Data Envelopment Analysis Cross-efficiency Evaluation Research Articles

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.

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.

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.

Assessing the performance of industrial water resource utilization systems in China based on a two-stage DEA approach with game cross efficiency

While shouldering the burden of economic development, China's industrial sector has significant water consumption and wastewater discharge, which has intensified the country's water shortage. To improve the efficiency of industrial water resource utilization system, data envelopment analysis (DEA) has been widely used to assess the performance of the system. The current network DEA approaches adopted to investigate the system all belong to the self-evaluation mode, and existing network DEA cross-efficiency evaluation approaches have shortcomings. Therefore, a two-stage DEA approach with game cross efficiency is proposed to evaluate the system. First, according to the operation process of the system, this paper decomposes the system into a general two-stage network structure: water use stage and wastewater treatment stage. Second, the DEA game cross-efficiency model is improved to the general two-stage DEA game cross-efficiency model to evaluate the overall efficiency of the system. Third, given the overall efficiency, an efficiency decomposition model is proposed to determine a set of weights for each decision-making unit to evaluate water use efficiency and wastewater treatment efficiency. Finally, the rationality of the proposed approach is illustrated by model comparison, and the efficiencies of industrial water resource utilization systems in 31 regions of China from 2010 to 2015 are evaluated based on the proposed approach. The results indicate that, from the overall efficiency perspective, no region in China is always evaluated as being overall efficient and the overall efficiencies of 17 regions show an increase before a decreasing trend or decreasing trend during the study period. In 11 regions, wastewater treatment efficiency is far lower than water use efficiency, and in 11 other regions, both sub-stages are inefficient. In terms of the three areas, the eastern area has the highest water use efficiency, the central area has the lowest efficiency of both sub-stages, and the western area has the highest wastewater treatment efficiency. Some recommendations are presented to ensure China's sustainable development.

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.

Portfolio Selection Using Data Envelopment Analysis Cross-Efficiency Evaluation with Undesirable Fuzzy Inputs and Outputs

In this paper, we discuss a portfolio selection problem based on fuzzy data envelopment analysis cross-efficiency evaluation wherein both undesirable fuzzy inputs and outputs have been considered. We first propose a data envelopment analysis cross-efficiency model, in which both undesirable inputs and outputs are considered. Furthermore, considering the imprecision of the data, we extend the crisp model to the fuzzy environment and propose a fuzzy data envelopment analysis cross-efficiency model with coexisting undesirable input and output data. We then apply the proposed model to the portfolio selection problem and present a novel mean-semivariance portfolio selection model based on fuzzy data envelopment analysis cross-efficiency scores, in which several realistic constraints are considered, including a budget, cardinality, buy-in thresholds, and no short selling constraints. After that, we employ the genetic algorithm (GA) to solve the proposed model. Finally, a real-life case study is presented to demonstrate the effectiveness of the proposed approaches.

Undesirable factors in stochastic DEA cross-efficiency evaluation: An application to thermal power plant energy efficiency

In this study using an input-oriented data envelopment analysis (DEA) model with undesirable outputs a new stochastic model called Expected Ranking Criterion is proposed. The proposed model employs statistical techniques to evaluate the efficiency of decision making units (DMUs) with stochastic data. Based on the proposed model, a stochastic DEA (SDEA) cross-efficiency model is suggested for ranking and discrimination of DMUs. Then, given the non-uniqueness of resulting optimal solution, a stochastic model is introduced for rating priorities by which cross-efficiency evaluation is performed using aggressive approach. Finally, the proposed models are implemented for evaluating 32 thermal power plants. The results show the applicability of the proposed models.

WITHDRAWN: A multi-objective model for Pareto optimality in data envelopment analysis cross-efficiency evaluation

Abstract This manuscript proposes a new approach for addressing the non-Pareto optimality problem in data envelopment analysis (DEA) cross-efficiency evaluation. First, we propose a multi-objective model with a new non-self-denial weight-selection principle to obtain Pareto-optimal cross-efficiency scores. Second, the sum-weighted approach is adopted to solve the multi-objective model. Third, despite the nonlinearity and high complexity of the sum-weighted model, we find that a set of Pareto-optimal cross-efficiency scores can always be obtained by using a common-weight evaluation result, and a set of common weights can be obtained by a simple linear program. Further, we investigate a previous benchmark study and show that with a special assignment of the given cross-efficiency scores in their procedure, the benchmark approach can also obtain Pareto-optimal cross-efficiency scores as a common-weight evaluation result. Compared with the weight-selection principles provided in the previous benckmark study, our non-self-denial principle is more reasonable and more acceptable among the DMUs since it enforces no additional nonendogenous constraints when each DMU selects its optimal weights. Additionally, we have proved that a set of Pareto-optimal cross-efficiency scores always consociate the mechanisms of peer-evaluation, self-evaluation, and common-weight evaluation in DEA since it can always be calculated by using a set of common weights. More importantly, compared with the previous benckmark study, which must solve numerous linear programs for each DMU to obtain a set of Pareto-optimal cross-efficiency scores, our calculation process requires solving only one linear program. Finally, the proposed method is applied to perform green supplier selection.

Cross-efficiency evaluation in data envelopment analysis based on prospect theory

Cross-efficiency evaluation in data envelopment analysis (DEA) is a useful tool in evaluating the performance of decision-making units (DMUs). It is generally assumed that decision makers (DMs) are completely rational in common cross-efficiency evaluation models, which fail to consider the DM's risk attitude that plays an important role in the evaluation process. To fill this gap, we investigate the cross-efficiency evaluation in DEA based on prospect theory. First, we introduce a prospect value of the DMU to capture the non-rational psychological aspects of a DM under risk. Second, based on the prospect value, we propose a new cross-efficiency model termed the prospect cross-efficiency (PCE) model. Particularly, some existing cross-efficiency evaluation models can be deemed as the special cases of the PCE model with suitable adjustments of the parameters. Furthermore, this paper provides an empirical example to evaluate cross-efficiency with several selected universities directly managed by the Ministry of Education of China to illustrate the effectiveness of the PCE model in ranking DMUs.

A secondary goal in DEA cross-efficiency evaluation: A “one home run is much better than two doubles” criterion

Data Envelopment Analysis (DEA) is a mathematical programming approach for assessing the relative efficiency of decision making units (DMUs). The cross-efficiency evaluation is an extension of DEA that provides a ranking method and eliminates unrealistic DEA weighting schemes on weight restrictions, without requiring a prior information. The cross-efficiency evaluation may have some shortages, e.g. the cross-efficiency scores may not be unique due to the presence of several optima. To rectify this issue, several secondary goals have been proposed in the literature. Some scholars have proposed several cross-efficiency evaluations based on maximising (minimising) the total deviation from their ideal point as an aggressive (benevolent) perspective. In some cases, minimising (maximising) the number of DMUs that achieve their target efficiencies, is more important than maximising (minimising) the total deviation from the ideal point. We propose some alternative models for the cross-efficiency evaluation based on the cardinality of the set of “satisfied DMUs”, i.e. the DMUs that achieve their maximum efficiencies. For aggressive (benevolent) cross-efficiency evaluation, among all the optimal weights for a specific unit, we choose the weights which can maximise its efficiency, and at the same time minimise (maximise) the number of satisfied units. We demonstrate how the proposed method can be implemented and illustrate the method using two examples.

Peer-judgment risk minimization using DEA cross-evaluation with an application in fishery

One of the shortcomings in the standard data envelopment analysis (DEA) self-evaluation models is the flexibility of choosing favorable DEA weights on inputs and outputs. This study uses the potential of DEA cross-efficiency evaluation and proposes a new mean–variance goal programming model for minimizing the risk of changing DEA weights for identification of high performed decision making units. The applicability of the proposed method in this paper is demonstrated through an application in Oman fishery, to address peer-judgment risk in fisheries. The suggested model also provides a list of fishers with maximum cross-efficiency scores.

A balanced data envelopment analysis cross-efficiency evaluation approach

Data envelopment analysis (DEA) is a frontier analysis procedure for evaluating the relative performance of decision making units (DMUs) with multiple inputs and multiple outputs. To improve its discrimination power, an important extension is proposed as cross-efficiency, which uses peer DMUs’ optimal relative weights to evaluate the relative performance. However, the existing cross-efficiency methods show an inconsistent and unbalanced evaluation standard, since each DMU might determine a different total (or mean) efficiency value across all DMUs. The different values imply that the DMUs that have assigned larger cross-efficiency scores will have a larger effect in aggregating the ultimate cross-efficiency scores and different DMUs’ effects are unbalanced in cross-efficiency methods. In this paper, we will deal with this unbalanced cross-efficiency evaluation problem. To this end, we first suggest a practical adjustment measure to rectify the traditional cross-efficiency, which will provide a common evaluation standard for all DMUs and make each DMU dispatch an identical total efficiency score across all DMUs. Further, we propose a game-like iterative procedure to obtain the optimal balanced cross-efficiency. Finally, we present both a numerical example and an empirical study derived from the literature and a real-world problem to demonstrate the usefulness and efficacy of the new balanced cross-efficiency evaluation approach. The work presented in this paper can extend the traditional cross-efficiency approaches to situations involving unbalanced evaluation standards, and make the evaluation results more practical significance.

Improved DEA Cross Efficiency Evaluation Method Based on Ideal and Anti-Ideal Points

A new model is introduced in the process of evaluating efficiency value of decision making units (DMUs) through data envelopment analysis (DEA) method. Two virtual DMUs called ideal point DMU and anti-ideal point DMU are combined to form a comprehensive model based on the DEA method. The ideal point DMU is taking self-assessment system according to efficiency concept. The anti-ideal point DMU is taking other-assessment system according to fairness concept. The two distinctive ideal point models are introduced to the DEA method and combined through using variance ration. From the new model, a reasonable result can be obtained. Numerical examples are provided to illustrate the new constructed model and certify the rationality of the constructed model through relevant analysis with the traditional DEA model.

DEA cross-efficiency evaluation and ranking method based on interval data

Data envelopment analysis (DEA) is an important method of efficiency evaluation. Cross-efficiency evaluation is one of the main aspects of research in the field of DEA that has been applied in various fields. In the traditional cross-efficiency evaluation model, the variable data of decision-making units is exact. Dynamic information is frequently unable to reflect the whole characteristic when determining the exact data. In this study, we select interval data to represent the dynamic information of some variables in the evaluation process. We then build a solution method based on interval efficiency and DEA cross-efficiency. This method retains the reflection of interval data on uncertain variable properties. Finally, the stochastic multi-criteria acceptability analysis 2 (SMAA2) is introduced to solve the whole sequence problem of interval efficiency. We present a case study from a set of 19 reservoir dams suffered from Wenchuan earthquake in Luojiang County, Sichuan Province to demonstrate the applicability of the proposed model.

A Revised Model of the Neutral DEA Model and Its Extension

The neutral data envelopment analysis (DEA) model is an alternative way to determine the weights in DEA cross-efficiency evaluation, while avoiding the difficulty in making a choice between the aggressive and benevolent formulations. However, the weights determined by the neutral model merely make the efficiency of part output bigger than other sets of weights. The neutral model is not able to make the efficiency of each output of the DMU biggest among the favorable weights. This neutral model is not purely “neutral” and not most favorable to the DMU. We proposed a revised model for the neutral model. Based on the idea that the DMU should choose a set of weights to maximize its own efficiency, this paper proposes a new cross-efficiency model. The weights determined by the two models are neutral, neither aggressive nor benevolent.

DEA cross-efficiency evaluation considering undesirable output and ranking priority: a case study of eco-efficiency analysis of coal-fired power plants

Data envelopment analysis cross-efficiency evaluation has been widely accepted as a useful tool for performance evaluation and ranking of decision making units. However, the non-uniqueness of optimal weights is a problem that has reduced the usefulness of this powerful method. In addition, current studies generally have not considered the situation in which undesirable outputs appear in the data envelopment analysis cross-efficiency evaluation. To solve these problems, firstly, we present an equitable model for efficiency evaluation of decision-making units with undesirable outputs and introduce a technique for cross-efficiency evaluation considering undesirable outputs. Then, a ranking priority model is proposed considering the decision making units' intentions of pursuing the best ranking positions. In addition, an aggressive model is given to guarantee the uniqueness of the optimal solution. The proposed approach can not only solve the problem of non-uniqueness of optimal weights in data envelopment analysis cross-efficiency evaluation but also considers undesirable outputs and ranking preferences of the decision-making units. Finally, the proposed approach is applied for eco-efficiency analysis of coal-fired power plants in a big data environment, and the results show that most coal-fired power plants in China have not performed well.

DEA cross-efficiency evaluation based on satisfaction degree: an application to technology selection

Data envelopment analysis (DEA) has been extended to cross-efficiency evaluation to provide better discrimination and ranking of decision-making units (DMUs). However, the non-uniqueness of optimal weights in the traditional DEA models (CCR and BCC models) has reduced the usefulness of the DEA cross-efficiency evaluation method. To solve this problem, we introduce the concept of the satisfaction degree of a DMU towards a set of optimal weights for another DMU. Then, a new DEA cross-efficiency evaluation approach, which contains a maxmin model and two algorithms, is proposed based on the satisfaction degrees of the DMUs. Our maxmin model and algorithm 1 can obtain for each DMU an optimal set of weights that maximises the least satisfaction degrees among all the other DMUs. Further, our algorithm 2 can then be used to guarantee the uniqueness of the optimal weights for each DMU. Finally, our approach is applied to a real-world case study of technology selection.

Extended secondary goal models for weights selection in DEA cross-efficiency evaluation

Data Envelopment Analysis (DEA) has been extended to cross-efficiency evaluation for ranking decision making units (DMUs) and eliminating unrealistic weighting schemes. Unfortunately, the non-unique optimal weights problem in DEA has reduced the usefulness of this extended method. Aiming at solving this problem, we first incorporate a target identification model to get reachable targets for all DMUs. Then, several secondary goal models are proposed for weights selection considering both desirable and undesirable cross-efficiency targets of all the DMUs. Compared with the traditional secondary goal models, the cross-efficiency targets are improved in that all targets are always reachable for the DMUs. In addition, the proposed models considered the DMUs’ willingness to get close to their desirable cross-efficiency targets and to avoid their undesirable cross-efficiency targets simultaneously while the traditional secondary goal models considered only the ideal targets of the DMUs. Finally, the calculation results of our proposed models are compared with those of some other traditional methods for two published examples: an efficiency evaluation of six nursing homes and an R&D project selection.

DEA cross-efficiency evaluation based on Pareto improvement

Cross-efficiency evaluation, as an extension tool of data envelopment analysis (DEA), has been widely applied in evaluating and ranking decision making units (DMUs). Unfortunately, the cross-efficiency scores generated may not be Pareto optimal, which has reduced the effectiveness of this method. To solve this problem, we propose a cross-efficiency evaluation approach based on Pareto improvement, which contains two models (Pareto optimality estimation model and cross-efficiency Pareto improvement model) and an algorithm. The Pareto optimality estimation model is used to estimate whether the given set of cross-efficiency scores are Pareto-optimal solutions. If these cross-efficiency scores are not Pareto optimal, the Pareto improvement model is then used to make cross-efficiency Pareto improvement for all the DMUs. In contrast to other cross-efficiency approaches, our approach always obtains a set of Pareto-optimal cross efficiencies under the predetermined weight selection principles for these DMUs. In addition, if the proposed algorithm terminates at its step 3, the evaluation results generated by our approach unify self-evaluation, peer-evaluation, and common-weight-evaluation in DEA cross-efficiency evaluation. Specifically, the self-evaluated efficiency and the peer-evaluated efficiency converge to the same common-weight-evaluated efficiency when the algorithm stops. This will make the evaluation results more likely to be accepted by all the DMUs.