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.

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 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.

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 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.

Uplatnění neparametrické metody DEA při zkoumání efektivnosti obcí a měst

2021 ◽  
Author(s):  
Marek Jetmar ◽  
Jan Kubát
Keyword(s):  
Public Services ◽  
Returns To Scale ◽  
Administrative District ◽  
Data Set ◽  
Average Value ◽  
Dea Models ◽  
Municipal Police ◽  
The Given ◽  
Variable Returns To Scale

The article deals with the application of data envelope analysis (DEA), in examining the efficiency of selected public services provided by municipalities and cities. The method is focused on calculating indicators for individual municipalities and groups of municipalities. When calculating the efficiency, the DEA model with variable returns to scale and superefficiency is used. The distance from the efficiency limit (data envelope) is not measured by Euclidean, as classical DEA models, but by Chebyshev distance. The analysis focuses on examining efficiency within groups of municipalities, defined according to the number of inhabitants and location in relation to development centers, but also these groups in the context of the entire data set. The created model allows to calculate the efficiency of each municipality and monitor its ranking within the given category, but also the type of municipality, administrative district or region. It then shows the practical results of the calculation of efficiency - the achieved average value on the example of schools and municipal police. The variability of the results achieved is subject to interpretation with respect to the services examined. Finally, the limits of DEA use are discussed with regard to the quality of available data and the overall appropriateness of the method for monitoring the efficiency of municipalities.

Floodwater Utilization Integrated Risk Evaluation Model Based on D-S Evidential Theory

2012 ◽  
Vol 599 ◽  
pp. 787-794
Author(s):  
Yuan Xiang Zhao ◽  
Yan Min Zhang
Keyword(s):  
Decision Making ◽  
Risk Evaluation ◽  
Evaluation Method ◽  
Evaluation Model ◽  
Water Environment ◽  
Flood Management ◽  
Water Resources Systems ◽  
Integrated Risk ◽  
Floodwater Utilization ◽  
Risk Evaluation Model

According to more and more serious problems of water scarcity, water pollution and deterioration of water environment in homeland, floodwater utilization becomes an important content in flood management and a critical solution for above problems. However, because of the uncertainty and subjective factor in the hydrology and water resources systems, floodwater utilization is a risk decision-making and the evaluation on the risk reasonably becomes an important decision-making reasoning problem. Traditional risk evaluation method considers uncertainty of things, but has little study on incompleteness of things and uncertainty of human’s subjective decision. An integrated risk evaluation model of floodwater utilization is presented based on D-S theory which can solve these problems successfully and with a case study, some benefit conclusions are provided.

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.

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