Cross-efficiency Evaluation Research Articles

An Improved DEA Prospect Cross-Efficiency Evaluation Method and Its Application in Fund Performance Analysis

It is well known that a traditional data envelopment analysis (DEA) cross-efficiency evaluation model assumes that the decision-makers are completely rational, which causes the evaluation results to be inconsistent with the actual situation. To remedy this, in this paper, we propose an improved DEA prospect cross-efficiency evaluation method called EPCE model. The EPCE model captures the risk attitude of decision-makers and retains the decision information in the evaluation process. In particular, this new approach generates a more practical, realistic weighting scheme to measure the cross-efficiency and provides a reliable technique for ordering the decision-making units (DMUs) from the perspective of multi-criteria decision analysis. Finally, to demonstrate the validity and reliability of the proposed approach, we show an empirical analysis of mutual fund investment selection from Chinese fund market.

Regret-rejoice two-stage multiplicative DEA models-driven cross-efficiency evaluation with probabilistic linguistic information

As a powerful efficiency evaluation tool, cross-efficiency measurement in data envelopment analysis (DEA) has been proverbially concerned. However, most of existing studies on cross-efficiency fail to notice the internal processes of decision-making units (DMUs) and the psychological behaviors of decision makers (DMs) simultaneously. To overcome this limitation, this study investigates the rejoice-regret probabilistic linguistic multiplicative DEA cross-efficiency evaluation method for two-stage system. First, considering the increasingly complex decision-making environment, probabilistic linguistic term set is employed to express inputs and outputs information, and a probabilistic linguistic multiplicative DEA (PLMDEA) model is designed. Then, the regret theory is adopted to construct a regret-rejoice cross-efficiency PLMDEA (RC-PLMDEA) model, in which the regret attitude of DMs is captured. Subsequently, as the internal process of each DMU is remarked, a regret-rejoice cross-efficiency two-stage PLMDEA (RCTS-PLMDEA) model is established. In the end, we provide an empirical application of evaluating commercial banks for examining the effectiveness and applicability of the designed method, and sensitive analysis and comparative analysis are also offered to highlight the merits and robustness of the constructed method.

Cross-efficiency evaluation and improvement in two-stage network data envelopment analysis

Cross-efficiency evaluation and improvement in two-stage network data envelopment analysis

A Pre-Generation of Emergency Reference Plan Model of Public Health Emergencies with Case-Based Reasoning.

In the early 21st century, the coronavirus alone has ravaged the world three times. Public health emergencies have caused a tremendous negative impact on public health, daily life, and global economic development, for having the characteristics of complexity and great harm. To tackle these problems, a pre-generation of emergency reference plan model of public health emergencies is proposed to better deal with the outbreak and spread of public health events. The method is divided into three stages. First, the modified SEIR model is used to predict the attribute values of the target case. Then, the similar case sets are extracted and filtered by calculating the similarity through the cross-efficiency evaluation method with the parallel system. Finally, the multi-stage emergency effect evaluation model is conducted so that the emergency plan with the best response effect at this stage can be made for reference. We collected 25 typical events of COVID-19 that occurred in 11 cities in China as historical case bases and target cases, respectively. The result of the experiment verified the feasibility and effectiveness of the proposed method. This paper presents a new perspective on making a public health emergency plan, which could improve the decision-making accuracy and efficiency, maximize the emergency effect and save precious time for emergency response. This model can provide rapid decision supports for decision-making for public services such as government departments, centers for disease control, medical emergency centers and transport authorities, etc.

Regret-based cross efficiency evaluation method in a general two-stage DEA system

Cross efficiency (CE) evaluation in data envelopment analysis (DEA) has significant advantages in ranking decision making units (DMUs). A variety of CE evaluation methods with different secondary goals are proposed in traditional black-box DEA models. At present, some scholars have studied the CE evaluation approaches in two-stage DEA systems. However, these studies commonly think of decision makers (DMs) as perfectly rational and ignore the influence of DMs’ psychological factors on the evaluation results. To conquer these limitations, this study introduces regret theory to portray DMs’ psychological preferences and investigates two-stage CE evaluation models based on regret theory. We bring in the comprehensive perceived utility of DMUs by combining direct utility and indirect utility at first, and then develop the regret-based two-stage cross efficiency (RTCE) models in a centralized and a decentralized decision environments respectively. The efficiency of Chinese “double first-class” universities are evaluated to verify our models and a completely ranking of them can be obtained. Finally, a comparative analysis is conducted to illustrate the effectiveness of our proposed models.

Efficiency Evaluation of a Forestry Green Economy under a Multi-Dimensional Output Benefit in China—Based on Evidential Reasoning and the Cross Efficiency Model

The efficiency evaluation of forestry green economy development is related to the direction of forestry development and plays an important role in balancing the economic and environmental issues within that forestry development. The existing research faces three challenges: first, the output indicator is singular; second, the perspective of a self-assessment is extremely limited; and third, the multi perspective fusion method is not in line with the mechanism of the cross efficiency evaluation model. To address these challenges and the characteristics of forestry development output, we constructed multi-level output indicators from four aspects: ecology, economy, society, and sustainability and used evidence reasoning to combine the output indicators. Based on the perspective of a cross evaluation among peers, four different cross efficiency values are defined from the evaluation relationship between the different decision-making units to obtain economic–aggressive, social–neutral, ecological–benevolent, sustainable–neutral, and comprehensive–neutral cross efficiencies. According to the relationship between self- and cross evaluation, an order conditional entropy cross efficiency aggregation model has been proposed and used to analyze the development efficiency of the forestry green economy in 31 Chinese provinces in 2019. Considering the uneven distribution of the forestry resources in China, the development in the 31 provinces and cities is divided into four types by discussing the relationship between the output indicators and efficiency, while the reasons for the unbalanced development and the poor comprehensive development are discussed according to five cross efficiencies.

A hybrid performance evaluation approach for urban logistics using extended cross-efficiency with prospect theory and OWA operator

Urban logistics performance evaluation can provide reference for further improving its level. However, most performance evaluation for urban logistics premises that decision-makers (DMs) are completely rational, which may not conform to the actual situation. Therefore, this article aims to consider the DMs’ psychological factors in the performance evaluation of urban logistics. Specifically, the cross-efficiency evaluation (CEE) method with the DMs’ psychological factors is used to measure the urban logistics efficiency in the central area of Yangtze River Delta (YRD) urban agglomeration in China in 2019. The main contributions in this article are to propose a hybrid CEE method with prospect theory and ordered weighted average (OWA) operator for urban logistics industry and to expand the evaluation perspectives of urban logistics performance. The main conclusions are obtained: (1) The DMs’ optimism level can indeed affect the efficiency value and ranking of urban logistics. (2) The aggregation based on the OWA operator is fair and reasonable because it can make all self-evaluation efficiencies play the same role. (3) To make the efficiencies and rankings of urban logistics in the central area of the YRD have credibility and discrimination, the DMs’ optimism level range is best between 0.8 and 0.8177.

Peer evaluation through cross-efficiency based on reference sets

Cross-efficiency evaluates the performance of decision making units (DMUs) from the perspective of all of the others, through their individual Data Envelopment Analysis (DEA) weights. The main weakness with this methodology lies on the existence of alternate optima for the weights, which may lead to different results depending on the choice that is made. In fact, this issue is typically addressed by implementing an alternative secondary goal for the selection of weights among those optimal solutions. The present paper proposes a different approach, which puts the focus on reducing the sensitivity of the results to the choice of weights rather than on establishing a criterion to make such choice. Thus, we seek evaluations more robust against the specification of weights. It is an approach based on the structure of the DEA efficient frontier instead of on the solutions of a given DEA model. Specifically, the cross-efficiencies are defined as the classical efficiency ratios, but using weights associated with all of the maximal efficient faces (MEFs) that form the DEA strong efficient frontier of the production possibility set (PPS). This provides a peer evaluation of DMUs as well, but from the perspective of different reference sets, namely those consisting of the DMUs that span the corresponding MEFs. It is clearly a major change in the standard approach of the cross-efficiency, which selects weights by reference sets instead of by DMUs individually. As a consequence, the cross-efficiency evaluation based on reference sets has proven to be less sensitive to alternative optimal weights, because they have more support from the DMUs. In addition, it ensures non-zero weights in the calculation of cross-efficiencies, which means that no variable is ignored in the evaluations.

A regret cross-efficiency ranking method considering consensus consistency

Data envelopment analysis (DEA) is a powerful nonparametric approach for assessing the performance of decision making units (DMUs). Traditional DEA models usually utilize a self-evaluation mode to evaluate DMUs, which have the following shortcomings such as efficiency overestimation and incomplete ranking. As the extension of traditional DEA, cross-efficiency (CE) evaluation remedies these limitations. It connects self-evaluation with peer-evaluation to appraise DMUs and rank them. However, most existing studies on CE evaluation utilize the arithmetic average method to aggregate self-evaluation efficiency and peer-evaluation efficiency, while ignoring the significance of self-efficiency and the irrational psychology of decision-makers (DMs). Observed by the aforementioned phenomena, this paper employs regret theory to portray the regret aversion behavior of DMs and further proposes a novel regret cross-efficiency aggregation (RCEA) method. Considering aggressive and benevolent cross-efficiency models, we apply the RCEA method to calculate the regret-based aggressive cross-efficiency and the regret-based benevolent cross-efficiency, and introduce a parameter reflecting the psychological preference of DMs to aggregate them. To attain consensus between DMUs’ expectations for efficiency and the ultimate integration results, we design a regret cross-efficiency adjustment algorithm. This algorithm provides a more acceptable evaluation result and derives a full ranking for all DMUs. Finally, the validity and feasibility of the proposed model are illustrated by evaluating the efficiency of scientific research activities in 13 universities in China.

Network data envelopment analysis with two-level maximin strategy

Network data envelopment analysis (NDEA), one of the most important branches of recent DEA developments, has been developed for examining the decision making units (DMUs) of a system with complex and internal component divisions. In this study we apply a maximin strategy to network DEA at two levels. At the individual DMU level, we evaluate the system’s performance by maximizing the minimum of the divisions efficiencies, which is based on the weak-link approach. At the all DMUs level, we evaluate the system’s performance by maximizing the minimum of the DMUs’ efficiencies, which is based on the maximin ratio efficiency model. With such two-level maximin strategy, we propose the two-level maximin NDEA model to evaluate efficiencies of all divisions as well as all DMUs at the same time. The model will provide unique and unbiased efficiency scores for all divisions in a system and improve incomparable efficiency scores and weak discrimination power of traditional DEA models. In addition, we discuss the cross efficiency evaluation based on the two-level maximin NDEA model. The proposed models are applied to the efficiency evaluation of supply chains for illustrations.

Uncertain Data Envelopment Analysis for Cross Efficiency Evaluation with Imprecise Data

Self evaluation and peer evaluation in data envelopment analysis (DEA) are effective means to comprehensively reflect the efficiencies of decision-making units (DMUs). However, when some of the inputs and outputs of DMUs cannot be accurately observed, the traditional evaluation methods will lose their applicability. This paper attempts to treat the imprecise inputs and outputs as uncertain variables based on uncertainty theory and hence to propose a new uncertain DEA model for cross-efficiency evaluation via the evaluation of both self efficiency and peer efficiency. Moreover, the equivalent form and the proof of the new model are also presented for accurate calculation. Finally, a numerical example is given to illustrate the evaluation results.

A neutral cross-efficiency measurement for general parallel production system

There are some problems in the efficiency evaluation for parallel systems. From the applicability of existing models, the parallel models based on self-evaluation may produce the low distinguishing power and unreasonable input–output weights. From the accuracy of efficiency, the weights of partial production-units may be assigned zero values, and thereby the fail of the production-units will lead to the incomprehensibility of system efficiency. The neutral cross-efficiency model maximizes the evaluated decision-making unit (DMU) and simultaneously makes each output of the DMU being as efficient as possible, which effectively avoids the difficulty in choosing between aggressive and benevolent models, and reduces the number of zero output weights. Based on this, this paper proposes the neutral cross-efficiency evaluation method fo r general parallel systems. First, the self-evaluation models for parallel system and its production-units are developed, and the model can enable each production-unit to participate in the evaluation effectively. Then, the neutral cross-efficiency model is proposed to overcome the defects of self-evaluation model. Particularly, the proposed model is also suitable to special general parallel systems with shared resources. More importantly, the proposed models assign different input–output weights for the production-units to avoid the production-units being forced to run under identical production mechanism. Finally, two real-world examples prove the availability and effectiveness of the proposed method.

Efficiency evaluation with regret-rejoice cross-efficiency DEA models under the distributed linguistic environment

Data envelopment analysis (DEA) is an effective mathematical method for evaluating the efficiencies of decision-making units (DMUs). However, in the process of cross-efficiency evaluation, DEA models commonly neglect the regret aversion psychological characteristics of decision makers (DMs). Therefore, this paper focuses on the construction of regret-rejoice cross-efficiency linguistic distribution DEA (RCE-LDDEA) method with regret theory, in which the input and output data by means of linguistic distributions and the regret aversion psychological characteristics of DMs are considered. First, a linguistic distribution DEA model is proposed to derive the self-evaluation efficiencies of DMUs with linguistic distribution evaluation information. Then, based on regret theory, a regret-rejoice cross-efficiency evaluation (RCEE) model is developed to evaluate the cross-efficiencies of DMUs. Subsequently, based on the regret-rejoice super-efficiency evaluation (RSEE) model, a RCE-LDDEA method is designed to generate the complete ranking of DMUs. Finally, an example for evaluating performance of 10 public hospitals in China is provided to illustrate the implementation of the proposed RCE-LDDEA method. The stability and advantages of the proposed RCE-LDDEA method is performed by sensitivity analysis and comparative analysis.

Individual rationality and overall fairness in fixed cost allocation: An approach under DEA cross-efficiency evaluation mechanism

This paper develops a new fixed cost allocation (FCA) approach that considers individual rationality and fairness using the data envelopment analysis (DEA) cross-efficiency evaluation. We propose two FCA principles from individual rationality: a novel self-lowest principle and the efficient after FCA principle. Under the precondition that the individual rationality principles are satisfied, we suggest determining the final FCA result based on two overall fairness principles: the lower bound principle and the cross-efficiency Pareto-optimality principle. A multi-objective FCA model is built following these principles. An algorithm and some rules are used to solve the multi-objective model and obtain the final cross-efficiency evaluation and FCA result. Our study contributes by explicitly showing the design of individual rationality and overall fairness in FCA using the DEA cross-efficiency evaluation mechanism. Finally, we compare the suggested approach with some previous ones using a numerical example and illustrate its usefulness through a truck fleet case study.

Hybrid game cross efficiency evaluation models based on interval data: A case of forest carbon sequestration

Cross-efficiency evaluation is an effective method for the ranking of decision-making units (DMUs) in data envelopment analysis, which is the performed method for peer-evaluation and self-evaluation. In most cross-efficiency evaluation methods, the peer evaluation result is completely constrained by the evaluator's optimal self-evaluation weights. DMUs are connected by a competitive relationship; therefore, they can be regarded as players in the game and the cross efficiency value can be regarded as payment because of this competition. DMUs need to consider the impact of their own weights on other DMUs to identify a set of weights for evaluating themselves. Based on the idea of non-cooperative games in the cross evaluation of DMUs, this paper considers the interval cross game efficiency of DMUs with the interval data. The interval data theory is combined, the best production state and the worst production state are taken as reference states, and four evaluation strategy models are proposed according to the opposition and coordination relationship. Then, the bijective and injective interval game cross models, as well as the algorithm corresponding to the four evaluation strategies are constructed. Moreover, the result of the self-evaluation is used as the initial parameter to prove the existence of the solution and the convergence of the algorithm. Based on the priority relationship of the evaluation results under different strategies, the interval entropy method is used to aggregate the results and obtain the final cross efficiency of the interval game. Furthermore, both the applicability and superiority of this model are exemplified by an example. Finally, based on the method of this paper, the efficiency of forest carbon sequestration in China are studied, seven natural regions in China are ranked by forest carbon sequestration efficiency values reasonably, and the current regions development of forest carbon sequestration in China are evaluated.

Weight profiles in cross-efficiency evaluation based on hypervolume maximization

In this paper, we propose and discuss a new model in order to obtain the weight profiles to be used in the calculation of cross-efficiency scores in Data Envelopment Analysis (DEA). In the standard DEA literature, total flexibility in the selection of weights has been strongly criticized due to the fact that some inputs and/or outputs may have no contribution (zero weights) to the efficiency scores. Although cross evaluation somewhat mitigates the effect of these unrealistic weighting schemes on the amalgamation of weights that standard DEA models produce, we propose a method that ensures strictly positive and balanced weights to be used in cross-efficiency evaluation. In particular, we propose an optimization model based on hypervolume maximization as a method for selecting a suitable weight profile for each evaluated unit to be used in cross-efficiency. The model is solved through Second-Order Cone Programming (SOCP). As a result, the solution obtained is unique and the Production Possibility Set (PPS) is not modified. Another advantage of the proposed method, among others, is that it does not need subjective expert opinions or full-dimension efficient facets of the polyhedral PPS, but if available, it can be easily incorporated into the model. The approach introduced is illustrated through a numerical example. We also present some theoretical results.

An extended cross-efficiency evaluation method based on information entropy with an application to the urban logistics industry

PurposeGreen economy and economic development with high quality have set higher requirements for the development of the urban logistics industry. It can grasp the recent development level of the urban logistics industry by measuring its environmental efficiency to guide its future development direction. The purpose of this study is to improve the environmental efficiency and development level of the urban logistics industry by using a reasonable evaluation method.Design/methodology/approachThis paper uses information entropy to directly aggregate index weights from different models to acquire comprehensive index weights (CIWs) for calculating peer-evaluation efficiency. Then, we weight self and peer-efficiencies to obtain final efficiency. The environmental efficiencies of the urban logistics industry in Anhui Province in 2019 are obtained according to the above method.FindingsSeveral findings are summarized below. The logistics industry in Anhui is in urgent need of improving environmental efficiency. The environmental efficiency of the logistics industry in North Anhui is the highest one, showing that the logistics industry in North Anhui has achieved a relative balance between economic development and environmental protection. Their final cross-efficiency values based on the CIWs are smaller than those based on the comprehensive efficiency. And the environmental efficiency of almost all urban logistics industries is lower than its economic efficiency. The findings show that the proposed method is feasible and more reasonable. More economic implications and suggestions are proposed.Originality/valueThis paper proposes an extended cross-efficiency evaluation method based on information entropy to measure the environmental efficiency of the urban logistics industry, effectively avoiding the overestimation of efficiency results.

Cross-Efficiency Evaluation and Decomposition with Directional Distance Function in Parallel Two-Stage Systems: An Application to Mutual Funds

Cross-Efficiency Evaluation and Decomposition with Directional Distance Function in Parallel Two-Stage Systems: An Application to Mutual Funds

Applying cross-efficiency evaluation methods for multi-objective emergency relief supply chain network model

Applying cross-efficiency evaluation methods for multi-objective emergency relief supply chain network model

Environmental efficiency of Xiangjiang River in China: a data envelopment analysis cross-efficiency approach

PurposeEnvironmental performance becomes a key issue for the sustainable development. Recently, incremental information technology is adopted to collect environmental data and improve environmental performance. Previous environmental efficiency measures mainly focus on individual decision-making units (DMUs). Benefited from the information technology, this paper develops a new environmental efficiency measure to explore the implicit alliances among DMUs and applies it to Xiangjiang River.Design/methodology/approachThis study formulates a new data envelopment analysis (DEA) environmental cross-efficiency measure that considers DMUs' alliances. Each DMUs' alliance is formulated by the DMUs who are supervised by the same manager. In cross-efficiency evaluation context, this paper adopts DMUs' alliances rather than individual DMUs to derive the environmental cross-efficiency measure considering undesirable outputs. Furthermore, the Tobit regression is conducted to analyze the influence of exogenous factors about the environmental cross-efficiency.FindingsThe findings show that (1) Chenzhou performs the best while Xiangtan performed the worst along Xiangjiang River. (2) The environmental efficiency of cities in Xiangjiang River is generally low. Increasing public budgetary expenditure can improve environmental efficiency of cities. (3) The larger the alliance size, the higher environmental efficiency. (4) The income level is negatively correlated with environmental efficiency, indicating that the economy is at the expense of the environment in Xiangjiang River.Originality/valueThis paper contributes to developing a new environmental DEA cross-efficiency measure considering DMUs' alliance, and combining DEA cross-efficiency and Tobit regression in environmental performance measurement of Xiangjiang River. This paper examines the exogenous factors that have influences on environmental efficiency of Xiangjiang River and derive policy implications to improve the sustainable operation.