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**Competition and integration in closed-loop supply chain network with variational inequality.**
*(English)*
Zbl 1264.91080

Summary: A closed-loop supply chain network involves the manufactured and remanufactured homogeneous products. It comprises operation links to represent business activities including manufacturing/remanufacturing activities, treatment activities for EOL products, transportation activities, and storage activities, which are performed by the firms. Among all closed-loop supply chain problems, the horizontal merger of oligopolistic firms is so important and attracting to both businessman and researchers. In this paper, the interaction of the competitive firms prior to horizontal merger is analyzed. Three networks including prior to horizontal merger, postpartial merger, and complete merger are studied. Simultaneously, three economical models for these networks on different conditions of mergers are established and discussed. The variational inequality formulations are used for these three models, whose solutions give out the production quantity of new products, and remanufactured products, the product flows for new products, remanufactured products and end-of-life products at every path, the demand quantity, the recovery quantity of end-of-life products and the equilibrium prices. Finally, numerical examples are tested and illustrated for the proposed models.

### MSC:

91B38 | Production theory, theory of the firm |

90B06 | Transportation, logistics and supply chain management |

90B50 | Management decision making, including multiple objectives |

90B70 | Theory of organizations, manpower planning in operations research |

49J40 | Variational inequalities |

90B10 | Deterministic network models in operations research |

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\textit{G. Zhou} et al., Math. Probl. Eng. 2012, Article ID 524809, 21 p. (2012; Zbl 1264.91080)

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### References:

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