A new data envelopment analysis method for ranking decision making units: an application in industrial parks

Relative efficiency of decision‐making units (DMUs) is assessed by classical data envelopment analysis (DEA) models. DEA is a popular technique for efficiency evaluation. There might be a couple of efficient DMUs. Classical DEA models cannot fully rank efficient DMUs. In this paper, a novel technique for fully ranking all DMUs based on changing reference set using a single virtual inefficient DMU is proposed. To this end, the first concept of virtual DMU is defined as average of all inefficient DMUs. Virtual DMU is a proxy of all inefficient DMUs. This new method proposes a new ranking method that takes into account impact of efficient DMUs on virtual DMU and impact of efficient DMUs on influences of other efficient DMUs. A case study is given to show applicability of the proposed approach.     

Common weights for fully ranking decision making units by regression analysis

Existing methods for generating common weights in data envelopment analysis (DEA) are either very complicated or unable to produce a full ranking for decision making units (DMUs). This paper proposes a new methodology based on regression analysis to seek a common set of weights that are easy to estimate and can produce a full ranking for DMUs. The DEA efficiencies obtained with the most favorable weights to each DMU are treated as the target efficiencies of DMUs and are best fitted with the efficiencies determined by common weights. Two new nonlinear regression models are constructed to optimally estimate the common weights. Four numerical examples are examined using the developed new models to test their discrimination power and illustrate their potential applications in fully ranking DMUs. Comparisons with a similar compromise approach for generating common weights are also discussed.     

一种考虑DMU间交叉竞争的博弈效率DEA评价方法

针对绩效评价过程中一般只考虑DMU与评价者之间的合作竞争而忽视DMU间的非合作竞争的博弈,引入交叉竞争的博弈理念,将评价问题界定为评价者与DMU间合作竞争与博弈、DMU间交叉竞争的博弈两大类;考虑到在交叉竞争的博弈情境下,DMU的指标值不再是固定不变,而是随之动态调整的特点,设计交叉竞争的博弈规则,并运用决策树法描述考虑交叉竞争博弈下的DEA评价与选择过程;变评价过程中效用值改变的途径由“基于权重的交换”转化为“基于交叉竞争博弈的指标值调整”,实施对DEA模型的改进,设计交叉竞争的博弈效率DEA评价方法,得出确定型、风险型和不确定型DEA方法的分类和交叉竞争的博弈效率评价过程;从经济学的博弈论和管理学的决策分析来解释DEA,实现更加直观的DMU评价过程和更符合客观实际的评价情景.最后通过算例验证所提出方法的可行性、有效性和保序性.     

Negative data in DEA: Recognizing congestion and specifying the least and the most congested decision making units

One of the important concepts of data envelopment analysis (DEA) is congestion. A decision making unit (DMU) has congestion if an increase (decrease) in one or more input(s) of the DMU leads to a decrease (increase) in one or more its output(s). The drawback of all existing congestion DEA approaches is that they are applicable only to technologies specified by non-negative data, whereas in the real world, it may exist negative data, too. Moreover, specifying the strongly and weakly most congested DMUs is a very important issue for decision makers, however, there is no study on specifying these DMUs in DEA. These two facts are motivations for creating this current study. Hence, in this research, we first introduce a DEA model to determine candidate DMUs for having congestion and then, a DEA approach is presented to detect congestion status of these DMUs. Likewise, we propose two integrated mixed integer programming (MIP)-DEA models to specify the strongly and weakly most congested DMUs. Note that the proposed approach permits the inputs and outputs that can take both negative and non-negative magnitudes. Also, a ranking DEA approach is introduced to rank the specified congested DMUs and identify the least congested DMU. Finally, a numerical example and an empirical application are presented to highlight the purpose of this research.     

A new DEA approach to fully rank DMUs with an application to MBA programs

Data envelopment analysis (DEA) can be used to evaluate the efficiencies of decision‐making units (DMUs) in various areas like education, healthcare, and energy. Several DEA methods are proposed for this purpose; however, some of these methods cannot provide a full ranking and others often overlook some considerations that arise with special characteristics of DMUs. We propose a new DEA‐based approach to achieve a full ranking of DMUs. Our approach takes various issues into account such as the initial efficiency score of the DMU, the DMUs that should be removed from the set for it to become efficient (if any) and its effects on the efficiency scores of other DMUs. We demonstrate the shortcomings of several other DEA methods and discuss how our approach overcomes these. We apply our approach to evaluate 50 MBA programs from Financial Times 2018 rankings and compare the results with the evaluations of other methods. As opposed to some methods, our approach has the advantage of differentiating between all efficient DMUs as well as inefficient ones. In addition, the results demonstrate that we can achieve a consistent ranking that considers different aspects of the problem setting. The generated scores are also used to sort DMUs in classes of preference.     

DEA nonradial efficiency based on vector properties

Classic data envelopment analysis (DEA) models determine the efficiency of productive units, called decision making units (DMUs). DEA uses as its methodology the equiproportional reduction of inputs or increase of outputs and the finding of a single target for each DMU. This target does not incorporate the preference of the decision maker. Later works propose obtaining alternative targets based on nonradial projections on the efficiency frontier that are obtained through nonproportional variations of inputs or outputs. However, the efficiencies are not calculated for these alternative targets. This impedes a comparison among the DMUs. Thus, diverse nonradial efficiency indexes have been proposed based on mathematical averages or weighted averages that do not consider the vectorial characteristics of the efficiency. In this work, we present a nonradial efficiency index based on the initial concept of efficiency associated with each alternative (nonradial) target obtained through a multiobjective model of an inefficient DMU.     

An ideal-seeking fuzzy data envelopment analysis framework

Data envelopment analysis (DEA) is a widely used mathematical programming approach for evaluating the relative efficiency of decision making units (DMUs) in organizations. Crisp input and output data are fundamentally indispensable in traditional DEA evaluation process. However, the input and output data in real-world problems are often imprecise or ambiguous. In this study, we present a four-phase fuzzy DEA framework based on the theory of displaced ideal. Two hypothetical DMUs called the ideal and nadir DMUs are constructed and used as reference points to evaluate a set of information technology (IT) investment strategies based on their Euclidean distance from these reference points. The best relative efficiency of the fuzzy ideal DMU and the worst relative efficiency of the fuzzy nadir DMU are determined and combined to rank the DMUs. A numerical example is presented to demonstrate the applicability of the proposed framework and exhibit the efficacy of the procedures and algorithms.     

Ranking units in DEA based on efficiency intervals and decision‐maker's preferences

Data Envelopment Analysis (DEA) uses the best favorable weight set for the inputs and outputs of each decision‐making unit (DMU) to obtain its best possible score. Hence, this score can be considered as an upper bound of the real efficiency score. If we also use the least favorable weight set of each DMU, then a lower bound of the efficiency score can also be obtained. So, instead of one score, we can find an interval that gives all possible values of the efficiency score for each DMU. The aim of this paper is to propose an approach for determining efficiency intervals and setting up a full ranking of DMUs based on these intervals. We incorporate explicitly the decision‐maker's preferences in two phases. The first phase is for obtaining efficiency intervals, by introducing some restrictions on the input and output weights. The second one is for ranking the intervals based on the combination of the lower and the upper bounds of the efficiency intervals. The developed formulations will be illustrated through some numerical examples.     

Optimal direct mailing modelling based on data envelopment analysis

Data envelopment analysis (DEA) is a mathematical programming technique that is frequently used for measuring and benchmarking efficiency of the homogenous decision‐making units (DMUs). This paper proposes a new use of DEA for customers scoring and particularly their direct mailing modelling. Moreover, because DEA models suffer from some weaknesses, that is, unrealistic weighting scheme of the inputs and outputs and incomplete ranking among efficient DMUs, the present paper compares different ways of solving these problems and concludes that common set of weights method, as a result of some advantages, outperforms other procedures.     

The voting analytic hierarchy process method for discriminating among efficient decision making units in data envelopment analysis

Making optimal use of available resources has always been of interest to humankind, and different approaches have been used in an attempt to make maximum use of existing resources. Limitations of capital, manpower, energy, etc., have led managers to seek ways for optimally using such resources. In fact, being informed of the performance of the units under the supervision of a manager is the most important task with regard to making sensible decisions for managing them. Data envelopment analysis (DEA) suggests an appropriate method for evaluating the efficiency of homogeneous units with multiple inputs and multiple outputs. DEA models classify decision making units (DMUs) into efficient and inefficient ones. However, in most cases, managers and researchers are interested in ranking the units and selecting the best DMU. Various scientific models have been proposed by researchers for ranking DMUs. Each of these models has some weakness(es), which makes it difficult to select the appropriate ranking model. This paper presents a method for ranking efficient DMUs by the voting analytic hierarchy process (VAHP). The paper reviews some ranking models in DEA and discusses their strengths and weaknesses. Then, we provide the method for ranking efficient DMUs by VAHP. Finally we give an example to illustrate our approach and then the new method is employed to rank efficient units in a real world problem.     

Common sets of weights as summaries of DEA profiles of weights: With an application to the ranking of professional tennis players

In this paper, we propose a DEA approach aimed at deriving a common set of weights (CSW) to be used to the ranking of decision making units (DMUs). The idea of this approach is to minimize the deviations of the CSW from the DEA profiles of weights without zeros of the efficient DMUs. This minimization reduces in particular the differences between the DEA profiles of weights that are chosen, so the CSW proposed is a representative summary of such DEA weights profiles. We use several norms to the measurement of such differences. As a result, the CSWs derived are actually different summaries of the chosen DEA profiles of weights like their average profile of their median profile. This approach is illustrated with an application to the ranking of professional tennis players.     

A cross-dependence based ranking system for efficient and inefficient units in DEA

Decision making units (DMUs) can be ranked using data envelopment analysis (DEA) technologies. This paper develops a new ranking system under the condition of variable returns to scale (VRS) based on a measure of cross-dependence efficiency (MCDE), where the evaluation for an efficient DMU is dependent of the efficiency changes of all inefficient units due to its absence in the reference set, while the appraisal of inefficient DMUs depends on the influence of the exclusion of each efficient unit from the reference set. The infeasibility problem that arises from the conventional super-efficiency models is eliminated. A new approach to ranking inefficient units is embedded in the proposed ranking system. Through an example, advantages of our proposal are demonstrated. A real application illustrates the effectiveness of the cross-dependence based ranking system.     

Additive centralized and Stackelberg DEA models for two‐stage system with shared resources

Data envelopment analysis (DEA) is a nonparametric programming method for evaluating the efficiency performance of decision making units (DMUs) with multiple inputs and outputs. The classic DEA model cannot provide accurate efficiency measurement and inefficiency sources of DMUs with complex internal structure. The network DEA approach opens the “black box” of DMU by taking its internal operations into consideration. The complexities of DMU's internal structure involve not only the organization of substages, but also the inputs allocation and the operational relations among the individual stages. This paper proposes a set of additive DEA models to evaluate and decompose the efficiency of a two‐stage system with shared inputs and operating in cooperative and Stackelberg game situations. Under the assumptions of cooperative and noncooperative gaming, the proposed models are able to highlight the effects of strategic elements on the efficiency formation of DMUs by calculating the optimal proportion of the shared inputs allocated to each stage. The case of information technology in the banking industry at the firm level, as discussed by Wang, is revisited using the developed DEA approach.     

Slacks-based measures of efficiency in imprecise data envelopment analysis: An approach based on data envelopment analysis with double frontiers

Data envelopment analysis (DEA) is a mathematical approach for evaluating the efficiency of decision-making units (DMUs) that convert multiple inputs into multiple outputs. Traditional DEA models assume that all input and output data are known exactly. In many situations, however, some inputs and/or outputs take imprecise data. In this paper, we present optimistic and pessimistic perspectives for obtaining an efficiency evaluation for the DMU under consideration with imprecise data. Additionally, slacks-based measures of efficiency are used for direct assessment of efficiency in the presence of imprecise data with slack values. Finally, the geometric average of the two efficiency values is used to determine the DMU with the best performance. A ranking approach based on degree of preference is used for ranking the efficiency intervals of the DMUs. Two numerical examples are used to show the application of the proposed DEA approach.     

New analytical hierarchical process/data envelopment analysis methodology for ranking decision‐making units

The analytical hierarchical process/data envelopment analysis (AHP/DEA) methodology for ranking decision‐making units (DMUs) has some problems: it illogically compares two DMUs in a DEA model; it is not compatible with DEA ranking in the case of multiple inputs/multiple outputs; and it leads to weak discrimination in cases where the number of inputs and outputs is large. In this paper, we propose a new two‐stage AHP/DEA methodology for ranking DMUs that removes these problems. In the first stage, we create a pairwise comparison matrix different from AHP/DEA methodology; the second stage is the same as AHP/DEA methodology. Numerical examples are presented in the paper to illustrate the advantages of the new AHP/DEA methodology.     

A procedure for large-scale DEA computations

Data envelopment analysis (DEA), a performance evaluation method, measures the relative efficiency of a particular decision making unit (DMU) against a peer group. Most popular DEA models can be solved using standard linear programming (LP) techniques and therefore, in theory, are considered as computationally easy. However, in practice, the computational load cannot be neglected for large-scale—in terms of number of DMUs—problems. This study proposes an accelerating procedure that properly identifies a few “similar” critical DMUs to compute DMU efficiency scores in a given set. Simulation results demonstrate that the proposed procedure is suitable for solving large-scale BCC problems when the percentage of efficient DMUs is high. The computational benefits of this procedure are significant especially when the number of inputs and outputs is small, which are most widely reported in the literature and practices.     

Cross efficiency evaluation method based on weight-balanced data envelopment analysis model

In this paper, the cross efficiency evaluation method, regarded as a DEA extension tool, is firstly reviewed for its utilization in identifying the Decision Making Unit (DMU) with the best practice and ranking the DMUs by their respective cross-efficiency scores. However, we then point out that the main drawback of the method lies in non-uniqueness of cross-efficiency scores resulted from the presence of alternate optima in traditional DEA models, obviously making it become less effective. Aiming at the research gap, a weight-balanced DEA model is proposed to lessen large differences in weighted data (weighted inputs and weighted outputs) and to effectively reduce the number of zero weights for inputs and outputs. Finally, we use two examples of the literature to illustrate the performance of this approach and discuss some issues of interest regarding the choosing of weights in cross-efficiency evaluations.     

DEA efficiency analysis: A DEA approach with double frontiers

Data envelopment analysis (DEA) is a method for measuring efficiency of peer decision-making units (DMUs). Conventional DEA evaluates the performance of each DMU using a set of most favourable weights. As a result, traditional DEA models can be considered methods for the analysis of the best relative efficiency or analysis of the optimistic efficiency. DEA efficient DMUs obtained from conventional DEA models create an efficient production frontier. Traditional DEA can be used to identify units with good performance in the most desirable scenarios. There is a similar approach that evaluates the performance indicators of each DMU using a set of most unfavourable weights. Accordingly, such models can be considered models for analysing the worst relative efficiency or pessimistic efficiency. This approach uses the inefficient production frontier for determining the worst relative efficiency that can be assigned to each DMU. DMUs lying on the inefficient production frontier are referred to as DEA inefficient while those neither on the efficient frontier nor on the inefficient frontier are declared DEA inefficient. It can be argued that both relative efficiencies should be considered simultaneously and any approach with only one of them would be biased. This paper proposed the integration of both efficiencies as an interval so that the overall performance score would belong to this interval. It was shown that efficiency interval provided more information than either of the two efficiencies, which was illustrated using two numerical examples.     

Improving the discrimination power and weights dispersion in the data envelopment analysis

Data envelopment analysis (DEA) has been a very popular method for measuring and benchmarking relative efficiency of peer decision making units (DMUs) with multiple input and outputs. Beside of its popularity, DEA has some drawbacks such as unrealistic input–output weights and lack of discrimination among efficient DMUs. In this study, two new models based on a multi-criteria data envelopment analysis (MCDEA) are developed to moderate the homogeneity of weights distribution by using goal programming (GP). These goal programming data envelopment analysis models, GPDEA-CCR and GPDEA-BCC, also improve the discrimination power of DEA.     

A study of optimal weights of Data Envelopment Analysis - Development of a context-dependent DEA-R model

The weight is one of the main issues of Data Envelopment Analysis (DEA), and relevant theoretical research indicates that many DEA mathematical models include redundant restraints on weight, resulting in underestimated efficiency, pseudo inefficiency, and difficulty in representing specific Input/Output relationships. This study proposes a context-dependent DEA-R model to address shortcomings resulting from redundant restraints on the weights of an efficient decision making unit (DMU), and converts the optimal weight to analyze the influences of redundant restraints on weights. The evaluation results of Taiwan medical centers show that the efficiency of the DMU is underestimated and pseudo inefficiency may occur due to redundant restraints on weight. Moreover, optimal weights are used as variables to conduct cluster analysis in order to determine the information of the weights. The results of cluster analysis indicate that it can assist DMUs in understanding the relationships between DMUs, and contribute to the development of a unique survival strategy for hospitals.