scholarly journals An Entropy-Based Cross-Efficiency under Variable Returns to Scale

Entropy ◽  
2019 ◽  
Vol 21 (12) ◽  
pp. 1205
Author(s):  
Chun-Hsiung Su ◽  
Tim Lu
Keyword(s):  
Evaluation Method ◽  
Returns To Scale ◽  
Peer Evaluation ◽  
Data Envelopment ◽  
Efficiency Evaluation ◽  
Dea Models ◽  
Constant Returns To Scale ◽  
Numerical Index ◽  
Variable Returns To Scale ◽  
Decision Making Units

Cross-efficiency evaluation is an effective methodology for discriminating among a set of decision-making units (DMUs) through both self- and peer-evaluation methods. This evaluation technique is usually used for data envelopment analysis (DEA) models with constant returns to scale due to the fact that negative efficiencies never happen in this case. For cases of variable returns to scale (VRSs), the evaluation may generate negative cross-efficiencies. However, when the production technology is known to be VRS, a VRS model must be used. In this case, negative efficiencies may occur. Negative efficiencies are unreasonable and cause difficulties in calculating the final cross-efficiency. In this paper, we propose a cross-efficiency evaluation method, with the technology of VRS. The cross-efficiency intervals of DMUs were derived from the associated aggressive and benevolent formulations. More importantly, the proposed approach does not produce negative efficiencies. For comparison of DMUs with their cross-efficiency intervals, a numerical index is required. Since the concept of entropy is an effective tool to measure the uncertainty, this concept was employed to build an index for ranking DMUs with cross efficiency intervals. A real-case example was used to illustrate the approach proposed in this paper.

scholarly journals A Fuzzy Approach to Support Evaluation of Fuzzy Cross Efficiency

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 882
Author(s):  
Shun-Cheng Wu ◽  
Tim Lu ◽  
Shiang-Tai Liu
Keyword(s):  
Decision Making ◽  
Evaluation Method ◽  
Optimization Problems ◽  
Evaluation Model ◽  
Returns To Scale ◽  
Efficiency Evaluation ◽  
Dea Models ◽  
Production Technologies ◽  
Constant Returns To Scale ◽  
Variable Returns To Scale

Cross-efficiency evaluation effectively distinguishes a set of decision-making units (DMUs) via self- and peer-evaluations. In constant returns to scale, this evaluation technique is usually applied for data envelopment analysis (DEA) models because negative efficiencies will not occur in this case. For situations of variable returns to scale, the negative cross-efficiencies may occur in this evaluation method. In the real world, the observations could be uncertain and difficult to measure precisely. The existing fuzzy cross-evaluation methods are restricted to production technologies with constant returns to scale. Generally, symmetry is a fundamental characteristic of binary relations used when modeling optimization problems. Additionally, the notion of symmetry appeared in many studies about uncertain theories employed in DEA problems, and this approach can be considered an engineering tool for supporting decision-making. This paper proposes a fuzzy cross-efficiency evaluation model with fuzzy observations under variable returns to scale. Since all possible weights of all DMUs are considered, a choice of weights is not required. Most importantly, negative cross-efficiencies are not produced. An example shows that this paper’s fuzzy cross-efficiency evaluation method has discriminative power in ranking the DMUs when observations are fuzzy numbers.

Measuring the financial efficiencies and performances of Turkish funds

2010 ◽  
Vol 60 (3) ◽  
pp. 295-320 ◽  
Author(s):  
F. Gökgöz
Keyword(s):  
Mutual Funds ◽  
Returns To Scale ◽  
Scale Efficiency ◽  
Portfolio Performance ◽  
Data Envelopment ◽  
Performance Indices ◽  
Programming Technique ◽  
Dea Models ◽  
Constant Returns To Scale ◽  
Variable Returns To Scale

Measuring the financial efficiencies of mutual funds in emerging markets has played an important role in finance literature. Charnes et al. (1978) advocated Data Envelopment Analysis (DEA), a valuable mathematical programming technique, which is used to measure the technical, pure and scale efficiencies of decision making units. The general form of DEA is the CCR model that depends on the assumption of constant returns to scale. Subsequently, Banker et al. (1984) developed an alternative DEA model which includes a variable returns to scale approach. The aim of this study is to measure and compare the financial efficiencies of Turkish securities and pension funds in the 2006–2007 period. In this respect, 36 securities mutual funds (SMFs) and 41 pension mutual funds (PMFs) have been evaluated comparatively according to classical portfolio performance measures and DEA models. Results from performance indices and DEA models reveal that PMFs have higher portfolio performances and financial efficiencies than SMFs in the 2006–2007 period. However, SMFs and PMFs have shown considerable increases in efficiency in the 2006–2007 period according to CCR and BCC models. Of the 77 funds studied, 23 funds in 2007 and 20 funds in 2006 demonstrated scale efficiency. Furthermore, the input ratios should be considerably improved for 2006 and 2007. But, mostly the output values of the funds were found to have remained unchanged in the case of PMFs and SMFs in 2007. The output ratios for 2006 should be considerably improved, especially in the case of SMFs. Finally, the DEA method is evaluated as a substantial quantitative tool for investors in analysing the financial efficiencies of funds in the capital markets.

scholarly journals Cost Efficiency Evaluation Based on a Data Envelopment Analysis Approach by Considering Undesirable Outputs on the Basis of the Semi-Disposability Assumption

2020 ◽  
Vol 25 (1) ◽  
pp. 4
Author(s):  
Mehdi Karami Khorramabadi ◽  
Majid Yarahmadi ◽  
Mojtaba Ghiyasi
Keyword(s):  
Decision Making ◽  
Data Envelopment Analysis ◽  
Cost Efficiency ◽  
Power Plants ◽  
Returns To Scale ◽  
Data Envelopment ◽  
Efficiency Evaluation ◽  
Undesirable Outputs ◽  
Constant Returns To Scale ◽  
Variable Returns To Scale

It is considerably important to calculate the cost efficiency in data envelopment analysis for the efficiency evaluation of decision-making units. The present paper develops the classical cost efficiency model in which all the input prices are constant and certain for each decision-making unit, considering undesirable outputs under the semi-disposability assumption. The proposed models are interval and uncertain under the constant returns to scale and also variable returns to scale assumptions, for the easy solution of which, their lower and upper bounds are obtained on the basis of the theorem presented in the text. In order to simulate the proposed models and show their scientific capabilities, additionally, 56 electricity producing thermal power plants in Iran were studied in 2015. Results of the present study show that under both assumptions of constant returns to scale and variable returns to scale, the highest cost efficiency bounds belonged to the combined and steam cycle power plants. Moreover, the average of lower and upper cost efficiency bounds of the power plants under study were 34% and 35%, respectively, in 2015, under the constant returns to scale assumption, and 52% and 54%, respectively, under the variable returns to scale assumption.

scholarly journals Energy Requirement Optimization of Greenhouse Vegetable Production Using Data Envelopment Analysis (DEA) Method in Algeria

2020 ◽  
Vol 23 (2) ◽  
pp. 60-66
Author(s):  
Ahmed Nourani ◽  
Abdelaali Bencheikh
Keyword(s):  
Decision Making ◽  
Data Envelopment Analysis ◽  
Returns To Scale ◽  
Scale Model ◽  
Energy Requirements ◽  
Data Envelopment ◽  
Greenhouse Vegetable ◽  
Constant Returns To Scale ◽  
Variable Returns To Scale ◽  
Decision Making Units

AbstractAlgeria has recently experienced an important agricultural development in terms of gardening in plastic greenhouses thanks to the favourable factors (climatic conditions, etc.). In order to optimize the energy requirements, data from 29 farmers were collected, who qualitatively represent the greenhouse vegetable producers from the most productive sub-provinces of Biskra region (south of Algeria). Considering the various parametric and non-parametric methods for energy consumption optimization, data envelopment analysis is the most common non-parametric method applied. Results showed that the mean radial technical efficiency assumptions of the samples under constant returns to scale and variable returns to scale models were 0.88 and 0.98, respectively. The 51.72% of decision-making units were efficient on the basis of the constant returns to scale model; 79.31% decision-making units were observed efficient on the basis of variable returns to scale model. Calculation of optimal energy requirements for vegetable greenhouse indicated that 108.50 GJ·ha−1 can be saved on machinery (1.38 GJ·ha-1); diesel fuel (4.68 GJ·ha−1); infrastructure (9.35 GJ·ha−1); fertilizers (17.08 GJ·ha−1); farmyard manure (12.05 GJ·ha−1); pesticides (3.93 GJ·ha−1); and electricity (60.03 GJ·ha−1).

scholarly journals The Efficiency of Waste Sector in Italy: An Application by Data Envelopment Analysis

2020 ◽  
Vol 24 (3) ◽  
pp. 225-238
Author(s):  
Massimo Gastaldi ◽  
Ginevra Virginia Lombardi ◽  
Agnese Rapposelli ◽  
Giulia Romano
Keyword(s):  
Data Envelopment Analysis ◽  
Environmental Performance ◽  
Returns To Scale ◽  
Sustainable Growth ◽  
Waste Reduction ◽  
Data Envelopment ◽  
Environmental Legislation ◽  
Dea Models ◽  
Developed Nations ◽  
Variable Returns To Scale

AbstractWith growing environmental legislation and mounting popular concern for the need to pursuing a sustainable growth, there has been an increasing recognition in developed nations of the importance of waste reduction, recycling and reuse maximization. This empirical study investigates both ecological and economic performances of urban waste systems in 78 major Italian towns for the years 2015 and 2016. To this purpose the study employs the non-parametric approach to efficiency measurement, represented by Data Envelopment Analysis (DEA) technique. More specifically, in the context of environmental performance we implement two output-oriented DEA models in order to consider both constant and variable returns to scale. In addition, we include an undesirable output – the total amount of waste collected – in the two models considered. The results show that there is variability among the municipalities analysed: Northern and Central major towns show higher efficiency scores than Southern and Islands ones.

scholarly journals A Cross-Efficiency Evaluation Method Based on Evaluation Criteria Balanced on Interval Weights

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1503 ◽  
Author(s):  
Hailiu Shi ◽  
Yingming Wang ◽  
Xiaoming Zhang
Keyword(s):  
Evaluation Method ◽  
Evaluation Criteria ◽  
Evaluation Criterion ◽  
Peer Evaluation ◽  
Data Envelopment ◽  
Efficiency Evaluation ◽  
Common Set Of Weights ◽  
The Cross ◽  
The Difference ◽  
Evaluation Approaches

Cross-efficiency evaluation approaches and common set of weights (CSW) approaches have long been suggested as two of the more important and effective methods for the ranking of decision making units (DMUs) in data envelopment analysis (DEA). The former emphasizes the flexibility of evaluation and its weights are asymmetric, while the latter focuses on the standardization of evaluation and its weights are symmetrical. As a compromise between these two approaches, this paper proposes a cross-efficiency evaluation method that is based on two types of flexible evaluation criteria balanced on interval weights. The evaluation criteria can be regarded as macro policy—or means of regulation—according to the industry’s current situation. Unlike current cross-efficiency evaluation methods, which tend to choose the set of weights for peer evaluation based on certain preferences, the cross-efficiency evaluation method based on evaluation criterion determines one set of input and output weights for each DMU. This is done by minimizing the difference between the weights of the DMU and the evaluation criteria, thus ensuring that the cross-evaluation of all DMUs for evaluating peers is as consistent as possible. This method also eliminates prejudice and arbitrariness from peer evaluations. As a result, the proposed cross-efficiency evaluation method not only looks for non-zero weights, but also ranks efficient DMUs completely. The proposed DEA model can be further extended to seek a common set of weights for all DMUs. Numerical examples are provided to illustrate the applications of the cross-efficiency evaluation method based on evaluation criterion in DEA ranking.

USING THE MINIMUM DISTANCE OF DMUs FROM THE FRONTIER OF THE PPS FOR EVALUATING GROUP PERFORMANCE OF DMUs IN DEA

2012 ◽  
Vol 29 (02) ◽  
pp. 1250010 ◽  
Author(s):  
G. R. JAHANSHAHLOO ◽  
J. VAKILI ◽  
S. M. MIRDEHGHAN
Keyword(s):  
Decision Making ◽  
Data Envelopment Analysis ◽  
Minimum Distance ◽  
Group Performance ◽  
Returns To Scale ◽  
Data Envelopment ◽  
Production Possibility ◽  
Variable Returns To Scale ◽  
Decision Making Units

Evaluating group performance of decision-making units (DMUs) is an application of data envelopment analysis (DEA) and usually provides a measure to compare the frontiers of the production possibility sets (PPSs) corresponding to different groups and the internal inefficiencies of DMUs associated with their group. In this paper, first, a method is presented for obtaining the minimum distance of DMUs from the frontier of the PPS by ‖⋅‖1, which itself can be a very important subject in DEA, and then, for stating an application of these distances, an approach is provided for evaluating group performance of DMUs based on the production ability of the PPSs such that both constant and variable returns to scale assumptions can be used in this method in contrast with some other methods. Therefore, providing the methods for both obtaining the minimum distance of DMUs from the frontier of the PPS and evaluating group performance of DMUs is the most important contribution of this paper.

scholarly journals Influence of Constant Returns to Scale and Variable Returns to Scale Data Envelopment Analysis Models in ICT Infrastructure Efficiency Utilization

2021 ◽  
pp. 158-181
Author(s):  
Yinka Oyerinde ◽  
Felix Bankole
Keyword(s):  
Data Envelopment Analysis ◽  
Human Development ◽  
Relative Efficiency ◽  
Returns To Scale ◽  
Data Envelopment ◽  
Information And Communication ◽  
Ict Infrastructure ◽  
Policy Direction ◽  
Constant Returns To Scale ◽  
Variable Returns To Scale

A lot of research has been done using Data Envelopment Analysis (DEA) to measure efficiency in Education. DEA has also been used in the field of Information and Communication Technology for Development (ICT4D) to investigate and measure the efficiency of Information and Communication Technology (ICT) investments on Human Development. Education is one of the major components of the Human Development Index (HDI) which affects the core of Human Development. This research investigates the relative efficiency of ICT Infrastructure Utilization on the educational component of the HDI in order to determine the viability of Learning Analytics using DEA for policy direction and decision making. A conceptual model taking the form of a Linear Equation was used and the Constant Returns to Scale (CRS) and Variable Returns to Scale (VRS) models of the Data Envelopment Analysis were employed to measure the relative efficiency of the components of ICT Infrastructure (Inputs) and the components of Education (Outputs). Results show a generally high relative efficiency of ICT Infrastructure utilization on Educational Attainment and Adult Literacy rates, a strong correlation between this Infrastructure and Literacy rates as well, provide an empirical support for the argument of increasing ICT infrastructure to provide an increase in Human Development, especially within the educational context. The research concludes that DEA as a methodology can be used for macroeconomic decision making and policy direction within developmental research.

scholarly journals Cross-Efficiency Evaluation Method with Compete-Cooperate Matrix

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Qiang Hou ◽  
Xue Zhou
Keyword(s):  
Decision Making ◽  
Data Envelopment Analysis ◽  
Evaluation Method ◽  
Peer Assessment ◽  
Data Envelopment ◽  
Efficiency Evaluation ◽  
Self Assessment ◽  
Dea Method ◽  
Decision Making Units

Cross-efficiency evaluation method is an effective and widespread adopted data envelopment analysis (DEA) method with self-assessment and peer-assessment to evaluate and rank decision making units (DMUs). Extant aggressive, benevolent, and neutral cross-efficiency methods are used to evaluate DMUs with competitive, cooperative, and nontendentious relationships, respectively. In this paper, a symmetric (nonsymmetric) compete-cooperate matrix is introduced into aggressive and benevolent cross-efficiency methods and compete-cooperate cross-efficiency method is proposed to evaluate DMUs with diverse (relative) relationships. Deviation maximization method is applied to determine the final weights of cross-evaluation to enhance the differentiation ability of cross-efficiency evaluation method. Numerical demonstration is provided to illustrate the reasonability and practicability of the proposed method.

Technical Efficiency of State Road Transport Undertakings in India - Data Envelopment Analysis

2012 ◽  
Vol 1 (2) ◽  
pp. 31-42 ◽  
Author(s):  
V. Prakash ◽  
J. Rajesh ◽  
M. Thilagam
Keyword(s):  
Decision Making ◽  
Data Envelopment Analysis ◽  
Technical Efficiency ◽  
Relative Efficiency ◽  
Fuel Efficiency ◽  
Returns To Scale ◽  
Road Transport ◽  
Data Envelopment ◽  
Variable Returns To Scale ◽  
Decision Making Units

Data envelopment analysis (DEA) is a method of analyzing the relative efficiency of similar types of organizations known as decision making units (DMU’s). In this paper, DEA model is applied to evaluate the relative technical efficiency of state road transport undertakings (SRTU’s) in India during the period 2011-2012. The authors have considered thirty-four SRTU’s functioning in India. The variables chosen to characteristic production units are the number of fleet held, staff strength and fuel efficiency as inputs and Passengers carried as output. The BCC model is input- oriented allowing for variable returns to scale (VRS), units are ranked and the projection analyses are given.

Sign in / Sign up

Export Citation Format

Share Document