本研究應用兩階段隨機規劃法(Two-stage Stochastic Programming),針對具有不確定性之封閉式永續供應鏈(Closed-Loop Sustainable Supply Chain)網路設計問題建構隨機多目標規劃模型(Stochastic Multi-objective programming model),其考量之特性包括流量配置、潛在逆物流廠址選擇、既有與潛在設施之產能擴充方案選擇與低碳製程技術投資、以及需求與回收數量之不確定性等,以ε-限制法作為本研究多目標求解方法,藉此方法產生柏拉圖最適解(Pareto-optimal solution)集合,權衡供應鏈總成本與二氧化碳排放量之關係。 本研究亦驗證兩階段隨機規劃模型之可行性,並且與確定性模型(Deterministic model)進行比較,其結果顯示考量需求與回收數量不確定性之永續供應鏈設計結果能較穩健(Robust)。透過參數分析,探討不同原物料成本與各回收率對於供應鏈網路設計之影響。例如,當原物料成本低廉時,企業將不願意藉由回收廢棄產品來滿足顧客需求;反之,當原物料成本昂貴時,對於建置逆物流系統之經濟效益愈顯著,同時回收數量的增加亦將導致二氧化碳排放量上升。最後,藉由本研究模式所產生之柏拉圖最佳解前緣(Pareto-optimal front)曲線,協助決策人員依據不同的二氧化碳排放限制,決定逆物流廠址選擇與廠區產能擴充程度,及進行產能擴充時選擇低碳製程技術的參考依據。
In this paper, we develop a two-stage stochastic programming approach for closed-loop sustainable supply chain network design problem under uncertainty, considering logistics flows, capacity expansion and technology investments of existing and potential facilities, and the uncertainty occurred in customer demand and return quantity. A two-stage stochastic programming model, that captures the trade-off between the total cost and the carbon dioxide (CO2) emission, is proposed from the economic and environmental perspective, respectively. In the numerical evaluation and results, the relationship between the total cost and carbon emission will be analyzed by the Pareto-optimal solution set. Moreover, the applicability of the two-stage stochastic programming model was verified and then compared with the model of certainty. The result shows the sustainable supply chain that considers the uncertainty of demand and return quantity is more robust. The effect of various raw material costs and recovery rates on the design of the supply chain network was discussed through parameter analysis.