兩階層數學規劃費率制訂之研究－以台灣玻璃容器資源回收機制為例

A Study on Bi-level Mathematical Programming for Setting Recycling and Treatment Fee to Recyclable Containers – A case of the Subsidy Decision to Recycling Glass Industries in Taiwan

彭孟吟(Meng-Yin Peng)

指導教授 ： 時序時

共同指導教授 ： 溫于平

淡江大學/管理學院/管理科學研究所碩士班/碩士(2008年)

https://doi.org/10.6846/TKU.2008.00532

摘要

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。由於兩者的目標不一致，透過此模型可反映出其衝突本質，而獲得妥協情況之下最佳解。
由於地球資源有限，減量、重複利用及資源回收再利用成為解決環境問題的三個主要方法。當前兩者無法徹底執行時，資源回收則為當今環境保護最重要之議題。我國環保署於民87年成立基管會制訂回收清除處理費率，推動各項公告應回收一般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。本研究簡化此一關係後，以兩階層數學規劃模型表達。高階基管會的目標為平衡基金預算以及回收率極大，低階廢玻璃回收處理業者則期望利潤極大。在雙方的目標不同但決策又彼此互相影響之下，適用於多階層數學規劃模型表達此一互動關係。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(KKT Conditions) 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 (0-1 non-linear programming problem)，再以Lingo一般化數學規劃軟體求解。分析結果發現，回收處理業者之回收意願受到二次料市場之資源化價值及回收處理成本之影響，而此兩者為回收補貼最重要之內涵，因此最適回收清除處理補貼費率亦因此有所變動。接著對回收清除處理費率進行參數分析，其結果顯示回收清除處理補貼費率及回收率與其朝同向變動。最後再將本研究所建立之兩階層規劃模型與現行之費率計算公式進行比較，發現本研究之模型係按兩階層之決策目標及限制建立，較符合實務上費率之互動情況，可供實務上進行費率制訂作業時之參考。

關鍵字

兩階層規劃 ； 玻璃資源回收 ； 補貼 ； 回收清除處理費率 ； 0-1 非線性規劃 ； KKT條件

並列摘要

T his study tries to make a subsidy decision to recycling glass industries in Taiwan through a bi-level programming problem (BLPP). The upper-level decision unit is Recycling Fund Management Board (RFMB), Environmental Protection Administration of ROC Government (Taiwan), and the lower-level's is the recycling industries. Since the objectives of both levels are usually conflict, the BLPP model can simulate the actual decision-making process and obtain an optimal solution under an interactive behavior.
Because the resources are always scarce, reducing, reuse and recycling (3R) are the important actions to save our resources, and recycling is the most important issue for protect our environment if the former two actions are invalid. In the year of 1998, RFMB has been established for controlling waste recycling materials by setting up the recycling and treatment fee to recycling industries for increasing recycling ratio, and the funds are collected from manufacturers and importers for their responsibility. The determination of recycling subsidy can affect recycling industries, manufacturers, and RFMB itself. We simplify the problem as a BLPP model. The upper-level's objective is to balance the input and output of the funds and maximize the amount of recycling materials; the lower-level's objective is to maximize the profits of the recycling industries. Here the glass containers are chosen as the target for ease of recycling and saving energy use in manufacturing process.
The BLPP can be transformed into a one-level problem via KKT optimality conditions, and then into a 0-1 non-linear programming problem by variable substitution. Thus, the optimal solutions can be obtained through Lingo software. As a result, the ratio of the collected glass containers to the whole produced containers, instead of the willingness of recycling, has been positively impacted by the price of processed recycling glass materials in a market and negatively influenced by the processing cost of the industries. In addition, the ratio is also positively affected by the amount of the recycling and treatment fee to recycling glass industries from RFMB. Afterwards, a parameter analysis on the amount of the subsidies is executed, and the result shows that the recycling ratio will grow as the amount is increased. Furthermore, after comparing current formulation to the BLPP model, we find that the model has a great advantage for accounting for both levels' objectives and constraints to mimic the decision making in the real world. Hence, the model can be regarded as a useful tool for tariff setting on recyclable containers in Taiwan in the future.

並列關鍵字

Bi-level programming problem ； Glass recycling ； Subsidy ； Recycling and treatment fee ； 0-1 nonlinear programming ； KKT conditions

參考文獻

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