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.     

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.     

Returns to growth in a nonparametric DEA approach

In this contribution, first the concept of returns to growth (RTG) of a high‐tech firm facing hyper‐competition in the new economy is introduced by describing a proportional relationship between growth in inputs and growth in outputs using the growth efficiency (GE) model of Sengupta. Second, both technology‐ and value‐based methods are suggested for estimating the RTG behavior of high‐tech firms. Third, although the GE concept seems closely related to the notion of total factor productivity change, this link remains unexplored: we suggest a link between both concepts. Finally, our empirical application to the Indian computer industry reveals that first, companies operating under increasing returns to scale (RTS) may exhibit constant or decreasing RTG; second, companies showing constant RTS may exhibit increasing or decreasing RTG; and third, companies showing decreasing RTS may exhibit constant or increasing RTG. These findings imply that RTS estimates need not provide proper information regarding the growth strategy behavior of high‐tech companies.     

Evaluation of Brazilian airlines nonradial efficiencies and targets using an alternative DEA approach

This paper evaluates the operational performance of airlines using an alternative data envelopment analysis (DEA) approach. We start by calculating the relative efficiency of each firm with the classical DEA. After identifying the set of efficient airlines that could be used as benchmarks for the inefficient firms, we employ a nonradial efficiency measure based on vector concepts that considers each efficient airline as a real target at once. This allows the assessment of efficiency scores using other targets than those automatically derived by the classical DEA, traditionally built on radial measures of efficiency. Although the results indicate a large number of negative efficiency scores, for most inefficient airlines, it was possible to identify at least one real target whose corresponding score was positive. In addition, the methodology herein adopted enriches benchmarking analysis, as it provides a set of alternative targets easily understood and accepted by the managers involved in the decision process.     

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.     

A new DEA‐based method for fully ranking all decision‐making units

Abstract: Decision makers always lay great emphasis on performance evaluation upon a group of peer business units to pick out the best performer. Standard data envelopment analysis models can evaluate the relative efficiency of decision‐making units (DMUs) and distinguish efficient ones from inefficient ones. However, when there are more than one efficient DMU, it is impossible to rank all of them solely according to standard efficiency scores. In this paper, a new method for fully ranking all DMUs is proposed, which is based on the combination of each efficient DMU's influence on all the other DMUs and the standard efficiency scores. This method is effective in helping decision makers differentiate all units' performance thoroughly and select the best performer.     

A maximum discrimination DEA method for ranking association rules in data mining

A data mining algorithm, such as Apriori, discovers a huge number of association rules (ARs) and therefore efficiently ranking all these rules is an important issue. This paper suggests a data envelopment analysis (DEA) method for ranking the discovered ARs using a maximum discrimination between the interestingness criteria defined for all ARs. It is shown that the proposed DEA model has a unique optimal solution which can be computed efficiently when the maximum discrimination between the criteria, the difference between DEA weights, is considered. The contribution of this study can be explained as follows: First, we show that using the conventional DEA model for ranking ARs may produce an invalid result because the weights corresponding to interestingness criteria would not discriminate between the criteria. This is investigated for a dataset consisting of 46 ARs with four criteria, namely support, confidence, itemset value and cross-selling. The paper also introduces the maximum discrimination between the weights of the criteria and obtains the optimal solution of the corresponding DEA model efficiently without the need of solving the related mathematical models. On the other hand, this model concludes less number of useful rule(s). A comparative analysis is then used to show the advantage of the proposed DEA method.     

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.     

Measuring efficiency of Vietnamese public colleges: an application of the DEA‐based dynamic network approach

In Vietnam, public colleges play a crucial role in shaping the socioeconomic and educational development strategies and providing a skilled labor force needed for the country's market‐oriented economy. Using balanced panel data for 2011–2013, we use the integrated data envelopment analysis based dynamic network model to examine dynamic changes in efficiencies of public colleges in the education sector. This model allows simultaneously estimating efficiencies of financial and academic operations and the overall dynamic changes of colleges in a network structure. Our findings indicate that the overall efficiencies of colleges are, on average, 0.741 while the average efficiencies of the financial and academic operations are 0.722 and 0.760, respectively. Furthermore, the in‐city colleges are more efficient than others, 0.776 and 0.728, respectively.     

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 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.     

A dimensional decomposition approach to identifying efficient units in large-scale DEA models

In this paper, we propose the use of a dimensional decomposition procedure together with lexicographic parametric programming to reduce computational burden when identifying the efficient decision making units in data envelopment analysis (DEA). The use of lexicographic parametric programming makes it possible to develop an efficient algorithm for the problems with few inputs and outputs. Based on this we propose the procedure which first partitions the original problem dimensionally into sub-problems and then identifies the efficient units of the sub-problems. Since those units are a subset of the weakly efficient solutions of the original problem, they are used as an initial approximation for the efficient units of the original problem. The efficiency of the approach is illustrated by numerical results.     

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.     

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.     

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.     

DEA models with a constant input for SRI mutual funds with an application to European and Swedish funds

Data envelopment analysis (DEA) allows one to take into account the degree of social responsibility of mutual funds, together with financial risk and return. This contribution proposes some DEA models in which the input and output variables are focused on the main determinants of investments in socially responsible investing (SRI) mutual funds. Unlike other DEA models, a constant initial capital and the final value of the investment are considered; this ensures the positivity of all variables, even during financial crises. The initial capital deposited by an investor is assumed to be equal for all funds, so that we have a constant input. The implications of the presence of a constant input in DEA models are studied, which have important consequences for the analysis of the performance of mutual funds, in particular with regard to the type of returns to scale. The models proposed are applied to the European data to evaluate the performance of SRI mutual funds in the period June 2006 to June 2009. Moreover, a specific analysis compares the performance of SRI and non‐SRI mutual funds, in order to determine if SRIs require a sacrifice in terms of financial rewards. Finally, a more detailed investigation is carried out for the Swedish SRI mutual funds.     

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.     

A new digital watermarking evaluation and benchmarking methodology using an external group of evaluators and multi‐criteria analysis based on ‘large‐scale data’

Digital watermarking evaluation and benchmarking are challenging tasks because of multiple evaluation and conflicting criteria. A few approaches have been presented to implement digital watermarking evaluation and benchmarking frameworks. However, these approaches still possess a number of limitations, such as fixing several attributes on the account of other attributes. Well‐known benchmarking approaches are limited to robust watermarking. Therefore, this paper presents a new methodology for digital watermarking evaluation and benchmarking based on large‐scale data by using external evaluators and a group decision making context. Two experiments are performed. In the first experiment, a noise gate‐based digital watermarking approach is developed, and the scheme for the noise gate digital watermarking approach is enhanced. Sixty audio samples from different audio styles are tested with two algorithms. A total of 120 samples were evaluated according to three different metrics, namely, quality, payload, and complexity, to generate a set of digital watermarking samples. In the second experiment, the situation in which digital watermarking evaluators have different preferences is discussed. Weight measurement with a decision making solution is required to solve this issue. The analytic hierarchy process is used to measure evaluator preference. In the decision making solution, the technique for order of preference by similarity to the ideal solution with different contexts (e.g., individual and group) is utilized. Therefore, selecting the proper context with different aggregation operators to benchmark the results of experiment 1 (i.e., digital watermarking approaches) is recommended. The findings of this research are as follows: (1) group and individual decision making provide the same result in this case study. However, in the case of selection where the priority weights are generated from the evaluators, group decision making is the recommended solution to solve the trade‐off reflected in the benchmarking process for digital watermarking approaches. (2) Internal and external aggregations show that the enhanced watermarking approach demonstrates better performance than the original watermarking approach. © 2016 The Authors. Software: Practice and Experience published by John Wiley & Sons Ltd.     

Embedding OWA under preference ranking for DEA cross-efficiency aggregation: Issues and procedures

Cross-efficiency (CE) evaluation is an extension of data envelopment analysis (DEA) used for fully ranking decision-making units (DMUs). The ranking process is normally performed on the matrix of CE scores. An ultimate efficiency score is computed for each DMU through an adequate amalgamation process. The preference ranking approach can be seen as an amalgamation technique based on the rank orders of the CE scores. In this paper, we review this approach by putting more emphasis on the aggregation aspect. We highlight the zero vote issue and we show that the latter has been neglected in the extant aggregation procedures. Consequently, we develop two ordered weighted averaging (OWA)-based procedures that attempt to meet effectively the requirements of an aggregation mechanism while exploiting the positive properties of the preference-ranking approach. The merits of the proposed procedures are evaluated on a sample of manufacturing systems by considering, for OWA weights generation, different OWA models with different orness degrees.     

Using the nonhomogeneous frontier two‐stage DEA model to assess the efficiencies of expense utilization and operation of the Taiwanese hotel industry

In conventional multistage data envelopment analysis (DEA) studies, different hotel types are mostly assumed to be in a single technology set. However, the assumption that a single technology can have multiple operating types has been criticized by researchers in the past. To overcome this shortcoming, the main propose of this study is to establish a combination of the models of Tone and Chen and Zhu in order to assess the efficiencies of two hotel types. We first provide evidence that there is an existing defect arising from the direct combination of the two models. The nonhomogeneous two‐stage model is established to evaluate the operational and expense utilization efficiencies for the Taiwanese international tourist hotels. The results verify that the defect from the direct combination of these models can be corrected by the new model. Empirical evaluation reveals that independent hotels have higher expense utilization efficiency and chain hotels have higher operational efficiency. The evaluation also indicates that tourist hotels can achieve best practices through a mutual learning strategy.