Cross-efficiency Evaluation Method Research Articles

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.

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.

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 method for non-homogeneous parallel network systems with imprecise data

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

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.

Evaluating efficiency of railway transportation based on cross‐efficiency evaluation method and relative entropy evaluation method in China

AbstractRailway transportation system is one of the most important components of the integrated transportation system. A functional and efficient railway transportation system can be conducive to sustainable development of society and economy, thus highlighting the importance of studies on railway transportation efficiency. Therefore, this research proposes the cross‐efficiency evaluation method based on the relative entropy evaluation method (CERE) to evaluate railway transportation efficiency in China. Firstly, the research constructs an evaluation indicators system for railway transportation efficiency from the perspective of input‐output. Secondly, the paper obtains cross‐efficiency matrix by using the cross‐efficiency evaluation method (CE). Then, the study takes the obtained the cross‐efficiency matrix as the decision matrix of multiple criteria decision‐making (MCDM) problem, and applies the relative entropy evaluation method to evaluate the efficiency of railway transportation. Finally, the empirical analysis of the efficiency evaluation results for 18 railway transportation companies shows that, in 2019, Taiyuan Railway Transportation Company has the highest efficiency score, owing probably to a greater coal railway transportation demand and an advanced railway heavy haul transportation technology; railway transportation companies in the Eastern China typically have the highest efficiency scores, owing probably to a greater regional railway transportation demand.

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.

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.

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.

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.

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.

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.

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.

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

Cross-Efficiency Evaluation under Probabilistic Hesitant Fuzzy Environment and Its Application to the Portfolio Selection Process

In the case of insufficient quantitative data, qualitative evaluation information is very important for investment decision-making. However, if it is completely based on qualitative evaluation information, the results may be subjective. In response to this problem, this paper proposes a method, namely, probabilistic hesitant fuzzy cross-efficiency evaluation (PHFCEE) method, based on probabilistic hesitant fuzzy theory, cross-efficiency data envelopment analysis (CEDEA). This method uses probabilistic hesitant fuzzy sets to collect qualitative evaluation information and then uses the cross-efficiency DEA model to fuse quantitative data and qualitative information. And finally, an investment portfolio is built based on the cross-efficiency value and its variance. In addition, this article gives the specific operating steps of the PHFCEE method and uses the construction of a portfolio of 10 stocks in the China CSI 300 Index as an example to illustrate the effectiveness of this method.

Cross-Efficiency Evaluation Method Taking Management Objectives as Reference Points from Peer Perspective

According to the management by objectives (MBO) theory, performance evaluations should take into account the achievement of management objectives (MOs). The most commonly used performance evaluation method — the cross-efficiency evaluation method — seldom considers the role of MOs as a reference point. According to the prospect theory, decision-makers underestimate the benefits that exceed the reference point; they also exaggerate the losses that fall below the reference point. This irrational psychology is more obvious when evaluating the performance evaluation of peers. As such, this paper proposes a cross-efficiency evaluation method based on prospect theory, which takes MOs as a reference point from a peer perspective. First, taking MOs as reference points, a decision-making unit (DMU) chooses a set of weights for each peer, in order to maximize or minimize the prospects of the peer, according to the benevolent or aggressive attitude of the DMU. In order to improve the adaptability of the method, the precise number of MOs is further extended to be an interval number. Finally, the relationship between models, which are based on precise MOs and interval MOs, is illustrated by propositions. Finally, numerical examples are provided to illustrate the applications of the proposed cross-efficiency evaluation method.

Two-stage cross-efficiency evaluation based on prospect theory

Cross-efficiency evaluation in data envelopment analysis (DEA) is effective for evaluating the efficiency of decision-making units (DMUs). The use of cross-efficiency evaluation methods based on prospect theory has recently increased. However, the internal structure of DMUs is often ignored in efficiency evaluation; further, a fixed status quo is often selected as the reference point to calculate relative gains and losses, which is not ideal in the context of prospect theory. To address these issues, we investigate the basic two-stage cross-efficiency evaluation in DEA based on prospect theory. An optimism coefficient is introduced to formulate parameterised dynamic reference points, and a target identification model is developed to obtain target efficiency values that are attainable for all DMUs. Based on the prospect value and target efficiency values, we propose multiple novel aggressive, benevolent, and neutral two-stage cross-efficiency evaluation models. The models proposed herein can be applied to various decision environments and arbitrarily extended to other network system structures. A case study in sustainable supplier selection is performed to demonstrate the effectiveness of the proposed models for DMU ranking. The sensitivity analysis results show that the psychological characteristics of the decision maker under risk affect the evaluation results.