Cross-efficiency Model Research Articles

The Operating Efficiency of Vocational and Senior High Schools in Xindian District of New Taipei City: Three Envelopment Models in DEA

<p class="1main-text">The purpose of this study is to apply a standard DEA model, cross-efficiency model and category variables DEA in evaluating operational efficiency for vocational and senior high schools in Xindan area, new Taipei city. The procedures this paper. Firstly, we do not consider neither different properties nor peer group for senior high or vocational school to evaluate their operational efficiencies by standard DEA model. Secondly, we apply DEA cross-efficiency (DEA-CE) model to perform self and peer-evaluation for the operational efficiency of the related different schools. Thirdly, we consider peer group and classify two groups in view of different properties to assess their performance by categorical variable DEA (CVDEA). Finally, by comparisons of the three performance results, the categorical variable model can better estimate operational efficiency for these vocational and senior high schools in the District of New Taipei City than that those of other two models.</p>

Entropy Cross-Efficiency Model for Decision Making Units with Interval Data

The cross-efficiency method, as a Data Envelopment Analysis (DEA) extension, calculates the cross efficiency of each decision making unit (DMU) using the weights of all decision making units (DMUs). The major advantage of the cross-efficiency method is that it can provide a complete ranking for all DMUs. In addition, the cross-efficiency method could eliminate unrealistic weight results. However, the existing cross-efficiency methods only evaluate the relative efficiencies of a set of DMUs with exact values of inputs and outputs. If the input or output data of DMUs are imprecise, such as the interval data, the existing methods fail to assess the efficiencies of these DMUs. To address this issue, we propose the introduction of Shannon entropy into the cross-efficiency method. In the proposed model, intervals of all cross-efficiency values are firstly obtained by the interval cross-efficiency method. Then, a distance entropy model is proposed to obtain the weights of interval efficiency. Finally, all alternatives are ranked by their relative Euclidean distance from the positive solution.

Data envelopment analysis cross-efficiency model in fuzzy environments

The fuzzy data envelopment analysis (FDEA) method lacks sufficient discrimination power to rank efficient decision making units (DMUs) with fuzzy data; moreover, it evaluates DMUs using only self-evaluation. This paper develops the fuzzy cross efficiency (FCE) DEA model that combines self-evaluation with peer-evaluation to eliminate the weaknesses of traditional FDEA. This method solves the efficiency evaluation problem in fuzzy environments from a new perspective. An effective method is provided to solve this model, and the ranking results of DMUs at different -levels are obtained. Finally, an example is given to illustrate the proposed method in greater detail.

Ecological Efficiency Based Ranking of Cities: A Combined DEA Cross-Efficiency and Shannon’s Entropy Method

In this paper, a method is proposed to calculate a comprehensive index that calculates the ecological efficiency of a city by combining together the measurements provided by some Data Envelopment Analysis (DEA) cross-efficiency models using the Shannon’s entropy index. The DEA models include non-discretionary uncontrollable inputs, desirable and undesirable outputs. The method is implemented to compute the ecological efficiency of a sample of 116 Italian provincial capital cities in 2011 as a case study. Results emerging from the case study show that the proposed index has a good discrimination power and performs better than the ranking provided by the Sole24Ore, which is generally used in Italy to conduct benchmarking studies. While the sustainability index proposed by the Sole24Ore utilizes a set of subjective weights to aggregate individual indicators, the adoption of the DEA based method limits the subjectivity to the selection of the models. The ecological efficiency measurements generated by the implementation of the method for the Italian cities indicate that they perform very differently, and generally largest cities in terms of population size achieve a higher efficiency score.

DEA Game Cross-Efficiency Model to Urban Public Infrastructure Investment Comprehensive Efficiency of China

In managerial application, data envelopment analysis (DEA) is used by numerous studies to evaluate performances and solve the allocation problem. As the problem of infrastructure investment becomes more and more important in Chinese cities, it is of vital necessity to evaluate the investment efficiency and assign the fund. In practice, there are competitions among cities due to the scarcity of investment funds. However, the traditional DEA model is a pure self-evaluation model without considering the impacts of the other decision-making units (DMUs). Even though using the cross-efficiency model can figure out the best multiplier bundle for the unit and other DMUs, the solution is not unique. Therefore, this paper introduces the game theory into DEA cross-efficiency model to evaluate the infrastructure investment efficiency when cities compete with each other. In this paper, we analyze the case involving 30 provincial capital cities of China. And the result shows that the approach can accomplish a unique and efficient solution for each city (DMU) after the investment fund is allocated as an input variable.

An integrated multi-objective Markowitz–DEA cross-efficiency model with fuzzy returns for portfolio selection problem

In this paper, a novel multi objective model is proposed for portfolio selection. The proposed model incorporates the DEA cross-efficiency into Markowitz mean–variance model and considers return, risk and efficiency of the portfolio. Also, in order to take uncertainty in proposed model, the asset returns are considered as trapezoidal fuzzy numbers. Due to the computational complication of the proposed model, the second version of non-dominated sorting genetic algorithm (NSGA-II) is applied. To illustrate the performance of our model, the model is implemented for 52 firms listed in stock exchange market of Iran and the results are analyzed. The results show that the proposed model is suitable in compared with Markowitz and DEA models due to considering return, risk and efficiency, simultaneously.

A Non-Oriented DEA Game Cross Efficiency Model for Supplier Selection

A Non-Oriented DEA Game Cross Efficiency Model for Supplier Selection

Efficiency Scores Analysis of Coal Mines using IRS, DRS and Cross Efficiency Models

Economic growth world over is driven by energy, whether in the form of finite resources such as coal, oil and gas or in renewable forms such as hydroelectric, wind, solar and bio-mass or its converted form, electricity(power). Increased energy consumption (especially of electricity) is inevitable with higher GDP growth. Coal was created by the fossilised remains of plants and has high carbon content. DEA is a multi-factor productivity analysis model for measuring the relative efficiency of a homogenous set of coal mines (DMU’s). For every inefficient coal mine, DEA identifies a set of corresponding efficient coal mines that can be utilized as benchmarks for improvement of performance and productivity. Benchmarking and ranking of coal mines based on efficiency scores using advanced DEA models like, Increasing Returns to Scale (IRS), Decreasing Returns to Scale (DRS), Cross Efficiency (CE) Models.

Evaluating energy efficiency for airlines: An application of VFB-DEA

In this paper, the energy efficiency of airlines has been studied with number of employees, capital stock and tons of aviation kerosene as the inputs and Revenue Ton Kilometers, Revenue Passenger Kilometers, total business income and CO2 emissions decrease index as the outputs. A new model, Virtual Frontier Benevolent DEA Cross Efficiency model (VFB-DEA), is proposed to calculate the energy efficiencies of 11 airlines from 2008 to 2012. Spearman correlation coefficient is applied to validate the applicability of the new model. The results indicate that capital efficiency is an important factor in driving energy efficiency, and the American financial crisis had a significant influence on the change in energy efficiency during this period.

Performance evaluation of logistics firms based on DEA model

Logistics plays an increasingly more important role in the whole national economy. However, China's logistics industry is still in its infancy, and its operation efficiency desperately needs to improve. This paper applies data envelopment analysis (DEA) to evaluate the operation efficiency of two categories, and a total number of 20 representative listed logistics firms in China. DEA CCR, BCC and cross-efficiency model are used to discover the level and reasons of efficiency and inefficiency of sample decision-making units (DMUs). Net permanent assets, total assets, number of employees and main business costs are selected as input measures; net profit, capital turnover rate and main business income are used as output measures. The results show that about half of sample logistics firms are efficient DMUs, indicating the overall developing situation of logistics industry in China is good; the efficiency of logistics firms is related to regional economy. Related suggestions for efficiency improvement of Chinese logistics industry are also presented.

The DEA Game Cross Efficiency Model Applied to the Brazilian Football Championship

Abstract In this paper, we use DEA to measure the Brazilian football teams efficiency in the season 2014. In this context, each team is a DMU, where we select three inputs: the number of home matches, the average attendance and the average points obtained at the last four seasons. The total points obtained at the season 2014 is the output. We evaluate the teams cross-efficiency by DEA game, which is an approach suitable when there is no cooperation among DMUs. This procedure also improves the efficiencies discrimination.

Cross-efficiency in DEA: A maximum resonated appreciative model

The occurrence of multiple optimal solutions is an important and interesting issue in data envelopment analysis (DEA), for it allows flexibility to estimate the optimal cross-efficiencies of all decision making units (DMUs). This paper uses the advantage of multiple optimal solutions, be in the cases of efficient and/or inefficient DMUs, to integrate both the first and second-order voices of all DMUs and proposes a most appreciative cross-efficiency DEA method. The paper deals with multiple optimal solution cases within the context of cross-efficiency models and suggest a model that is most appreciative for all DMUs being cross-evaluated by all others. The merits and appreciative superiority of the proposed method is proven theoretically; and illustrated practically through a ranking study chosen from the literature.

The DEA Game Cross-efficiency Model for Supplier Selection Problem under Competition

As the most important responsibility of purchasing management, the problem of supplier evaluation and selection has always received a great deal of attention from practitioners and researcher s. This management decision is a challenge due to the complexity and various criteria involved. Many methods based on data envelopment analysis(DEA) emerged, especially the cross efficiency. But it exists some limitations, such as the cross efficiency value is often non-un ique, average cross efficiency measure is not good because it is not pareto solution. This paper considers the competition between the su ppliers and presents game cross efficiency which is based on DEA to assess supplier performance. This method can get a unique efficiency and it is pareto solution. Numerical example is used to illustrate application and feasibility of the proposed methodology.

Applying a Peer-Restricted Cross-Efficiency Approach to Measuring the Performance of International Tourist Hotels in Taipei

Data envelopment analysis technique has been frequently utilized to assess hotel performance. However, studies that utilize this approach tend to use a self-evaluation method, in which a great number of non-zero weights are selected to maximize the efficiency scores. Aiming at addressing this shortcoming, this study utilizes a peer-restricted, cross-efficiency evaluation approach that does not only eliminate zero weight of the variables during performance evaluation but also reduces the differences between profiles of the weights. Both the peer-restricted, cross-efficiency model and the classic benevolent cross-efficiency approach are applied to measure the efficiency and to provide complete ranking orders for all the international tourists hotels (ITHs) in Taipei between the years of 2008 and 2009. Implications for hotel management in ITHs are discussed.

The Analysis of Shunting Locomotives' Operating Efficiency Based on Gray-DEA

In order to explore the configuration of the railway freight shunting locomotives, improve the efficiency of locomotive operation; a DEA cross evaluating method based on grey incidence analysis is presented in this paper. This method is based on collecting underlying data of factors that influence the shunting operation efficiency in train service depot, which utilizes grey incidence analysis to establish corresponding evaluation indicators system. Furthermore, the method as well adopts DEA and DEA cross efficiency model to analyze, evaluate and estimate the efficiency of shunting locomotives operation in train service depots. A sorting result of the efficiency of shunting locomotives operation in each train service depot has been acquired with help of programming using MATLAB 7.0. What the result indicates is that the DEA cross efficiency evaluating model based on grey incidence analysis can reflect the actual state of the efficiency of shunting locomotives operation in each train service depot. Eventually, based on a projection analysis of non-DEA's three decision-making units, key factors that influence the efficiency of shunting locomotives operation are identified, which can provide decision support for further improvement of the configuration and operation in train service depots.

Using DEA cross-efficiency evaluation for suppliers ranking in the presence of non-discretionary inputs

Supply chain includes all activities associated with the flow and transformation of goods from the raw material stage through to the end user. Supplier selection is one of the most important parts of supply chain management (SCM). For selecting suppliers, data envelopment analysis (DEA), as a multiple criteria decision making tool, has been applied for several times. However, sometimes in supplier selection problem, there may exist some criteria that are beyond the control of a management. These criteria are called non-discretionary or exogenously fixed factors. Since in traditional treatment of non-discretionary inputs in DEA, free reign is given when deciding for each decision making unit (DMU) which outputs and inputs to emphasise, many different avenues are present by which a DMU can appear efficient. Therefore, it is common to have many DMUs that are relatively efficient. In addition, since each DMU has its own set of weights, all of its weight might be put on a single output and input. As a result, the objective of this paper is to propose a cross-efficiency model which is able to consider non-discretionary inputs. A numerical example demonstrates the application of the proposed model in supplier selection context.

Enhancement of equity portfolio performance using data envelopment analysis

This paper examines the applicability of data envelopment analysis (DEA) as a basis of selection criteria for equity portfolios. It is the first DEA application for constructing a combined equity investment strategy that aims to integrate the benefits of both value investing and momentum investing. The 3-quantile portfolios are composed of a comprehensive sample of Finnish non-financial stocks based on their DEA efficiency scores that are calculated using three variants of DEA models (the constant returns-to-scale, the super-efficiency, and the cross-efficiency models). The performance of portfolios is evaluated on the basis of the average return and several risk-adjusted performance metrics throughout the 1994–2010 sample period.The results show the capability of the DEA approach to add value to equity portfolio selection. The outperformance of the top 3-quantile DEA portfolios in contrast to both the comparable bottom portfolio and the stock market average is statistically significant on the basis of all performance measures employed. The outperformance is slightly more significant when the stock price momentum is included in the DEA variables. The methodology employed offers an interesting alternative for detecting the outperforming stocks of the future by capturing both the price momentum and several dimensions of relative value simultaneously. DEA is particularly useful as a multicriteria methodology in cases in which the number of stocks in the sample is large. It therefore also has useful implications to practical portfolio management.

Developing a new cross-efficiency model with undesirable outputs for supplier selection

Inappropriate selection of suppliers will have an adverse impact on the overall performance of the firm. One of the techniques that can be used for selecting supplier is data envelopment analysis (DEA). Traditional DEA models such as Charnes–Cooper–Rhodes and Banker–Charnes–Cooper can only measure radial efficiency (weak efficiency). To measure strong efficiency in DEA, Tone (2001) proposed slacks-based measure (SBM). This model deals directly with the input excesses and output shortfalls. The objective of this paper is to propose a neutral SBM with undesirable outputs for selecting the best supplier. A numerical example demonstrates the application of the proposed model.

Goal programming approaches for data envelopment analysis cross efficiency evaluation

Abstract Cross efficiency evaluation has long been proposed as an alternative method for ranking the decision making units (DMUs) in data envelopment analysis (DEA). This study proposes goal programming models that could be used in the second stage of the cross evaluation. Proposed goal programming models have different efficiency concepts as classical DEA, minmax and minsum efficiency criteria. Numerical examples are provided to illustrate the applications of the proposed goal programming cross efficiency models.

A cross-efficiency model based on super-efficiency for ranking units through the TOPSIS approach and its extension to the interval case

One of the most important approaches for ranking decision-making units in data envelopment analysis is the cross-efficiency method. The main idea of cross-efficiency is to use data envelopment analysis in peer evaluation, instead of only a self evaluation. However, in the cross-efficiency method, optimal weights corresponding to evaluation of decision-making units may not be unique. In this research with modifying the cross-efficiency method we are going to overcome this problem. Then with regard to the changes and using the TOPSIS method we present a new super-efficient method to rank all decision-making units. Furthermore, we extend the proposed method to the case that data are intervals.