本論文提出兩個集中式閉環式供應鏈與兩個分離式閉環式供應鏈，探討不同的回收方式將如何影響供應鏈成員的決策。透過建置數學模式，找出供應鏈中成員最佳的利潤，以及利用數值方法來提供更多的管理意涵。本篇論文相較於文獻中其他論文的差異為：(1)在供應鏈中，製造商考慮產品品質的改進，以及(2)考慮兩個零售商競爭的情況。另外，我們假設不同階層的成員從事Stackelberg Game，最後給予結論與未來可以擴展的研究。

In this paper, we develop two centralized closed-loop supply chain models with two competing retailers and two decentralized closed-loop supply chain models with two competing retailers, and investigate how the different methods of collecting products affect the members of channel decisions. And then, we develop the mathematical formula to find the optimal profits of all the members in the closed-loop supply models, and utilize a numerical approach to provide more managerial insights. In contrast to previous works, (1) the manufacturer considers the investment in improving the quality of the products in the closed-loop supply chain (2) with two competing retailers. For the channel members in the different echelons, we consider Stackelberg game to model the competing behavior, where the manufacturer is the role of the Stackelberg leader. Finally, we given conclusions and some extensions of our models.

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