多項指標之績效評量模式之研析

Abstract

本研究計畫共包含三個研究子題，分別敘述如下。 本研究計畫為先前國科會研究計畫之延續，愈為深入。本研究旨在探討私人企業或公家機構的決策管理者，管理其下屬若干個單位(簡稱UOAs，units of assessment或是DMUs，decision-making units)，且以若干個投入指標及若干個產出指標用來績效評量。本研究計畫的三個子題互相關聯，均在求DMU的績效排序。但是所訴求的目標與解決的方法各不相同，在管理的意涵上各具特色，但是卻又具互補性質。若干個投入指標及若干個產出指標，以一組權重加權後，來計算各DMU總虛擬投入與總虛擬產出的比值。本研究之目標其評比的結果在管理上具實用價值。 子題一 多指標績效評比之獎金分配程序 企業至年終，管理者依今年盈餘定出總獎金預算的範圍。根據此預算並依照績效分配獎金給各部門員工。然而，績效評估為一多指標問題，在選擇各指標所對應的權重時，總人事成本往往難以符合企業預算且公正評估各受評單位的績效值。因此，本研究以數學規劃為基礎，提出一套有系統的兩階段流程，來解決獎金分配的難題。第一階段，找出Units of assessment(UOAs)績效的最小界限，接著經由第二階段微調，以滿足管理需求與管理者所期望的績效分配。最後依造績效分發獎金。本研究應用範圍極廣，能應用於不同產業與不同管理需求。管理者只須根據偏好設定參數，並依照流程經由模式一與模式二的運算，即可得到一組權重。在此組權重的評估下，人事成本得到有效的控制、離群值將不影響其他受評單位的績效表現、管理者更能控制各單位績效獎金之間的差異。 子題二 群體對候選人投票排序時處理相同排名的方法 本研究之目的為分析一種普遍的投票結果。一群評審欲針對若該候選人加以排序，每位評選先對候選人加以排序，彙總排序的結果得知每位候選人在各項名次的得票次數。作者先前的研究發展出的非線性規劃模式可求得各名次的權重，以這組權重來計算各候選人的得票加權總分，再以此總分做為排序。若有總分相同時，則為同名次。此現象在實務上造成困擾，本研究之目的乃處理同名次之問題。以上述的排名模式為第一階段，本研究再增第二階段之處理程序，其中主要為提出新的非線性規劃模式，來將因總分相同而排名相同的候選人加以排序。 子題三 多指標評比以共同權重之交叉績效來排名 在多指標的評量問題下，高階管理人常常面臨到要如何制定指標的權重，以客觀的方法將下屬單位(DMU, decision-making unit)排序。本篇文章提出一三階段的程序，第一階段先讓每個DMU輪流當主角，以資料包絡分析法(DEA)之CCR模式計算出其最高之績效值。第二階段以每個DMU在第一階段所求出之績效值當作基準，選擇一組指標的權重使得其他DMU與主角之績效值差距之總和為最小。不同於參考文獻中非線性規劃模型之計算，我們提出線性規劃模型，避免了一項關鍵常數ε值的設定所產生之不確定性。第三階段帶入交叉效率的技巧，利用第二階段所求出之各主角的權重去計算其他DMU的交叉績效值。每個DMU的總交叉績效值，作為排序依據。並以台灣17個林區進行評估為例導引計算之程序。

The proposal contains three related topics. Topic 1 An analytical procedure for bonus allocation with multiple performance indices At the end of accounting period, the manager will set up a limit for bonus budgets according to this year’s surplus. Then, the bonus is allocated to each unit. However, performance evaluation is a multi-indices issue. Therefore, selecting the corresponding weights to each index may be difficult and troublesome due to not knowing how to evaluate the units under equity and total labor cost won’t usually meet the bonus budgets. This paper provides a two-phase analytical procedure based on Mathematical Programming to solve bonus allocation problems under the perspective of an enterprise. Our model can control labor costs effectively and detect outliers on equal terms, avoiding units with special performances to affect the evaluation of other units. It is designed to help managers adjusting the bonus range of most employees to a desired level according to their performances. Moreover, the units we assessed are common in nature, so we employ common weights during evaluation. The model we proposed is flexible enough for all industries, the manager can easily adjust the parameters to satisfy their managerial requirements under effective labor cost management. Topic 2 A procedure to discriminate candidates in tie of a group voting system This research is aimed to develop a procedure to analyze the voting result of a voting group. Each voter of the group ranks several candidates in his/her preference order. The first phase of our procedure is employing our previous developed model that determines a set of weights for the places in the order therefore the candidates could be ordered according to their aggregated scores. The model is unable to discriminate the candidates in tie with the aggregated score. In this research, we propose to append a decision process as the second phase that consists of a nonlinear mathematical programming model to discriminate candidates in tie. Topic 3 Cross-efficiency analysis with common weights for the multiple indices performance evaluation Managers usually employ multiple indices to assess decision-making units (DMU) under their governance. We developed a three-phase procedure to rank the DMUs. The typical data envelopment analysis (DEA) CCR model is implemented in Phase-one to compute each DMU’s most favorable efficiency score. In Phase-two, we constructed a general non-linear mathematical programming model to obtain a set of weights attach to the performance indices for each DMU so that the total differences between his most favorable efficiency score and the other DMUs’ cross-efficiency scores is minimized. Additionally, based upon the general non-linear model, we considered three criteria for the differences measurement: the rectilinear, Euclidian and mini-max distances. In the case of rectilinear distance measurement, the non-linear model is converted into a linear model, and furthermore the critical coefficient ε is eliminated so that the precise result is obtained. Phase-three is summarizing the relative efficiency scores obtained in Phase-two. The total and average cross-efficiency score for each DMU is computed. DMUs are ranked according to the total or average scores. We illustrate the procedure by the data set of 17 forests in Taiwan form the published paper by Kao and Yang (1992).