Cross-efficiency Evaluation Research Articles

Regret cross-efficiency evaluation using attitudinal entropy approach

Data envelopment analysis (DEA) is a popular nonparametric tool for measuring the performance of decision making unit (DMU). Cross-efficiency evaluation is an efficient means to rank DMUs, which compensates for efficiency overestimation and incomplete ranking of conventional DEA models. With respect to incomplete rational cross-efficiency evaluation, the common methods construct models with two extreme efficiencies as reference, such as efficiency values of the aggressive and benevolent models. In addition, they only explore the irrational preferences of decision maker (DM) at a certain stage in the evaluation process. They fail to investigate the cross-efficiency evaluation synthetically under incomplete rationality and characterize the complexity of the individuals’ decision making. To fill this gap, a new method must be proposed. This paper proposes a new cross-efficiency termed regret cross-efficiency model using attitudinal entropy approach (RACE), which constructs a secondary goal model from a comprehensive perspective under the framework of regret theory, and introduces attitudinal entropy to aggregate the cross-efficiencies. Besides, this paper presents some empirical examples to illustrate the validity and robustness of the RACE method.

Cross-Efficiency Evaluation Method with Performance Level as a Management Objective in Consideration of Bounded Rationality

According to management by objectives (MBO) theory, the significance of management objectives must be considered as a reference point in a performance evaluation. Cross efficiency evaluation has always been considered to be one of the important performance evaluation methods. However, few studies to date have considered the impact of management objectives on cross efficiency. According to prospect theory, the choice of reference point will cause irrational psychology in decision makers. A management objective is a natural reference point, which will cause a ‘gain and loss’ psychology in enterprises and may create irrational psychology. Performance level is an important index by which to evaluate resource allocation, which in turn can be regarded as an important enterprise management objective. This paper proposes a cross efficiency evaluation method based on performance level. Cross efficiency evaluation models are constructed, based on the irrational psychology that occurs under organization objectives, personal objectives and composite objectives. This method not only considers the bounded rational behavior of enterprises, but is also more flexible. A numerical example is given to illustrate the application of the bounded rational cross efficiency evaluation method in data envelopment analysis (DEA) ranking.

A Southeast Asia National Aviation Company benchmarking by regret theory-based data envelopment analysis model

National airlines play a pivotal role in fostering economic growth, facilitating trade, and promoting tourism. With Asia's aviation economic expansion and diverse cultural landscapes, the aviation industry has a role in linking nations, facilitating cultural exchange, and enhancing cross-border cooperation. In the aftermath of the global COVID-19 pandemic, the aviation industry in Asia has faced unprecedented challenges. This study aims to provide an overview of the performance of nine national airlines in the Asian aviation market, using cross-efficiency evaluation combined with the Regret theory based on the DEA model. Traditional DEA models often utilize a self-evaluation mode to evaluate DMUs, resulting in drawbacks such as overestimating efficiency and incomplete ranking. Cross-efficiency evaluation has addressed these limitations. However, cross-efficiency evaluation overlooks the significance of the irrational psychology of decision-makers (DMs). Hence, this study utilizes the Regret theory to depict the regret aversion behavior of DMs. The integration of emotional factors in assessing operational performance offers a holistic view of airlines' challenges and opportunities after the COVID-19 pandemic, ultimately facilitating informed decision-making and strategic planning for the industry's revival.

A compromise programming approach for cross efficiency measurement in basic two-stage network system

Data envelopment analysis (DEA) is a technique that allows each decision-making unit (DMU) to calculate efficiency using the most favorable weights for inputs and outputs. The resulting efficiency scores are incomparable and difficult to discriminate. Cross-efficiency is a concept for solving the problem of incomparability among the efficiencies of a set of DMUs that are calculated from different weights and is helpful for ranking. In basic DEA, several cross-efficiency evaluation methods with various secondary purposes have been presented, however, the internal mechanism of the DMUs in cross-efficiency evaluation is often neglected. In this study, we use the composition approach for a basic two-stage structure, so that the efficiencies of the divisions are estimated first, and then the overall efficiency of the system is obtained. To solve the linear bi-objective model in the combination approach, we consider a compromise programming problem to find the solution that is as close as possible to the ideal point. Finally, a secondary objective model is proposed to select a weight among the optimal weights of the compromise model, which also guarantees the efficiency of the optimal weight for the bi-objective problem. We use the optimal solution obtained from this model to evaluate cross-efficiency and rank DMUs for a series two-stage system. The proposed approach enables us to rank the DMUs by assessing the performance of each DMU and each of its separate divisions. The validity of the suggested network cross-efficiency evaluation is demonstrated by a numerical example from the literature.

Relative uniqueness or uniqueness? A new cross-efficiency evaluation approach with weight priority strategy

Due to a large number of studies on cross-evaluation strategies, the theoretical problem of DEA cross-efficiency approach has been transformed from the non-uniqueness of the optimal solution to the relative uniqueness, because the existing cross-evaluation strategies can only reduce the possibility of non-unique solutions, but cannot prove the existence of a unique optimal solution. This paper illustrates the relative uniqueness of optimal solution of the cross-efficiency approach with traditional cross-evaluation strategies, and the graphic method and theoretical analysis are used to explain the reasons of relative uniqueness. Based on the data characteristic of inputs and outputs, the weight priority rule is made for constructing the new cross-evaluation strategy, and its optimal solution is proved to be unique. In addition, the weight priority strategy can also be introduced into traditional strategies as a supplementary strategy, and then the unique optimal solution can be obtained on the premise of preserving the characteristics of traditional strategies. In general, this paper solves the non-uniqueness and relative uniqueness problem of optimal solution in the DEA cross-efficiency approach, and then the reliability and robustness of the approach are thus improved.

An optimisation model for sustainable multi-commodity transportation planning

This paper aims to establish a supply chain model that significantly reduces economic and environmental costs. It comprises all activities related to procurement, production, and distribution planning. The proposed multi-objective multi-commodity optimisation model deals with the four conflicting objectives of reducing costs and emissions and choosing top-priority suppliers and the most efficient vehicles. We apply an integrated AHP (analytic hierarchy process) and TOPSIS (technique for order preference by similarity to an ideal solution) technique to determine the weights of suppliers, depending on three indices of criteria, alternatives, and raw material. This paper proposes a cross-efficiency evaluation method using data envelopment analysis (DEA) to ensure that the cross-evaluation of different types of vehicles for evaluating peers is as consistent as possible. The mutually contradictory objectives give rise to several Pareto-optimal solutions. The optimal compromise solutions are found using a lexicographic goal programming technique. We present a real-world case to demonstrate the effectiveness of the proposed methodology, followed by numerical comparisons and additional insights.

Cross-efficiency aggregation based on interval conditional entropy: An application to forest carbon sink efficiency

Cross-efficiency evaluation is an extension of data envelopment analysis (DEA), which can effectively distinguish between decision-making units (DMUs) through self- and peer-evaluation. The cross-efficiency of each DMU in a set of DMUs is measured in terms of intervals when the input–output data are represented by the number of intervals. Based on the interval cross-efficiency matrix, the interval entropy is defined in terms of the likelihood. Then, considering the influence of peer evaluation, the interval conditional cross-efficiency entropy is proposed and an aggregation model of the interval conditional cross-efficiency entropy is presented to create a ranking index for DMUs. Finally, a simple example is provided to illustrate the effectiveness of the proposed method, which is applied to the evaluation of forest carbon sink efficiency in China. The results indicate that the final cross-efficiencies of all 30 provinces range from 0 to 0.6. Among these provinces, those with a relatively high efficiency include Guangdong, Guizhou, Hainan, Shandong, and Qinghai.

Stock assessment using Cumulative Prospect Theory in DEA cross-efficiency model

Market volatility is becoming increasingly common as numerous factors are implemented in the financial system. As a result, portfolio managers and individual investors require reliable methods to assess stock performance. This study examines stock assessments using cross-efficiency evaluations in cases where negative data is present. An alternative approach to achieve this goal is to use an RDM DDF-based cross-efficiency model which oversees the negative data. We expand the RDM-based cross-efficiency analysis, which uses row and column average values to select portfolios and identify different groups for stock management. To explore the psychological factors that influence the choices made by stock market investors, we incorporate the cumulative prospect theory value for each stock as an output and the variance as an input to evaluate the overall efficiency of the assets. For the empirical analysis, our study focuses on a sample of 30 stocks listed on the Nifty-50 on India's National Stock Exchange. The results of our empirical study verify that the proposed method can serve as an effective tool for stock selection. This demonstrates how the chosen portfolio gives companies a more diversified and well-balanced approach for selecting stocks, thus improving logical decision-making.

Science and technology resource allocation evaluation of research institutions considering the risk preference of decision makers

With the increasing emphasis on research institutions in China, there is a growing imperative to evaluate the efficacy of resource allocation in science and technology (S&T) investments. However, limited research has been conducted on the efficacy of resource allocation in research institutions while considering decision makers’ risk preference behavior. In order to address this issue, the present study employs a prospective cross-efficiency evaluation model that incorporates decision makers’ risk preferences. This model is utilized to assess the efficiency of S&T resource allocation in research institutions across 13 industries in China. After conducting empirical analysis, it has been observed that decision makers’ risk preferences significantly influence the efficiency outcomes of S&T resource allocation in research institutions. Finally, this study proposes appropriate measures and recommendations for S&T resource allocation in research institutions.

The cross-efficiency evaluation model with judgmental information: Cooperative game and optimal coordination perspective

In the actual efficiency evaluation process, it frequently occurs that the quantitative input and output data of each decision-making unit is difficult to obtain due to the limitation in data measurement and the absence of prior information. Instead, the form of judgment information can be selected to express the input–output state of the evaluated decision-making units compared with the reference level. Traditional cross-efficiency evaluation methods do not involve this case and cannot be well used in this situation. Based on the above problems, a multiplicative cross-efficiency evaluation model with judgmental information is constructed, and the optimal adjustment model is provided by introducing deviation variables to deal with the inconsistent issue of data features. In addition, for the case of multiple optimal solutions, the maximizing and minimizing secondary objective models of the multiplicative cross-efficiency are established respectively to reasonably identify the corresponding optimal weights. Simultaneously, in order to effectively depict the interaction between decision-making units, the characteristic functions of JM-cross efficiency cooperative game and the multiplicative Shapley value are established based on benevolent and aggressive cross-efficiency matrices. Moreover, in order to avoid the extreme ranking results that are oriented by high impact decision-making units, a series of optimization coordination models are developed, and an optimal efficiency ranking vector generation method with strong applicability and decision flexibility is proposed. The optimal efficiency ranking vector not only creates a precise match with the given Shapley index of the multiplicative cross-efficiency game, but also bounds between the minimum and the maximum average efficiency. Finally, the validity and rationality of the discussed models are illustrated by a concrete example.

Cross-efficiency Evaluation under Non-Decreasing Returns to Scale and Weight Restrictions

Cross-efficiency Evaluation under Non-Decreasing Returns to Scale and Weight Restrictions

DEA cross-efficiency models with prospect theory and distance entropy: An empirical study on high-tech industries

Cross-efficiency evaluation with the data envelopment analysis (DEA) model is an effective way to assess performance and provide a complete ranking of decision-making units. However, it is generally assumed that decision makers are perfectly rational in the cross-efficiency model, which fails to consider the subjective preferences of decision-makers. Moreover, the arithmetic average method is usually adopted to aggregate efficiency scores in traditional cross-efficiency methods, which underestimates the importance of self-evaluation. To address these issues, we extend cross-efficiency with the DEA model by incorporating prospect theory and the distance entropy function. First, we calculate the prospect values of decision-making units to describe the non-rational subjective preferences under the risk of decision-makers. Second, based on prospect cross-efficiency, a new distance entropy function is developed to aggregate the ultimate prospect cross-efficiency values. More specifically, some traditional cross-efficiency evaluation models can be considered special cases of prospect cross-efficiency models with appropriate adjustments to the parameters. Finally, an empirical example is used to evaluate the prospect cross-efficiency results with the high-tech industries of 29 provinces in China to illustrate the applicability and effectiveness of the proposed model in ranking observations.

Directional distance based cross-efficiency evaluation and decomposition for parallel two-stage systems: An application to equity funds

As an effective approach in ranking decision making units (DMUs), cross-efficiency evaluation is only extended to two basic network systems: series and parallel, which is not applicable to the common complex network system in reality. By using the directional distance function (DDF), this paper extends the cross-efficiency evaluation to a complex system called the parallel two-stage system, which consists of several independent parallel processes and each of them is a sub-system with a general two-stage series structure. The proposed method is able to decompose the cross-efficiency measure of the system into the weighted average of those of processes, stages and overall stages, respectively, and as a result, successfully achieves the layer-by-layer decomposition of cross-efficiency measures under complex nested networks. An empirical study on 40 open-ended equity funds in China from 2018 to 2020 verifies that the newly proposed method not only has a stronger performance discrimination power than self-evaluation, but also can identify the relationships among efficiencies of the system, processes and stages, and meanwhile it can reflect the effects of processes and stages on the system. More importantly, our method has a better practical value for actual fund investment selection.

Cross-efficiency evaluation method for non-homogeneous parallel network systems with imprecise data

Cross-efficiency evaluation method for non-homogeneous parallel network systems with imprecise data

A new cross-efficiency meta-frontier analysis method with good ability to identify technology gaps

Cross-efficiency evaluation and meta-frontier analysis (MFA) have been widely used to measure performance in many areas. However, cross-efficiency MFA (CMFA) has rarely been studied due to its potential violation of the basic MFA property, that is, the efficiency relative to the group frontier is not less than that relative to the meta-frontier. In this paper, we deduce the conditions under which the cross-efficiency score generated by the current CMFA method relative to the group frontier is smaller than that relative to the meta-frontier, and the conditions under which the current CMFA method is unable to identify the technical gaps between the group frontiers and the meta-frontier. To guarantee the basic property and identify technical gaps, we introduce a new CMFA method, where the efficiencies relative to the group frontiers are first cross-evaluated by the traditional cross-evaluation approach and then those relative to the meta-frontier are cross-evaluated by using modified data envelopment analysis models. Compared with the existing CMFA method, our approach has the following advantages: it can successfully ensure that the cross-efficiencies and cross-efficiency scores relative to the group frontiers are not less than those relative to the meta-frontier; it has a good identification of technology gaps and provides more detailed information about the inefficiency; all the mathematical programming models involved in our CMFA method are feasible. Theoretical analyses and numerical examples support the practicality and superiority of our method.

Fuzzy cross-efficiency evaluation based on prospect theory and regret theory

Cross-efficiency in data envelopment analysis is widely used in production as an evaluation method that includes input and output indicators and allows for self-evaluation and mutual evaluation of decision making units (DMUs). However, as the application scenarios continue to expand, the traditional methods gradually fail to meet the needs. Many researchers have proposed improved methods and made great progress in weight determination, but the existing studies still have shortcomings in considering the psychological behavior of decision makers (DMs) and there is still relatively little research on cross-efficiency in fuzzy environments. In this paper, we proposed a method to apply CRITIC to determine weights and introduce both prospect theory and regret theory into the evaluation method of cross-efficiency to obtain the prospect cross-efficiency matrix and regret cross-efficiency matrix respectively, and then applied the Pythagorean hesitant fuzzy operator to aggregate them to achieve the ranking of DMUs through the fraction function. This largely takes into account the subjective preference and regret avoidance psychology of DMs. The applicability of this paper’s method is also verified through an example of shopping for a new energy vehicle. Finally, the effectiveness of this paper’s method is verified by comparing three traditional methods with this paper’s method, which provides an effective method for considering risk preferences in the decision-making process.

Global correlation coordination model for ranking decision-making units based on cross-efficiency game

DEA cross-efficiency evaluation method can rank decision making units (DMUs) more reasonably than the classical DEA model, but the existing cross-efficiency evaluation methods still have many deficiencies. The most evident drawback is that the potential multiple solutions of the optimal weights lead to the non-uniqueness of the cross-efficiency value. Moreover, the traditional cross-efficiency ranking methods neglect the interaction between DMUs. It is a common scenario that the decision-making unit will incline to give high evaluation scores to those in same coalition, and relatively low evaluation scores to those with different coalitions on the contrary in the process of cross-efficiency evaluation. Aiming at solving the above problems, this study proposes a cross-efficiency game model considering correlation coordination degree among DMUs. The generalized Shapley value of cross-efficiency game is defined, and its desirable properties are proved in detail. Finally, a global correlation coordination (GCC) model is developed for ranking decision-making units comprehensively. The comparative example and practical application on R&D efficiency evaluation are provided to illustrate the rationality and feasibility of the GCC model.

Cross-Efficiency Evaluation Framework for Assessing the Sustainability of Agriculture Farms with Biogas Plants: Mathematical Modeling and Solution Approach

Cross-Efficiency Evaluation Framework for Assessing the Sustainability of Agriculture Farms with Biogas Plants: Mathematical Modeling and Solution Approach

A dynamic network data envelopment analysis cross-efficiency evaluation on the benefits of bus transit services in 33 Chinese cities

ABSTRACT Our objective in this paper is to evaluate the benefits of bus transit. To obtain the more accurate and highly discrimination results, this study establishes an evaluation indicator system from a stakeholder perspective and proposes a novel combined method consisting of dynamic network data envelopment analysis, cross-efficiency evaluation, and Shannon entropy aggregation method. An empirical study of bus transit systems in 33 key Chinese cities from 2016 to 2019 is provided. The results show that the benefit of bus transit in most key cities was ineffective. In contrast to production efficiency, focusing on improving service effectiveness is more conducive to improving the benefits of bus transit. Small cities have higher benefits than large cities. Meanwhile, the benefits of bus transit vary geographically. This evaluation outcome provides a more appropriate basis for decision-making related to the benefits of public transit services, as well as for operational and management studies.

On a Choquet Integral DEA Cross-Efficiency Evaluation Method Involving the Satisfaction of Decision-Making Units and Weight Balance of Indicators

The secondary goal approach is an effective way to address the problem of the non-uniqueness of the optimal weights The secondary goal approach is an effective way to address the problem of the non-uniqueness of the optimal weights for decision-making units (DMUs) in the cross-efficiency evaluation process of data envelopment analysis (DEA). However, on the one hand, existing secondary-goal models seldom consider the willingness of DMUs to accept and be satisfied with the cross-efficiency evaluation results of DEA. On the other hand, the problem of zero weights and excessive differences of indicators has not been given enough attention. Furthermore, the traditional DEA approach ignores interactions between indicators. To overcome these problems, in the context of considering the interaction of input (or output) indicators, this study introduces the idea of the minimum dissimilarity of weights and constructs an improved method for evaluating the cross-efficiency of the secondary goal based on the DMUs’ satisfaction. In this method, the 2-additive Choquet integral is used as a more feasible attempt to reflect the pairwise interaction between input (or output) indicators to improve the differentiation of DEA evaluation results. Additionally, the satisfaction targets of DMUs are adjusted according to the three ethical principles of fairness (fraternity), utilitarianism and equity in social choice theory to obtain a choice of optimal weights that is consistent with the values of individual DMUs. This paper validates the performance of the improved DEA method through comparative analysis of arithmetic cases. Then the method is applied to the study of the input–output efficiency assessment of the water–energy–food nexus in China.