Environmental damage in recent years has led to a global warming crisis. To achieve worldwide environmental protection, each government must work out policies to reduce carbon emissions and increase recycle products. In the meantime, for their reputation and the own interests, each enterprise must adapt strategies to reduce its environmental impact. To support such policy making for both government and enterprise, this study proposes a bi-level mixed-integer nonlinear programming (BL-MINLP) model to develop subsidy and penalty strategies for governments and enterprises engaged in the collection and recovery operations of environmental protection. In this bi-level model, the government is the leader (higher level) who intends to reduce environmental impacts and seek the financial balance in environmental subsidy and penalty policies for the recovery and carbon emission. The enterprise is the follower (lower level) who wants to minimize its operational costs of recycling and refunding subject to the unit subsidy and unit penalty decisions of the government. This hierarchical structure conforms to each industry sector.
Based on the environmental concern, with balanced finance and minimized the environmental costs, the government determines a reasonable unit subsidy and unit penalty of carbon emission and product recovery. On the other hand, under such policies by the government, to minimize its costs, the enterprise can decide the upper bound carbon emitted from transportation and determine the product recovery rate based on the unit refund, which encourages customers to return their used products.
This study applies the BL-MINLP model and Karush-Kuhn-Tucker approach to solve the trade-off problem between the government and the enterprise. The results of this study help both the government and the enterprise make optimal decisions. Sensitivity analysis was carried out on parameters related to the recovery rate and the carbon emission from transportation to facilitate the effective control and management.

本研究利用多階混合整數非線性規劃來描述政府與公司之間的策略衡量問題。在本研究模型中，政府在多階規劃中是屬於高階之領導，公司則是屬於低階之遵循者。在政府希望回收率與碳排放量政策收支平衡以及環境成本最小化的前提之下，制訂合理的逆物流碳排放量、回收率的補助金與罰款金，一方面可以鼓勵公司配合政策，另一方面則可以強制公司配合。根據政府訂定的獎懲標準，公司在其成本最小化下，決定碳排放量、回收率以及發放給顧客的獎勵回收價格，使得政府與公司兩者不僅將各自環境成本最小化外，還可減低環境衝擊。本研究利用Karush-Kuhn-Tucker方法將原本兩階的模型經由轉換成為一階非線性模型，以利全域最佳解的獲得。因此，根據本研究分析數據，政府與公司兩者皆可做出最佳決策並各自達到其目標。最後，針對與回收率和碳排放量相關參數作敏感度分析，以利有效的控制與管理。

行政院環境保護署國家溫室氣體登錄平台>資訊下載區,”溫室氣體排放係數管理表6.0版(99.07)”, http://www.ghgregistry.tw/Tool/tools.aspx?Type=1
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