多指標績效評量之共同權重研析(I)

Abstract

本研究計畫共包含五個研究子題，分別敘述如下： 子題一 多指標評量時以規模大小將受評者分組且各組以共同權重評比 Classify DEA units by scales and with common sets of weights 子題二 調整現有各受評單位之各投入與產出量以提高整體績效 Reallocating multiple inputs and outputs of units to improve the overall performance 子題三 多指標多受評單位最折衷的綜合績效 The most compromised aggregated performance score for the units with multiple inputs and outputs 子題四 決定以多指標排序各單位時的一組共同權重 Determine a set of common weights for multiple performance indices to rank operation units 子題五 多指標排序各下屬單位時計算各單位績效值的共同中心 Determine the common center for the performance scores of operation units with multiple indices

Topic 1 Classify DEA units by scales and with common sets of weights Managers periodically classify the DEA units that are under their governance with multiple input and output values in decision process. In this paper, we introduce the procedure for ranking one group of operating units. In the first step, a linear programming model is used to determine the most compromised common set of weights that are attached to performance indices. This is done to derive one objective comprehensive score. To avoid the extreme units affecting the common weights, a statistical method is employed in the second step for testing the hypothesis. This is done in order to find out whether the units in the comprehensive scores are homogenous when the common set of weights is applied. If the hypothesis is accepted, the units are ranked according to their comprehensive scores. Otherwise, in the third step, the units are classified into several subgroups according to their scales as per Ward’s method. Each subgroup is then reassessed in three steps until all units of each subgroup have homogenous comprehensive scores. Therefore, a specific common set of weights are used to rank the units that belong to each subgroup. Topic 2 Reallocating multiple inputs and outputs of units to improve the overall performance The aim of this project is to develop a procedure to improve an organization’s overall performance. There are several units under the governance of the decision maker of the organization. The units are assessed by multiple input and output indices. We will study the real case of a commercial bank in Taiwan. In one of the district in Taiwan, the bank owns 25 local branches. We collect the data of five inputs and four outputs indices. We propose a two-phase procedure for the district manager to improve his performance. In Phase One, we construct a linear programming model to obtain a most favorable set of weights for the input and output indices for the district manager’s performance. The model is a slack-based measurement of the data envelopment analysis for the overall performance. The solution of the model would indicate the new allocations for the inputs and outputs for the 25 branch banks. In Phase 2, we discuss the possible situations that the new allocations obtained from Phase 1 may not applicable. Since both inputs and outputs in the new allocations could be increased or decreased without the consideration of the conditions of each local branch bank. For each branch bank, the decision makers of the bank may set a limitation for each index in the change between new and current allocation. To have the limitation the decision makers needs to examine the applicable capability of the branch bank on the index. We add all the possible limitations to the model in Phase 1 to have the second model. The district manager would have a new applicable plan for allocating the level of each input and output for each branch bank. In addition, the most favorable set of weights for the inputs and outputs indices for having the district manager’s performance is obtained.

Topic 3 The most compromised aggregated performance score for the units with multiple inputs and outputs This research is to develop a procedure to measure the performance the groups of units under the governance of a manager. The units are assessed by multiple independents and dependents criteria. We construct a non-linear programming model to measure the overall performance of the units with a set of weights for the criteria. With the common set of weights, performance scores of the units would either greater or less than the overall performance score. With the overall performance score, also called as Centroid Transform Effectiveness (CTE), the total of gaps of the units to the CTE is minimized. We illustrate the model with the real data of companies belong to two industries in Taiwan. We assess the companies with the obtained common set of weights. In addition, we compare the two industries’ performance. Topic 4 Determine a set of common weights for multiple performance indices to rank operation units Managers of public or private sectors are often dealing with the ranking of operation units under their governance with multiple inputs and outputs indices. We propose a method to obtain a most compromised set of common weights attached to the indices to measure the aggregate performance scores for the operation units. Three situations are considered. The first situation is the highest scores are no more than 1 and the total of scores is maximized. The second situation is the lowest score is 1 and the total of scores is minimized. The third situation is some of the scores are more than or equal to 1 and some of them are less than 1. The total difference of the scores to the datum 1 is minimized. Three nonlinear mathematical models are constructed to the three situations. We develop a method to convert the nonlinear models to linear models to have the exact solutions. Topic 5 Determine the common center for the performance scores of operation units with multiple indices Managers of public or private sectors are often dealing with the ranking of operation units under their governance with multiple inputs and outputs indices. We propose a method to obtain a most compromised set of common weights attached to the indices to measure the aggregate performance scores for the operation units. Three situations are considered. The first situation is the highest scores are no more than Θ and the total of scores is maximized. The second situation is the lowest score is Θ and the total of scores is minimized. The third situation is some of the scores are more than or equal to Θ and some of them are less than Θ. The total difference of the scores to the common center Θ is minimized. Three nonlinear mathematical models are constructed to the three situations. We develop a method to convert the nonlinear models to linear models to have the exact solutions.