以多指標評比受評單位時之共同權重分析

Abstract

一般常見的組織，如銀行、醫院、學校…等等，其管理者經常處理以多指標評比其轄下單位的問題。管理者常會期望決定各指標的權重，以計算各單位的綜合績效，進一步將各單位加以排序，並探討組織內部績效變異的趨勢。而建立共同權重的方式簡單可以分為兩類，事前管理者主觀決定與事後客觀由資料本身來決定，在本研究則是以後者的方式探討組織內部各單位的績效與排序。以搜尋標竿的機制下來決定共同權重以進行排序，透過設定虛擬標竿並最小化所有單位與虛擬標竿的差異來完成，而與虛擬標竿保持無差異之單位即是實質標竿。若以資料包絡分析法的數學模式架構來分析，即是以組織管理者的角度客觀決定一組共同權重，以進行組織內部的各單位排序。另外，為避免績效值上限值造成組織內部各單位績效發展上的阻礙，本研究衍生出第二種數學模式，消除績效值上限為1的限制，並以中立妥協的角度產生一組共同權重來進行排序。此一模式類似於回歸分析最小化各單位之間的差異，而其最大不同在於可同時處理多項應變數。最後，我們將此兩種共同權重的分析流程，透過數個範例進行應用上的模擬。

Managers in many fields such as banks, hospitals, and schools frequently assess units under their governance with multiple performance indices. In order to rank the units intuitively with a comparable score, managers always try to determine a common set of weights attached to the indices across all the units. The determination of weights is divided into two ways. One is predetermined subjectively by the manager; the other is determined objectively by the data itself. The methodologies proposed in this research belong to the latter. We propose a procedure to determine the common weights by searching the benchmark unit. One virtual benchmark is defined as units with an efficiency score of 1.0 and all units are asked to approach the virtual benchmark as closely as possible. The units with zero gaps to the virtual benchmark are the real benchmark. In the structure of the data envelopment analysis, the determination of common weights in this research means that the organization manager determines the favorable weight to maximize the organization efficiency. Additionally, in order to avoid the bias in measurement due to the upper bound of efficiency, we develop the second procedure to determine one compromise common set of weights, by eliminating the restriction imposing the upper bound of 1.0 on the efficiency score. The model we propose is similar to the regression analysis model, with the main difference being that the former can handle multiple dependent variables. Finally, the procedures are applied in several numerical cases.