Due to environmental issues and legislative requirements, the disposition of the solid-waste problems is attracting tremendous attention nowadays. The most important issue of environmental protection nowadays is the recycling. For this reason, the Recycling Fund Management Board (RFMB), founded by the Environmental Protection Administration of Taiwan, has been established for controlling waste recycling materials by setting up the fee rate to recycling industries and manufacturers. The determination of fee rate will affect all the members in the recycling system. Hence, in this study, we attempt to optimize the operations of the RFMB through the decision of a subsidy rate for the domestic glass recycling industry. The hierarchical and interactive nature between the two parties is modeled by bi-level programming (BLP), where the RFMB plays the higher-level decision makers while the recycling industry is the lower-level counterpart. Since the objectives of both levels are usually conflict, the BLP model can simulate the actual decision-making process and obtain an optimal solution under an interactive behavior. Further, this study will make a detailed discussion about how to find an efficient compromise solution that make the decision makers can cooperate and achieve optimal results. In order to solve the problem by optimization software, the bi-level formulation is transformed to a single level problem via Karush-Kuhn-Tucker (KKT) optimality conditions and is further transformed to a 0-1 mixed integer programming problem by variable substitution. The problem is solved with real-world data, and the obtained solutions are analyzed. The results suggest that the proposed approach can improve the operations of the RFMB.

近年來，各國政府開始意識到自然環境資源為耗損財，產品汙染成分與不當的廢棄品處理方式，對環境會產生深遠的影響。因此，綠色供應鏈與環保產品的概念逐漸風行，而各項環保議題與法令也因應而出。而在這些議題中，資源回收為當今環境保護最重要的議題之首。為了因應這個議題，我國環保署成立了基管會來制訂相關的回收清除處理費率，並推動各項可回收廢棄物之資源回收工作，希望藉此提高回收率。但此費率制訂除了影響基管會之運作外，亦牽涉到被徵收費率之責任業者及受費率補貼之回收處理業者。因此，本研究利用兩階層數學規劃模型解析台灣地區廢玻璃容器回收費率制訂問題，其中高階為環保署基金管理委員會，而低階為回收處理業者。高階基管會的目標為平衡基金預算，而低階廢玻璃回收處理業者則期望利潤極大。由於雙方的目標不一致但決策又彼此互相影響，故本研究即利用此一互動關係建立兩階層之廢玻璃容器回收費率制定模型。本模型為兩階層非線性規劃問題，為簡化求解過程，首先以KKT最佳化條件轉換以及變數替換，將此模型轉換為一 0-1非線性規劃問題，再以Lingo一般化數學規劃軟體求解。透過此模型除了可反映出其目標衝突的本質，並可利用數值案例探討模式可能存在的趨勢。此外，本研究更進一步探討回收體系之參與者在利益產生衝突時應如何找到最佳的合作策略，使得兩者可以進行合作，以達到兩者目標最佳化之結果。

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