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.     

Common weights data envelopment analysis with uncertain data: A robust optimization approach

One of the primary issues on data envelopment analysis (DEA) models is the reduction of weights flexibility. There are literally several studies to determine common weights in DEA but none of them considers uncertainty in data. This paper introduces a robust optimization approach to find common weights in DEA with uncertain data. The uncertainty is considered in both inputs and outputs and a suitable robust counterpart of DEA model is developed. The proposed robust DEA model is solved and the ideal solution is found for each decision making units (DMUs). Then, the common weights are found for all DMUs by utilizing the goal programming technique. To illustrate the performance of the proposed model, a numerical example is solved. Also, the proposed model of this paper is implemented by using some actual data from provincial gas companies in Iran.     

A modified slacks‐based ranking method handling negative data in data envelopment analysis

Performance ranking for a set of comparable decision‐making units (DMUs) with multiple inputs and outputs is an important and often‐discussed topic in data envelopment analysis (DEA). Conventional DEA models distinguish efficient units from inefficient ones but cannot further discriminate the efficient units, which all have a 100% efficiency score. Another weakness of these models is that they cannot handle negative inputs and/or outputs. In this paper, a new modified slacks‐based measure is proposed that works in the presence of negative data and provides quantitative data that helps decision makers obtain a full ranking of DMUs in situations where other methods fail. In addition, the new method has the properties of unit invariance and translation invariance, and it can give targets for inefficient DMUs to guide them to achieve full efficiency. Two numerical examples are analysed to demonstrate the usefulness of the new method.     

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.     

Measurement of overall performances of decision-making units using ideal and anti-ideal decision-making units

Data envelopment analysis (DEA) is a method for evaluating relative efficiencies of decision-making units (DMUs) which perform similar functions in a production system, consuming multiple inputs to produce multiple outputs. The conventional form of DEA evaluates performances of DMUs only from the optimistic point of view. In other words, it chooses the most favorable weights for each DMU. There is another approach that measures efficiency of a DMU from the pessimistic point of view. This approach chooses the most unfavorable weights for evaluation of each DMU. In this paper, we propose to integrate both efficiencies in the form of an interval in order to measure the overall performance of a DMU. The proposed DEA models for evaluation of efficiencies are called bounded DEA models. The proposed approach will be compared using a numerical example. Another example regarding performance evaluation of 50 bank branches in Iranian cities will be presented to demonstrate the advantages, simplicity, and utility of this approach in real-life situations.     

Allocating fixed resources and setting targets using a common-weights DEA approach

Data envelopment analysis (DEA) is a data-driven non-parametric approach for measuring the efficiency of a set of decision making units (DMUs) using multiple inputs to generate multiple outputs. Conventionally, DEA is used in ex post evaluation of actual performance, estimating an empirical best-practice frontier using minimal assumptions about the shape of the production space. However, DEA may also be used prospectively or normatively to allocate resources, costs and revenues in a given organization. Such approaches have theoretical foundations in economic theory and provide a consistent integration of the endowment-evaluation-incentive cycle in organizational management. The normative use, e.g. allocation of resources or target setting, in DEA can be based on different principles, ranging from maximization of the joint profit (score), combinations of individual scores or game-theoretical settings. In this paper, we propose an allocation mechanism that is based on a common dual weights approach. Compared to alternative approaches, our model can be interpreted as providing equal endogenous valuations of the inputs and outputs in the reference set. Given that a normative use implicitly assumes that there exists a centralized decision-maker in the organization evaluated, we claim that this approach assures a consistent and equitable internal allocation. Two numerical examples are presented to illustrate the applicability of the proposed method and to contrast it with earlier work.     

A concept of fuzzy input mix-efficiency in fuzzy DEA and its application in banking sector

Data envelopment analysis (DEA) is a linear programming based non-parametric technique for evaluating the relative efficiency of homogeneous decision making units (DMUs) on the basis of multiple inputs and multiple outputs. There exist radial and non-radial models in DEA. Radial models only deal with proportional changes of inputs/outputs and neglect the input/output slacks. On the other hand, non-radial models directly deal with the input/output slacks. The slack-based measure (SBM) model is a non-radial model in which the SBM efficiency can be decomposed into radial, scale and mix-efficiency. The mix-efficiency is a measure to estimate how well the set of inputs are used (or outputs are produced) together. The conventional mix-efficiency measure requires crisp data which may not always be available in real world applications. In real world problems, data may be imprecise or fuzzy. In this paper, we propose (i) a concept of fuzzy input mix-efficiency and evaluate the fuzzy input mix-efficiency using α – cut approach, (ii) a fuzzy correlation coefficient method using expected value approach which calculates the expected intervals and expected values of fuzzy correlation coefficients between fuzzy inputs and fuzzy outputs, and (iii) a new method for ranking the DMUs on the basis of fuzzy input mix-efficiency. The proposed approaches are then applied to the State Bank of Patiala in the Punjab state of India with districts as the DMUs.     

Two-stage DEA model with additional input in the second stage and part of intermediate products as final output

Data envelopment analysis (DEA) has been proved to be an excellent approach for measuring performance of decision making units (DMUs) that use multiple inputs to generate multiple outputs. In many real world scenarios, inputs or outputs may be shared among various activities. This paper proposes a two-stage DEA model with additional input in the second stage and part of intermediate products as final output. We first discuss the non-cooperative condition in order to determine the upper and lower bounds of the efficiencies of sub-DMUs in different stages. A parametric transformation is described to solve the non-linear programming of the overall cooperative efficiency model. An application is provided.     

A new network epsilon-based DEA model for supply chain performance evaluation

Supply chain performance evaluation problems are inherently complex problems with multilayered internal linking activities and multiple entities. Data Envelopment Analysis (DEA) has been used to evaluate the relative performance of organizational units called Decision Making Units (DMUs). However, the conventional DEA models cannot take into consideration the complex nature of supply chains with internal linking activities. Network DEA models using radial measures of efficiency are used for supply chain performance evaluation problems. However, these models are not suitable for problems where radial and non-radial inputs and outputs must be considered simultaneously. DEA models using Epsilon-Based Measures (EBMs) of efficiency are proposed for a simultaneous consideration of radial and non-radial inputs and outputs. We extend the EBM model and propose a new Network EBM (NEBM) model. The proposed NEBM model combines the radial and non-radial measures of efficiency into a unified framework for solving network DEA problems. A case study is presented to exhibit the efficacy of the procedures and to demonstrate the applicability of the proposed method to a supply chain performance evaluation problem in the semiconductor industry.     

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.     

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.     

Data Envelopment Analysis Based on Choquet Integral

Data envelopment analysis (DEA) is a widely used technique in decision making. The existing DEA models always assume that the inputs (or outputs) of decision‐making units (DMUs) are independent with each other. However, there exist positive or negative interactions between inputs (or outputs) of DMUs. To reflect such interactions, Choquet integral is applied to DEA. Self‐efficiency models based on Choquet integral are first established, which can obtain more efficiency values than the existing ones. Then, the idea is extended to the cross‐efficiency models, including the game cross‐efficiency models. The optimal analysis of DEA is further investigated based on regret theory. To estimate the ranking intervals of DMUs, several models are also established. It is founded that the models considering the interactions between inputs (or outputs) can obtain wider ranking intervals.     

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.     

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.     

A bargaining game model for efficiency decomposition in the centralized model of two-stage systems

Data envelopment analysis (DEA) is a non-parametric approach for measuring the relative efficiencies of peer decision making units (DMUs). The centralized model has been widely used to examine the efficiencies of two-stage systems, where all the outputs from the first stage are the only inputs to the second stage. Since there may exist some flexibility in decomposing the overall efficiency between the two stages when multiple optimal weights exist, we develop a Nash bargaining game model to obtain a fair efficiency decomposition for the two stages while keeping the overall efficiency unchanged under this circumstance. The minimal achievable efficiencies for the two stages are used as the breakdown point and the unique bargaining decomposition of the overall efficiency is obtained subsequently. The Nash bargaining game model is applied to evaluate the performance of 10 branches of China Construction Bank.     

A learning performance evaluation with benchmarking concept for English writing courses

This paper adopts data envelopment analysis (DEA), a robust and reliable evaluation method widely applied in various fields to explore the key indicators contributing to the learning performance of English freshmen writing courses in a university of Taiwan from the academic year 2004 to 2006. The results of DEA model applied in learning performance change our original viewpoint and reveal that some decision-making units (DMUs) with higher actual values of inputs and outputs have lower efficiency because the relative efficiency of each DMU is measured by their distance to the efficiency frontier. DMUs may refer to different facet reference sets according to their actual values located in lower or higher ranges. In the managerial strategy of educational field, the paper can encourage inefficient DMUs to always compare themselves with efficient DMUs in their range and make improvement little by little. The results of DEA model can also give clear indicators and the percentage of which input and output items to improve. The paper also demonstrates that the benchmarking characteristics of the DEA model can automatically segment all the DMUs into different levels based on the indicators fed into the performance evaluation mechanism. The efficient DMUs on the frontier curve can be considered as the boundaries of the classification which are systematically defined by the DEA model according to the statistic distribution.     

A fuzzy DEA model with undesirable fuzzy outputs and its application to the banking sector in India

Data envelopment analysis (DEA) is a widely used technique for measuring the relative efficiencies of decision making units (DMUs) with multiple inputs and multiple outputs. However, in real life applications, undesirable outputs may be present in the production process which needs to be minimized. The present study endeavors to propose a DEA model with undesirable outputs and further to extend it in fuzzy environment in view of the fact that input/output data are not always available in exact form in real life problems. We propose a fuzzy DEA model with undesirable fuzzy outputs which can be solved as crisp linear program for each α in (0, 1] using α-cut approach. Further, cross-efficiency technique is applied to increase the discrimination power of the proposed models and to rank the efficient DMUs at every α in (0, 1]. Moreover, for better understanding of the proposed methodology, we present a numerical illustration followed by an application to the banking sector in India. This is the first study which attempts to measure the performance of public sector banks (PuSBs) in India using fuzzy input/output data for the period 2009–2011. The results obtained from the proposed methodology not only depict the impact of undesirable output on the performance of PuSBs but also analyze efficiently the influence of the presence of uncertainty in the data over the efficiency results. The findings show that the efficiency results of many PuSBs vary with the variation in α during the selected period.     

Evaluation and ranking DMUs in the presence of both undesirable and ordinal factors in data envelopment analysis

In the last decade,ranking units in data envelopment analysis(DEA) has become the interests of many DEA researchers and a variety of models were developed to rank units with multiple inputs and multiple outputs.These performance factors(inputs and outputs) are classified into two groups:desirable and undesirable.Obviously,undesirable factors in production process should be reduced to improve the performance.Also,some of these data may be known only in terms of ordinal relations.While the models developed in the past are interesting and meaningful,they didn t consider both undesirable and ordinal factors at the same time.In this research,we develop an evaluating model and a ranking model to overcome some deficiencies in the earlier models.This paper incorporates undesirable and ordinal data in DEA and discusses the efficiency evaluation and ranking of decision making units(DMUs) with undesirable and ordinal data.For this purpose,we transform the ordinal data into definite data,and then we consider each undesirable input and output as desirable output and input,respectively.Finally,an application that shows the capability of the proposed method is illustrated.     

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.     

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.