具分享投入與產出的兩製程生產線的DEA效率評量方法

Abstract

本篇論文計算一群性質相等且產線包含兩子系統的公司，每個子系統分別擁有各自的投入指標，轉換為各自的產出指標，而在兩個子系統間有一組中間指標相互連結，此兩個子系統分享一額外的投入指標，且分攤一組額外的產出指標，其中分享與分攤的比例預先由決策者決定上下限。每間公司輪流計算，運用線性DEA模型求得投入、產出與中間項的影子價格，並得到最佳之綜合績效值。以GBM-CRS之對偶模型計算投入須減少的影子差額與產出需增加的影子差額，而受評單位firm o進行修正，使其達到包絡面將被量測的主角與其餘相對公司比較並計算，本篇論文應用資料包絡分析模型GBM-bc(劉復華, 2017a)計算投入與產出的影子價格，並求得最佳綜合績效值，主角為了能夠達到與相對公司比較所形成的包絡面，以GBM-CRS之對偶模型計算主角之投入需減少的影子差額以及產出需增加的影子差額，在第一步驟中，中間指標是不可辨認之指標，以GBM-bc (劉復華, 2017b)模型，將主角無法辨認的中間指標區分為類產出(aa-inputs)指標和類投入(aa-outputs)指標，並且計算各子系統分享與分攤的比例。第二步驟利用GBM-bc(劉復華, 2017a)模型計算出整系統的最佳綜合績效值，而求得各指標的影子價格與影子差額，減少計算的影子差額，得知包絡面上之投入與類投入指標的目標值；另一方面曾像求得的影子差額，了解包絡面上之產出與類產出指標的目標值，得知主角以何間公司為標竿。每間公司輪流當主角且計算，並可根據每間公司之綜合績效值進行排序。

We need to assess a group of selected firms in an industry and their production lines contain two stages. Each stage has a dedicated bundle of inputs and outputs and the two stages share the other bundle of inputs and outputs. There is a set of intermediate items, (links) between the two stages. The lower and upper bounds of the ratios of the sharing inputs and outputs are prespecified. All firms take turns be the one to evaluate itself. Let firm o evaluates itself against the peer firms. We employed linear programming DEA model to measure the shadow prices of the inputs, outputs and links to obtain the best efficiency score. The dual model of GBM-CRS is to measure the shadow slacks of inputs to be reduced and the outputs to be added so that firm o would improve himself to the best imaginary frontier of the peer firms. In Phase-I of our procedure, we treat the links as non-discretionary in the linear programming model of GBM-bc (Liu, 2017b). The optimal best efficiency score is computed and the links are partitioned into analog-as-input (aa-inputs) and analog-as-outputs (aa-outputs). The ratio of each sharing inputs and outputs are determined as well. In Phase-II, a linear programming model of GBM-bc model (Liu, 2017a) aims to measure the shadow prices and shadow slacks of the inputs, aa-inputs, outputs and aa-outputs. The model determines the best efficiency score of the overall production system as well. Reducing the evaluated shadow slacks, the targets of inputs and aa-inputs on the best efficiency frontier are defined. On the other hand, adding the obtained shadow slacks, the locations of outputs and aa-outputs on the best efficiency frontier are pointed. The benchmark firms of firm o are identified as well. Once each firm assessed himself, all the firms are ranked according to their efficiency scores.