Abstract: To characterize the dynamics and complexity in the operations of closed loop supply chain (CLSC), a multi-period CLSC network equilibrium model is built under manufacturer-collection channel considering the factors of environmental constraints and government subsidies comprehensively, in which the demand market is assumed to vary dynamically among multi-period planning horizons. Moreover, the adjacent planning period is connected via channel member's holding inventories and EOL products collection. On this basis, variational inequality theory is utilized to characterize the optimal behaviors and equilibrium conditions of non-cooperative manufacturers, retailers and consumer markets respectively, and then the governing multi-period CLSC network equilibrium model is derived. The projection and contraction algorithm is proposed to solve numerical examples and make sensitivity analysis. The results show that the increase of remanufacturing conversion rate is conductive to the improvement of all the channel members' profits and consumer welfares. Despite collection rate can be raised through charging the manufacturers disposal fee for non-recovery EOL products by resource recycling factories, the benefits of the retailers and CLSC systems decrease. The government should implement subsidy mechanisms and promote channel members' cooperation to improve the performances of the CLSC network. These conclusions can provide supports for the channel members in CLSC to make decisions dynamically and for the government to make subsidy policies in reality.

Key words: closed-loop supply chain, network equilibrium, variational inequalities, multi-period, government subsidies