將一組屬下分群並評量績效

Abstract

私人或公家機構之管理者常以一組投入與產出之績效評量指標來評比其屬下之各單位，本研究以線性規劃模型-新修正之最折衷權重分析法(MMCWA)來決定各評量指標之權重。其中，加權後之投入項與產出項的總和分別稱為虛擬投入與虛擬產出，而虛擬投入與虛擬產出的比值與差額分別稱為綜合績效值與虛擬差額。本研究建立了將屬下單位分群的計算程序，計算各群內各單位的績效值之誤差平方和(Error of Sum Squares, ESS)，此程序的目標為最小化各群之ESS總和。根據最佳分群後各單位之綜合績效值發放下屬單位績效獎金。分群後各群須改善其投入與產出以增進效率，本研究建立一資源分配模型，將所需改善的量分配於該群的各單位之間。

The governors of private and public sectors frequently need to assess its subordinates by a set of inputs and outputs performance indices. We employ the linear programming model of the modified Most Compromised Weights Analysis (MMCWA) to determine an optimal common set of weights for the performance indices. The summations of the weighted input values and output values are called the sector’s virtual input and virtual output, respectively. Their ratio and difference denote the sector’s aggregated performance score and virtual gap. We developed a procedure to partition the set of subordinates into groups. Employ MCWA to each group, its Error Sum of Squares (ESS) equals the sum of squared deviations about the scores’ mean of the subordinates in the group. At the best group partition, ESS value of each group is minimized and the sum of the ESS values is minimized. Subordinates in a group are assessed by a common set of weights and are ranked afterward. In each group, the total slacks in each input and output determined by MMCWA need to be allocated to the subordinates. We developed a resource allocation model that the maximum sum of the ratios of slack to input and slack to output of those subordinates is minimized.