Venue:
Computers and Industrial Engineering
Year:
2012

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Abstract

We establish nonlinear complementarity formulations for the supply chain network equilibrium models. The formulations have simple structures and facilitate us to study qualitative properties of the models. In this setting, we obtain weaker conditions to guarantee the existence and uniqueness of the equilibrium pattern for a supply chain. A smoothing Newton algorithm that exploits the network structure is proposed for solving these models. Not only is the smoothing Newton algorithm proved to be globally convergent without requiring the assumptions of monotonicity and Lipschitz continuity, but also it can overcome the flaw that the performance of the modified projection method heavily depends on the choice of the predetermined step size. Numerical results indicate the advantages of the nonlinear complementarity formulation and the smoothing Newton algorithm.