اکتشاف برآورد کمتر بهره وری مدل CCR: بر اساس بخش های پزشکی با استفاده از مدل تحلیل پوششی داده
|کد مقاله||سال انتشار||تعداد صفحات مقاله انگلیسی||ترجمه فارسی|
|4350||2011||6 صفحه PDF||سفارش دهید|
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Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Expert Systems with Applications, Volume 38, Issue 4, April 2011, Pages 3155–3160
Data Envelopment Analysis (DEA) is one of the best-known efficiency evaluation methods due to its advantages in selection of weights. Many research papers have extensively discussed the issue of weight restrictions, rather than those implied in the model itself. However, this often leads to a failure to represent the relations of certain weights, as well as underestimation of the efficiency of Decision Making Units (DMUs). When analyzing the medical sectors of Taiwan with the developed models and CCR, it is found that efficiency underestimation by efficient DMUs is more serious than that of inefficient DMUs. In addition, underestimation occurs when weights are concentrated in the same output, however, every output of referenced DMU is the same times of corresponding output of targeted DMU.
Efficiency is an important topic, and Data Envelopment Analysis (DEA) is one of the most famous efficiency evaluation methods. A mathematical model is established in DEA to judge efficient frontiers, and evaluate if the Decision Making Unit (DMU) is efficient. In addition, DEA permits to propose an improved package for inefficient DMU. The concept of a non-dominated solution proposed by Pareto and an index-based efficiency representation concept proposed by Farrell provide the basis for DEA (Cooper, Seiford, & Tone, 2002). With the introduction of the concept of non-dominated solutions and indices, Charnes, Cooper, and Rhodes (1978) developed a group of optimal mathematical equations for judging the efficient frontier, and calculating efficiency, which was called DEA, and the first group of mathematical expressions was named CCR, the abbreviated name of the authors. Many studies have focused on the analysis of weight restrictions, since selection of weight represents one of DEA’s advantages (e.g. Allen et al., 1997, Liu and Chuang, 2009, Pedraja-Chaparro et al., 1997 and Podinovski, 2007). Tracy and Chen (2005) first proposed that weight hypothesis may lead to underestimation from additional weight restrictions. However, CCR, based on (∑vx)/(∑uy)(∑vx)/(∑uy) or (∑uy)/(∑vx)(∑uy)/(∑vx), implies inherent weight restrictions, and has never been extensively discussed. Such restrictions may lead to a failure to represent the relations of certain weights, thus, output-oriented DEA-R was developed to address such problems (Despic, Despic, & Paradi, 2007). Since unnecessary and unreasonable weight hypothesis would cause CCR to underestimate the efficiency of a DMU, an input-oriented DEA-R model was developed. Another research pointed out that, this hypothesis not only underestimated efficiency, but also resulted in false low efficiency solutions (an efficient DMU was judged as an inefficient DMU). Therefore, this paper aims to further discuss the underestimation issues of an efficient DMU, and provide a deeper understanding of the instance when underestimation occurs. Andersen and Petersen, 1993 and Seiford and Zhu, 2003 developed a super-efficient model and a dependent model, respectively, to discuss efficient and inefficient DMUs. As both the super-efficient and dependent models were developed based on CCR, the problem of efficiency underestimations occur. Thus, this research intends to develop a pro-rated super-efficient evaluation model in an attempt to study how the efficient DMU was underestimated, and the instance when underestimation occurred. The remainder of this paper is organized as follows: Section 1 describes the issues of efficiency underestimation, as well as two subjects that have not been discussed, which are underestimation of an efficient DMU, and when exactly does the instance of underestimation occur. Regarding the underestimation of an efficient DMU, this section discusses two high-efficiency models, with/without weight restrictions. Section 2 reviews the super-efficient model based on CCR, and proposes a super-efficient model based on DEA-R (excluding weight restrictions). Taking medical centers in Taiwan as an example, Section 3 compares the efficiency and optimal weights of CCR and DEA-R-based super-efficient models, and gains insight into the underestimation issues of an efficient DMU, as well as possible underestimation instances. The time point of underestimation is further discussed in Section 4. Finally, results and discussions are presented in Section 5.
نتیجه گیری انگلیسی
Based on past studies on underestimation, this paper suggests that the CCR-based model has occasional underestimations when evaluating high efficiency DMUs, and thus, proposes to use Super-DEA to discuss the underestimation problems of DMUs. There are four main findings: (1) in this case, since the underestimation problem of a high efficiency DMU is more serious than that in the low efficiency DMU, this model is necessary; (2) based on the comparison and analysis of optimal weights, it is known that the number of weights is less, and the unreasonable weight limitation assumption leads to underestimations in efficiency when using (∑vx)/(∑uy)(∑vx)/(∑uy) or (∑uy)/(∑vx)(∑uy)/(∑vx) as the base of the model; (3) to determine exactly when underestimation will occur, this study analyzes the DMU that was not underestimated from another perspective, and finds that when DEA-R-I weights are concentrated on one output, and DEA-R-I efficiency, θoθo, and CCR-I efficiency, View the MathML sourceθ¯o, are the same, there is no underestimation; (4) it is proven that when DEA-R-I weights are not concentrated on one output, DEA-R-I efficiency, θoθo, and CCR-I efficiency, View the MathML sourceθ¯o, are not the same; with the exception of every output of referenced DMU is the same times of corresponding output of the targeted DMU. Therefore, it is demonstrated that after executing DEA-R, whether CCR is underestimated can be determined. In other words, DEA-R not only can be used to replace CCR to evaluate efficiency, and thus, avoid underestimations and weight limits, but also to predict whether CCR underestimation would occur. The examples of special subsidies for further education in Taiwan, merger of DRAM factories, and evaluation of hospitals have demonstrated the practical value of this study. In the first example, the Taiwanese government, with the goal of assisting the colleges of universities to become top colleges recognized worldwide, proposed the Five-year Fifth Billion plan to fund the development or research facilities of colleges. However, since different colleges can excel in their own domains, the scope of subsidy may be too broad. Therefore, it is no longer necessary to discuss whether schools should possess a leading position in their respective domains, instead, the focus should be the magnitude of the achievements. Only by funding the colleges with the greatest magnitude could the colleges be further advanced. As a result, a more accurate model is needed to calculate the efficiency of DMUs. In the second example, due to the financial crisis and long-term fluctuation, the DRAM industry is facing serious obstacles. Thus, the government aims to integrate DRAM factories in order to reach an appropriate scale. However, almost all DRAM companies are experiencing losses. Thus, it is necessary to identify the strengths of each company and the leading magnitude in order to determine the main body of mergers. From another perspective, the government would assist inefficient companies to merge with efficient companies to improve efficiency. Similarly, in DMU 4, if the efficient DMU is underestimated as an inefficient DMU, it would cause the company to be merged. In such case, a more accurate model is needed to calculate the efficiency of DMU. Lastly, to effectively control the national health insurance budget, in addition to limiting the global budget, the government also plans to downgrade inefficient hospitals to reduce expenditures. If a hospital is indeed efficient, but determined as inefficient, it would be downgraded, causing serious problems for the hospital. After downgraded, the payment for each outpatient visit and hospitalization would be reduced, thus, the total revenue of the hospital would also be reduced. The hospital may need to downsize the staffs or increase the physicians’ working hours to maintain the total revenue. As a result, doctors would not have sufficient time for research, and the management strategies of the hospital may need to be drastically changed (transforming from a research and medical care institution to a sole medical care institution). As seen, accurate evaluations of DMU efficiency are very important in practice. This study developed a new DEA model based on Super-high and ratio concepts. This model not only can avoid underestimating the efficiency of efficient DMU, but can also be used to determine whether underestimation would occur. In the future, this model can be employed to evaluate efficiency and prevent problems caused by underestimation.