مطالعه مدل ‌های تحلیل پوششی بدون ورودی‌ های صریح A study of DEA models without explicit inputs

Table 5 provides the original evaluation scores of CES 2002 of the 15 basic research institutes. The second column presents the aggregated final scores E, which combine the scores in qualitative and quantitative evaluations, and produce Rank E. The fourth column presents the scores E1, which reflect the research institutes’ quantitative output evaluation without consideration of inputs, and produce Rank 1. The sixth column presents the scores E2 for their research sustainability evaluation, which actually are more or less the CES efficiency evaluation, and produce Rank 2. In Table 5, the 15 basic research institutes are ranked according to the research efficiency Rank 2 for easy comparisons with Table 4. Table 5 and 2 have clearly shown several institutes have higher total scores due to their big sizes. For instance, Unit 6 was ranked A mainly due to its higher research outputs score. Units 4–۵, ۷–۸ were all ranked C in efficiency but three of them were ranked overall B again due to their output scores. Next we compare the DEA results with the CES research sustainability evaluation results (Rank 2), where the weighted sum of the six indexes in Table 3 is used as the score. Firstly we compare the group ranking based on Model (14) (Ranks of Model 14) in Table 4 and Rank 2 based on the research institutes’ research sustainability in Table 5. The top 4 DMUs have the same ranking results. For the worst performed DMUs, Unit 4 and Unit 5 are ranked B in Ranks of Model (14) but C in Rank 2, while Units 10 and 12 are also ranked differently. Thus there are substantial differences (four out of eight—۵۰%) in the classification of Group C via the two approaches. Such results are understandable as the two approaches are based on very different principles, Then we compare the Ranks of Model (15) in Table 4 (Rank of Model (1) is very similar) with Rank 2 in Table 5. Model (15) has taken some value judgements of the DMs into account. The research institutes in Group A of Model (15) are still the same as those of Rank 2. The classifications of Group C under the two approaches are much closer—now only 25% difference. For example, Unit 12 is in Group C by using Model (14), but has relatively strong performance in obtaining external research funding per staff (7th out of 15). Thus it is ranked B by using Model (15). In terms of the group ranking, the two ranks above are more consistent. Therefore, we believe this DEA model is applicable to the efficiency evaluation of CAS. The ranks of the research institutes in the same group are quite different. Nevertheless, similar ranks are not expected since two every different approaches are employed. In summary, we think it is feasible to apply DEA-WEI in future CAS performance evaluation, and it is necessary to apply the DEA-WEI models incorporating value judgements of the DMs. ۵٫ Conclusion Motivated by the different applications of the DEA models without explicit inputs, in this paper we take an axiom approach to examine these DEA models in order to cover as wide applications as possible. This approach leads to a uniform presentation of the DEA-WEI models, some of which are derived explicitly in this paper. One advantage is that it is much easier to use these models when only index indicators are available. Furthermore these DEA models are applicable to efficacy evaluations where inputs are not directly taken into account. The multiplier form DEA-WEI models look similar to ratio approach, but allow flexibility of weights selection for the assessed DMUs. Furthermore, we discuss how to incorporate the DMs’ value judgment in these DEA models using weight restrictions and preferences, and further present a practical application of research evaluation in CAS. We find that the DEA models without explicit inputs have some unique advantages and should be applied to more real-life applications. The empirical results show that it is feasible to apply DEA-WEI in future CAS evaluation, and it is necessary to incorporate value judgements of the DMs into DEA-WEI models. Thus these DEA-WEI models provide a possible approach to deal with the main controversies of the existing CAS research evaluations.