Cross-efficiency Method Research Articles

Assessment of Iranian airlines using network cross-efficiency DEA and the regret theory

Network Data Envelopment Analysis (NDEA) has been extensively applied to evaluate the air transportation sector. NDEA provides a tool for evaluating the internal processes of Decision-Making Units (DMUs). Optimistic Network Cross-Efficiency (ONCE) has recently been extended to the basic two-stage system. However, there are still two main shortcomings that need to be addressed. First, the ONCE evaluates DMUs based only on the optimistic viewpoint, neglecting the pessimistic viewpoint. The optimistic viewpoint assumes that there is only one set of reference points, which includes the best practice DMUs. The first contribution of this study is to develop a new Pessimistic Network Cross-Efficiency (PNCE) method. This method is based on a new set of reference points, which includes the worst-performing DMUs. The PNCE is developed as an extension of the ONCE. Second, both the ONCE and newly developed PNCE methods may lead to unrealistic results because they neglect the subjective preferences of Decision Makers (DMs). These NDEA models employ the Arithmetic Mean (AM) as the cross-evaluation aggregation method, which not only underestimates the importance of self-evaluation but also overestimates the importance of peer evaluations. Consequently, ONCE and PNCE may lead to biased efficiency results. To address this drawback, the second contribution of this study is to develop a new Aggregation method based on the Regret theory and Consensus (ARC). This method aims to reflect the psychological preferences of DMs when estimating cross-evaluation weights. To achieve this goal, we obtained new optimistic and pessimistic efficiencies by utilizing the newly developed ONCE-ARC and PNCE-ARC methods. Subsequently, a Double-Frontier Network Cross-Efficiency with ARC (DFNCE-ARC) is developed as a more comprehensive NDEA. Finally, a practical application is conducted to assess the performance of a set of Iranian airlines, demonstrating the usefulness and applicability of DFNCE-ARC.

An optimistic-pessimistic game cross-efficiency method based on a Gibbs entropy model for ranking decision making units

The game cross-efficiency method, a commonly utilized approach for ranking decision-making units in tie-breaking scenarios, is based on secondary goals. However, in certain data envelopment analysis ranking problems, the classical game cross-efficiency method may fail to differentiate all decision-making units effectively. To address this limitation, it is prudent to explore the development of a new method that can enhance the ranking performance of the classical game cross-efficiency approach. In this study, we propose a novel Gibbs entropy linear programming model that integrates both optimistic and pessimistic perspectives of the classical game cross-efficiency method for data envelopment analysis ranking problems. To validate the reliability and utility of our proposed method, we present three examples: the six nursing homes problem, numerical example 2, and an application involving twenty Thai provinces with cash crop data. The reliability of the proposed method is assessed using Spearman’s correlation coefficient (rs) on the numerical examples. The results demonstrate that the rs values for both the proposed method and the classical game crossefficiency method, specifically for the six nursing homes problem, numerical example 2, and the application involving twenty Thai provinces, are determined to be rs=0.998, 0.998, and 0.986 respectively.

Evaluation of intercity road passenger transportation using a novel double-frontier game-regret-cross-efficiency

The Cross-Efficiency (CE) method, based on Data Envelopment Analysis (DEA), is a commonly used approach to measure the efficiency of Decision-Making Units (DMUs). Various secondary goal models can yield different efficiency results. The recently developed Game CE (GCE) method aims to address this issue and achieve convergence efficiencies. However, the conventional GCE was developed under the unrealistic assumption that Decision Makers (DMs) are perfectly rational, as it relies on the arithmetic mean aggregation method. Additionally, the GCE evaluates DMUs based on efficient reference points, disregarding the pessimistic perspective. The study introduces a new aggregation method called Regret-Consensus Aggregation (RCA) that captures the subjective preferences of DMs. GCE-RCA scores are obtained by incorporating RCA into the GCE. A new method called Game Cross In-Efficiency (GCIE) with RCA (GCIE-RCA) has been developed to incorporate anti-efficient reference points into the evaluation process. A Double-Frontier GCE based on the RCA (DFGCE-RCA) is developed from two perspectives. The DFGCE-RCA is implemented to evaluate the performance of the Iranian Inter-City Road Passenger Transportation (IC-RPT) system based on six key performance indicators. DFGCE-RCA has several advantages in addition to those of GCE. Firstly, considering two perspectives provides more comprehensive results. Additionally, it can capture the subjective perspectives of DMs. Lastly; it enables the aggregation process to reach a consensus.

A Multi-Attribute Group Decision-Making Method Based on Trust Relationship and DEA Regret Cross-Efficiency

In multiattribute group decision-making (MAGDM) problems, the data envelopment analysis (DEA) cross-efficiency method is an effective tool to evaluate each decision-making unit. However, this method usually assumes that the decision-maker (DM) is completely rational, which ignores the risk psychology of the DM in the decision-making process. To compensate for this deficiency, this article proposes an MAGDM method based on trust relationships and DEA regret cross-efficiency. First, we construct a modified model based on the CCR model. Then, we propose the DEA regret cross-efficiency method. This method involves the risk psychology of the DM in the decision-making process. Next, a weighting model is developed to aggregate the cross-efficiency comprehensive utility matrix. Subsequently, we construct trust propagation and trust aggregation models to obtain the weights of experts. Finally, the MAGDM method based on trust relationships and DEA regret cross-efficiency is designed to rank all alternatives. A numerical example is provided to illustrate the superiority and rationality of our proposed method.

Embracing fairness within a cross-efficiency hierarchical network DEA system

Several scholars have utilized hierarchical network Data Envelopment Analysis modeling techniques to assess the performance of complex structures. However, there has been limited consideration given to the integration of a peer-appraisal setting within a self-evaluation hierarchical context. This aims to enhance discriminatory power and mitigate the issue of unrealistic weighting scheme. To this end, our study extends the single-stage hierarchical additive self-evaluation model of Kao (Omega 51:121–127, 2015. https://doi.org/10.1016/j.omega.2014.09.008), by integrating the well-established cross-efficiency method. An original combination of a maxmin secondary goal model and the Criteria Importance Through Inter-criteria Correlation (CRITIC) method is proposed, to expand the basic hierarchical self-evaluation model. The maxmin model addresses the issue of the non-unique optimal multipliers obtained from the self-evaluation model, ensuring a more realistic weight scheme. The CRITIC method, that tackles the aggregation problem by objectively determining weights of criteria, rewards the minority and is conducive to a fairer evaluation. Results indicate that the proposed approach is more likely to obtain a unique efficiency and ranking score for the units under consideration. This study entails a numerical experimentation aimed at evaluating the efficiency of a set of 20 universities while validating the applicability of our proposed approach. To conclude, the practical applications of this methodological framework could encompass assessing services within the higher education sector or fostering sustainable development across various operations within a hierarchical structure.

Managing non-cooperative behaviors in consensus reaching process: A novel multi-stage linguistic LSGDM framework

Large-scale group decision-making (LSGDM) is a complex process involving numerous decision-makers (DMs). However, considering such a large number of DMs increases the complexity of the process. it seems necessary to pay much more attention to aspects such as a proper dimensionality reduction for scalability, consensus processes with automatic feedback, and effective management of non-cooperative DMs. To address such aspects, this paper presents a novel framework for LSGDM, based on Extended Comparative Linguistic Expressions With Symbolic Translation (ELICIT). We first extend the K-means clustering algorithm by incorporating individual assessments and trust relationships to classify DMs into subgroups, enhancing decision-making efficiency. We then develop a feedback mechanism based on two optimization consensus models for ELICIT information, that automatically provides optimal recommendations. An essential aspect of our proposal is the management of non-cooperative behaviors by utilizing the normal distribution to detect and penalize misbehaviors. Furthermore, we introduce a Data Envelopment Analysis (DEA) cross-efficiency method based on ELICIT values to rank all alternatives once an acceptable group consensus degree is reached. The framework’s effectiveness is demonstrated through a practical application case study, accompanied by a parametric analysis. Comparisons with existing LSGDM methods highlight the superiority of our proposal in terms of efficiency.

Assessment of airline industry using a new double-frontier cross-efficiency method based on prospect theory.

Cross-efficiency method (CEM) is a well-known technique based on data envelopment analysis that provides policymakers with a powerful tool to measure the efficiency of decision-making units. However, there are two main gaps in the traditional CEM. First, it neglects the subjective preferences of decision-makers (DMs), and therefore, cannot reflect the importance of self-evaluation compared to peer-evaluations. Second, it ignores the importance of anti-efficient frontier in the overall evaluation. The present study aims to incorporate the prospect theory into the double-frontier CEM to deal with these drawbacks while considering the preferences of DMs towards gains and losses. To address these drawbacks, this paper utilizes an aggregation method based on the prospect theory and consensus degree (APC) to reflect the subjective preferences of DMs. The second issue is also addressed by incorporating APC into the optimistic and pessimistic CEMs. Finally, the double-frontier CEM aggregated using APC (DAPC) is obtained by aggregating two viewpoints. As a real case study, DAPC is applied to evaluate the performance of 17 Iranian airlines based on three inputs and four outputs. The findings demonstrate that both viewpoints are influenced by DMs' preferences. The ranking results achieved for more than half of the airlines based on the two viewpoints are significantly different. The findings confirm that DAPC deals with these differences and leads to more comprehensive ranking results by considering both subjective viewpoints simultaneously. The results also show that to what extent DAPC efficiency for each airline is influenced by each viewpoint. In this regard, the efficiency of is most influenced by the optimistic point of view (80.92%), and on the other hand, the efficiency of is most influenced by the pessimistic viewpoint (73.45%). KIS is the most efficient airline, followed by PYA. On the other hand, IRA is the least efficient airline, followed by IRC.

Domain-specific valuation of university technologies using bibliometrics, Jonckheere–Terpstra tests, and data envelopment analysis

Although university technology licencing has been the subject of many studies, a major gap remains in the literature regarding ways to assess the economic value of university technologies. We propose an analytical framework for the domain-specific valuation of university technologies using bibliometrics, Jonckheere–Terpstra tests, and data envelopment analysis (DEA). First, 18 potential quantitative indicators of the economic value of university technologies are extracted from technology transaction, patent, and publication databases using bibliometrics. Second, given the heterogeneity across technology fields, significant indicators suited to a technology field of interest are identified using the Jonckheere–Terpstra tests. Third, a composite indicator is developed as a proxy for the economic value of university technologies using the DEA cross-efficiency method. Finally, the validity and utility of the analytical framework are examined using correlation analysis and the Jonckheere–Terpstra test. Accordingly, we explore the different implications of quantitative indicators in the valuation of university technologies across technology fields. A case study of the technologies registered in the Office of Technology Licensing at Stanford University confirms that the proposed analytical framework is valuable as a complementary tool for the valuation of university technologies.

New concepts for bootstrap-based cross-efficiency and relative weight analysis and an application to China's governance-finance-innovation-sustainability system

As for small (or medium-sized) data sets, there are limited number of samples. In such contexts, the cross-efficiency method can hardly be used for statistical tests. To overcome the difficulty, this study introduces a new method (bootstrap cross-efficiency). Our method contributes to the DEA literature, since it produces sufficient weight samples and can be used for genuine hypothesis tests. Meanwhile, this study makes another methodological contribution by proposing a new method of relative weight analysis. The new method provides us with insightful information on stage-based priority. Empirically, this study contributes to the sustainability analysis by providing an extended governance-finance-innovation-sustainability system and focuses on the analysis of Chinese provinces from 2009 to 2019. To the best of our knowledge, such work cannot be found in the existing studies. There are three main conclusions. First, China experienced considerable progress in overall efficiency measures during the examined periods. Such progress was mainly induced by government sector, R&D sector and industrial sector. Second, in terms of sector priority, R&D sector ranked first, which was followed by government sector and industrial sector. R&D sector and government sector accounted for about 64% of total relative weights. Financial sector played a minor role, but its importance grew over time. Finally, significant heterogeneity was confirmed in efficiency measures and coordination levels across groups and provinces.

Data envelopment analysis cross-efficiency method of non-homogeneous decision-making units

Faced with a large number of the efficiency evaluation problems with non-homogeneous decision-making units (DMUs) in reality, the existing efficiency evaluation methods are always unfair in terms of evaluation perspective and inputs/outputs allocation. Therefore, this paper adopts the concept of network data envelopment analysis (DEA) to define the inclusion relationship of production structure between non-homogeneous DMUs. Sequentially, the DEA cross-efficiency model and its corresponding cross-evaluation strategy are constructed by combining the self-evaluation perspective with peer-evaluation perspective, and then the efficiency of these DMUs can be evaluated in a more objective and reasonable way. Actually, the cross-evaluation perspective can fully reflect the effect of non-homogeneous structure on efficiency. In addition, the inclusion relationship is extended to a mixed relationship, and the application scope of the new cross-efficiency method is thus further expended. Finally, two examples are provided to illustrate the effectiveness of the new method.

A Novel Multiobjective Game IDEA Cross-Efficiency Method Based on Boolean Possibility Degree for Ranking Biomass Materials With Interval Data

The concept of processing biomass materials into charcoal briquettes is a viable solution for every developing nation’s energy crisis problem. However, the important properties of each biomass material must first be considered, in order to find suitable biomass materials for processing into charcoal briquettes. Sometimes these qualities are measured with imprecise values, making it exceedingly challenging to rank biomass materials’ decision-making units (DMUs). This problem is one of the interval data envelopment analysis (IDEA) ranking problems that make it difficult to calculate and rank all DMUs. In this paper, the concepts of the Game IDEA cross-efficiency method and Boolean possibility degree were utilized to solve the IDEA ranking problems. Unlike existing IDEA ranking models, a new multi-objective Game IDEA cross-efficiency (MO-G-IDEA-CE) method was used to obtain the Game interval cross-efficiency (GICE) scores of each DMU simultaneously. After that, the Boolean possibility degree was used to transform GICE scores into crisp values for ranking all DMUs. Three numerical examples including a simple numerical example, China’s primary schools and seven biomass materials problems are provided to demonstrate and validate the effectiveness of the proposed model. For the case study of seven biomass materials, after the Spearman correlation test, the correlation coefficients ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r_s</i> ) for the proposed method and Wang’s method and Wu <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al</i> .’s method are calculated as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r_s</i> = 1.000 and 0.964 respectively. In addition, it is worth noting that the proposed MO-G-IDEA-CE method has a very high correlation with the other ranking methods for all three numerical examples.

Selecting a green supplier utilizing the new fuzzy voting model and the fuzzy combinative distance-based assessment method

• In this paper, the selection of a Green Supplier is performed using a new hybrid Multi Attribute Decision Making-Data Envelopment Analysis method. • The fuzzy version of the Preferential Voting model is designed in this paper. • A new secondary goal model using the Combinative Distance-based Assessment method is proposed in the Cross Efficiency ranking method. • The proposed new method for Selecting a Green Supplier in an Automotive Group has been implemented. Significant increase in environmental concerns has led organizations to consider the necessary measures to apply green supply chain management to improve their environmental and economic performance. An important way to implement green supply chain management is to revise the methods of purchasing and selecting green suppliers. In this paper, a new fuzzy Data Envelopment Analysis (DEA) model for green supplier selection by collecting expert votes is presented. Then a way to improve the cross-efficiency method to achieve a complete ranking is suggested. In the improved method, a new secondary goal model based on the concepts of the Fuzzy COmbinative Distance-based ASsessment (CODAS) method will be presented. The proposed models were then used to select a green supplier in an automotive group. In the present case study, a complete ranking for green suppliers is obtained.

Application of Data Envelopment Analysis to Evaluate Investments in the Modernization of Collective Management Irrigation Systems in Valencia (Spain)

Climate change and increased competition for water resources are generating growing concern about how to improve water-use efficiency in agriculture. In turn, this has prompted substantial investments in the installation of water-saving technologies in irrigation systems. The first aim of this research is to use data envelopment analysis to quantify, in terms of gross water savings (GWS), the local-scale efficiency of the irrigation policies adopted in an area of Spain suffering from a structural water deficit. Second, the cross-efficiency method is used to produce a ranking of the irrigation organizations analysed, in order to identify patterns of water-use efficiency performance that can guide future lines of investment. The results reveal that water-use efficiency prior to modernization is a key determinant of the efficiency achieved in terms of GWS at local scale. However, the investments targeted at irrigation modernization often have objectives other than water savings. These and other aspects should be taken into account when allocating public funds to irrigation modernization.

Using cross efficiency method integrating regret theory and WASPAS to evaluate road safety performance of Chinese provinces

Currently, the road safety performance of a national- or province-level is absorbing much attention from practitioners and academics. A variety of models based on Data Envelopment Analysis (DEA) have been presented to appraise road safety performance in previous literature. However, the main weakness of these methods is that the decision-maker’s psychological behavior is neglected. Besides, Cross Efficiency Method (CEM) adopts the weighted average to aggregate the cross efficiencies which may lead to information loss. To address these limitations, a hybrid road safety evaluation model was constructed by integrating CEM, regret theory, and Weighted Aggregated Sum Product Assessment (WASPAS) to appraise the road safety performance of Chinese provinces. In the presented model, regret theory is employed to depict the psychological behavior of the decision-maker. Then entropy weight method is utilized to calculate the weight of self-evaluation and peer-evaluation. To reduce information loss, WASPAS is adopted to fuse the cross efficiencies and derive the ranking of decision-making units. Finally, the presented model is employed to assess the road safety efficiency in the province of mainland China. The results show that the mean of road safety efficiency score for the eastern, central, and western areas is gradually decreasing. Furthermore, the outcomes of a comparative analysis represent that the results obtained by the proposed model outperform the CEM and DEA road safety model.

A modified DEA cross efficiency method with negative data and its application in supplier selection

A modified DEA cross efficiency method with negative data and its application in supplier selection

An evaluation of cross-efficiency methods: With an application to warehouse performance

Cross-efficiency measurement is an extension of Data Envelopment Analysis that allows for tie-breaking ranking of the Decision Making Units (DMUs) using all the peer evaluations. In this article we examine the theory of cross-efficiency measurement by comparing a selection of methods popular in the literature. These methods are applied to performance measurement of European warehouses. We develop a cross-efficiency method based on a rank-order DEA model to accommodate the ordinal nature of some key variables characterizing warehouse performance. This is one of the first comparisons of methods on a real-life dataset and the first time that a model allowing for qualitative variables is included in such a comparison. Our results show that the choice of model matters, as one obtains statistically different rankings from each one of them. This holds in particular for the multiplicative and game-theoretic methods whose results diverge from the classic method. From a managerial perspective, focused on the applicability of the methods, we evaluate them through a multidimensional metric which considers their capability to rank DMUs, their ease of implementation, and their robustness to sensitivity analyses. We conclude that standard weight-restriction methods, as initiated by Sexton et al. [48], perform as well as recently introduced, more sophisticated alternatives.

Data envelopment analysis cross efficiency evaluation with reciprocal behaviors

Data envelopment analysis (DEA) has proven to be a powerful technique for performance evaluation since its inception. Since the traditional DEA approaches lack discrimination power among efficient decision-making units (DMUs), the cross efficiency method has been proposed for peer appraisal in the literature. However, the previous cross efficiency approaches imposed a single and identical evaluation strategy across all DMUs simultaneously. In addition, all the related studies have considered a static issue without the dynamic alternation of evaluation strategies. In this paper, the reciprocal behaviors among DMUs are considered to address the cross efficiency evaluation, and a novel threshold value is used to determine positive or negative reciprocal behaviors by comparing the peer-evaluated efficiency with the threshold value based efficiency. This study assumes that a DMU would show positive behavior and apply a benevolent strategy toward other DMUs that evaluate it friendly, while it also shows negative behavior and apply an aggressive strategy toward DMUs that evaluate it hostilely. Furthermore, a game-like iteration process is developed for each DMU to determine and further adjust its evaluation strategy toward other DMUs in the evaluation process. Afterward, we calculate the optimal ultimate cross efficiency score with reciprocal behaviors. Finally, the proposed approach is applied to both a numerical example and an empirical study of 31 Chinese manufacturing industries to demonstrate its usefulness and efficacy.

Efficiency evaluation in data envelopment analysis using strong defining hyperplanes

Cross-efficiency analysis in DEA generally uses a two-stage procedure: first, optimize a DMU’s individual efficiency score; next, push the efficiencies of all DMUs in a desired direction. In order to reduce subjective judgement in the second step, we provide a cross-efficiency method using only strong defining hyperplanes of the underlying technology. We develop a new DEA-based algorithm, and prove its finiteness and correctness. To reduce the computational burden, we show how one can combine the procedure with a known beneath-and-beyond procedure. Numerical investigations—comprising real-world data—demonstrate the superiority of the new method.

An Application of Data Envelopment Analysis and Machine Learning Approach to Risk Management

An integrated method comprising DEA and machine learning for risk management is proposed in this paper. Initially, in the process of risk assessment, the DEA cross-efficiency method is used to evaluate a set of risk factors obtained from the FMEA. This FMEA-DEA cross-efficiency method not only overcomes some drawbacks of FMEA, but also eliminates several limitations of DEA to offer a high discrimination capability of decision units. For risk treatment and monitoring processes, an ML mechanism is utilized to predict the degree of remaining risk depending on simulated data corresponding to the risk treatment scenario. Prediction using ML is more accurate since the predictive power of this model is better than that of DEA which potentially contains errors. The motivation for this study is that the combination of the DEA and ML approaches gives a flexible and realistic choice in risk management. Based on a case study of logistics business, the results ascertain that the short-term and urgent solutions in service cost and performance are necessary to sustainable logistics operations under the COVID-19 pandemic. The prediction findings show that the risk of skilled personnel is the next concern once the service cost and performance strategies have been prioritised. This approach allow decision-makers to assess the risk level for handling forthcoming events in unusual conditions. It also serves as a useful knowledge repository such that appropriate risk mitigation strategies can be planned and monitored. The outcome of our empirical evaluation indicates that the proposed approach contributes towards robustness in sustainable business operations.

Ranking of units by corrected cross-efficiency method using optimal weights in the smallest interval

An important method for ranking of decision making units (DMUs) in data envelopment analysis (DEA) is cross-efficiency method. This study proposes a secondary multi-objective model for calculating optimal weights with least dispersion. Firstly, these weights are placed in the smallest interval. Secondly, the cross-efficiency of each of the other units has the least deviation from the CCR efficiency of the same unit. Therefore, optimal weights are obtained which have the least dispersion. As result, the zero optimal weights which lead to the triviality of the relevant index, are avoided as far as possible. Hence, using the average cross-efficiency, the results of the ranking would be more reasonable. Using the proposed model for ranking of six nursing homes, the results show that this model is more accurate. Finally, in order to improve performance of the emergency department of a hospital, the proposed model is used to rank 11 defined scenarios.