動態網路DEA之績效分析模式

Abstract

(Tone & Tsutsui, 2014)提出Dynamic Network DEA，其分析多時序下一連續製程的績效評量。網路中每一個時序中，由上而下有多個節點(Node)，每個節點代表該時序下的該製程，相鄰的兩製程之間有一組中間指標Pass-by，以一連線(Link)表示之。時序屬於動態過程，一個製程在前後兩個時序之間有一組中間指標Carry-over，以一連線表示之。每個製程在每個時序即是網路上的一個節點，每一節點有一組外部投入與一組產出至外部的指標。本研究目的為評量各個決策單位(decision-making unit, DMU)在此網路下之績效值。我們必須制定每項指標的權重，也需分析每個指標需改善的數量，各DMU才可達到高績效的前緣。我們建立線性規劃模型，計算每個DMU(主角)相對於全部DMU的績效值，得知它的標竿DMU。在模型中僅計算外部的每項投入項與每項產出項的改善量，內部的每項中間指標則彈性調整，可為增量或減量。因此每一個中間指標將有兩個權重值，分別以它相鄰兩端的節點為基準，此兩權重的和為零。經由模型運算，中間指標分成增量與減量兩種。因此對於一個須增量的中間指標，它對於一端的節點而言視同產出項目時，對於相鄰的另一端的節點而言卻是視同投入；反之，對於一個須減量的中間指標，它對於一端的節點而言視同投入項目時，對於相鄰的另一端的節點而言卻是視同產出。各中間項目配合投入與產出項而調節增減數量，達成提升總績效值至高效率包絡面，它相鄰兩端的節點各別之效率值將隨之有所增減，此將間接判別出著手改善績效時的輕重緩急。文獻中對於中間項目的權重，均與投入與產出項一致性的處理方式，每項只有一個權重。此種分析屬於創見，克服了文獻中所觸及的多種偏差與困難。我們可進行對於主角的敏感度分析。

(Tone & Tsutsui, 2014) proposed Dynamic Network DEA model that analyzes the performance of a set of decisions-making units (DMUs) through a series of processes in a consecutive time periods. A node in the network represents a specific process at a specific time period. There is a set of intermediate indicators “Pass-by” between two adjacent processes and the two nodes are linked by non-directional link. The production system is dynamic since the performance might be changed at different time periods. For a process, there is a set of intermediate indicators “Carry-over” to the next time period and the two nodes are linked by a non-directional link. At each node, the flow-in arc represents a set of input indicators and the flow-out arc represents a set of output indicators. To measure each DMU’s efficiency, we desire to determine the set of weights of all DMUs that are processed in the Dynamic Network. We need to measure the slack of each indicator to be improved so that the DMU could be projected on the efficiency frontier. We propose a linear programming model for the Dynamic Network DEA. In the model, the reduction of inputs and addition of outputs are the main objective to measure the efficiency. The optimal solutions of the slack of each intermediate indicator could be either positive or negative. That depends on the signs of its pair weights and sum of the pair weights is zero. Each intermediate indicator acts as an output indicator to an end node and acts as an input indicator to the other end node. Each intermediate adjust the number of increase or decrease with inputs and outputs and promotion the overall efficiency scale to the frontier. One could have sensitivity analysis of the weight for each indicator.