Ranking decision making units by imposing a minimum weight restriction in the data envelopment analysis

It has been widely recognized that data envelopment analysis (DEA) lacks discrimination power to distinguish between DEA efficient units. This paper proposes a new methodology for ranking decision making units (DMUs). The new methodology ranks DMUs by imposing an appropriate minimum weight restriction on all inputs and outputs, which is decided by a decision maker (DM) or an assessor in terms of the solutions to a series of linear programming (LP) models that are specially constructed to determine a maximin weight for each DEA efficient unit. The DM can decide how many DMUs to be retained as DEA efficient in final efficiency ranking according to the requirement of real applications, which provides flexibility for DEA ranking. Three numerical examples are investigated using the proposed ranking methodology to illustrate its power in discriminating between DMUs, particularly DEA efficient units.     

Adding and removing an attribute in a DEA model: theory and processing

We present a theoretical and computational study of the impact of inserting a new attribute and removing an old attribute in a data envelopment analysis (DEA) model. Our objective is to obviate a portion of the computational effort needed to process such model changes by studying how the efficient/inefficient status of decision-making units (DMUs) is affected. Reducing computational efforts is important since DEA is known to be computationally intensive, especially in large-scale applications. We present a comprehensive theoretical study of the impact of attribute insertion and removal in DEA models, which includes sufficient conditions for identifying efficient DMUs when an attribute is added and inefficient DMUs when an attribute is removed. We also introduce a new procedure, HyperClimb, specially designed to quickly identify some of the new efficient DMUs, without involving LPs, when the model changes with the addition of an attribute. We report on results from computational tests designed to assess this procedure's effectiveness.     

Estimating consumers' willingness to pay for individual quality attributes with DEA

In a highly competitive environment, a product's commercial success depends increasingly more upon the ability to satisfy consumers' preferences that are highly diversified. Since a product typically comprises a host of technological attributes, its market value incorporates all of the individual values of technological attributes. If the willingness-to-pay (WTP) for individual quality attributes of a product is known, one can conjecture the overall WTP or the imputed market price for the product. The market price listed by the producer has to be equal to or lower than this WTP for the commercial survival of the product. In this paper, we propose a methodology for estimating the value of individual product characteristics and thus the overall WTP of the product with DEA. Our methodology is based on a model derived from consumer demand theory on the one hand, and the recent developments in DEA on the other hand. The paper also presents a real case study for the mobile phone market, which is characterized by its high speed of innovation. On the theoretical side, we expect our framework to provide a possibility of combining DEA and consumer demand theory. We also expect that the empirical application will shed some light on the nature of the process of product differentiation based on consumers' valuation.     

A new methodology for evaluating sustainable product design performance with two-stage network data envelopment analysis

Sustainable product design has been considered as one of the most important practices for achieving sustainability. To improve the environmental performances of a product through product design, however, a firm often needs to deal with some difficult technical trade-offs between traditional and environmental attributes which require new design concepts and engineering specifications. In this paper, we propose a novel use of the two-stage network Data Envelopment Analysis (DEA) to evaluate sustainable product design performances. We conceptualize “design efficiency” as a key measurement of design performance in terms of how well multiple product specifications and attributes are combined in a product design that leads to lower environmental impacts or better environmental performances. A two-stage network DEA model is developed for sustainable design performance evaluation with an “industrial design module” and a “bio design module.” To demonstrate the applications of our DEA-based methodology, we use data of key engineering specifications, product attributes, and emissions performances in the vehicle emissions testing database published by the US EPA to evaluate the sustainable design performances of different automobile manufacturers. Our test results show that sustainable design does not need to mean compromise between traditional and environmental attributes. Through addressing the interrelatedness of subsystems in product design, a firm can find the most efficient way to combine product specifications and attributes which leads to lower environmental impacts or better environmental performances. This paper contributes to the existing literature by developing a new research framework for evaluating sustainable design performances as well as by proposing an innovative application of the two-stage network DEA for finding the most eco-efficient way to achieve better environmental performances through product design.     

Network-based method for ranking of efficient units in two-stage DEA models

This study presents a methodology that is able to further discriminate the efficient decision-making units (DMUs) in a two-stage data envelopment analysis (DEA) context. The methodology is an extension of the single-stage network-based ranking method, which utilizes the eigenvector centrality concept in social network analysis to determine the rank of efficient DMUs. The mathematical formulation for the method to work under the two-stage DEA context is laid out and then applied to a real-world problem. In addition to its basic ranking function, the exercise highlights two particular features of the method that are not available in standard DEA: suggesting a benchmark unit for each input/intermediate/output factor, and identifying the strengths of each efficient unit. With the methodology, the value of DEA greatly increases.     

A new integrated DEA model for finding most BCC-efficient DMU

In many applications of widely recognized technique, DEA, finding the most efficient DMU is desirable for decision maker. Using basic DEA models, decision maker is not able to identify most efficient DMU. Amin and Toloo [Gholam R. Amin, M. Toloo, Finding the most efficient DMUs in DEA: an improved integrated model. Comput. Ind. Eng. 52 (2007) 71–77] introduced an integrated DEA model for finding most CCR-efficient DMU. In this paper, we propose a new integrated model for determining most BCC-efficient DMU by solving only one linear programming (LP). This model is useful for situations in which return to scale is variable, so has wider range of application than other models which find most CCR-efficient DMU. The applicability of the proposed integrated model is illustrated, using a real data set of a case study, which consists of 19 facility layout alternatives.     

An epsilon-free approach for finding the most efficient unit in DEA

Data envelopment analysis (DEA), considering the best condition for each decision making unit (DMU), assesses the relative efficiency and partitions DMUs into two sets: efficient and inefficient. Practically, in traditional DEA models more than one efficient DMU are recognized and these models cannot rank efficient DMUs. Some studies have been carried out aiming at ranking efficient DMUs, although in some cases only discrimination of the most efficient unit is desirable. Furthermore, several investigations have been done for finding the most CCR-efficient DMU. The basic idea of the majority of them is to introduce an integrated model which achieves an optimal common set of weights (CSW). These weights help us identify the most efficient unit in an identical condition.     

Applying inverse DEA and cone constraint to sensitivity analysis of DMUs with undesirable inputs and outputs

In this paper, the inverse data envelopment analysis (DEA) with the preference of cone constraints will be discussed in a way that in the decision-making units, the undesirable inputs and outputs exist simultaneously. Supposing that the efficiency level does not change, if the unit under assessment increases the level of the desirable outputs and decreases the level of the undesirable outputs, how will it affect the amount of the desirable input level and the undesirable input level? To answer this question, the application of the inverse DEA with preference of cone constraints is suggested. The suggested approach, while maintaining the efficiency level, increases the level of its undesirable input and decreases the level of its desirable input by selection of strongly efficient solutions or some weakly efficient solutions of the multiple objective linear programming (MOLP) model. While maintaining the efficiency level, the suggested approach by selection of strongly efficient solution or some of the weakly efficient solutions of the MOLP model can increase the undesirable input level and decrease the desirable input level. Similarly, the suggested approach can be applied if the decision-making unit increases its undesirable input level and decreases the desirable input level so that the undesirable output level decreases and the desirable output level increases while maintaining the efficiency level. As an illustration, two numerical examples are rendered.     

In the determination of weight sets to compute cross-efficiency ratios in DEA

Data envelopment analysis (DEA) measures the production performance of decision-making units (DMUs) which consume multiple inputs and produce multiple outputs. Although DEA has become a very popular method of performance measure, it still suffers from some shortcomings. For instance, one of its drawbacks is that multiple solutions exist in the linear programming solutions of efficient DMUs. The obtained weight set is just one of the many optimal weight sets that are available. Then why use this weight set instead of the others especially when this weight set is used for cross-evaluation? Another weakness of DEA is that extremely diverse or unusual values of some input or output weights might be obtained for DMUs under assessment. Zero input and output weights are not uncommon in DEA. The main objective of this paper is to develop a new methodology which applies discriminant analysis, super-efficiency DEA model and mixed-integer linear programming to choose suitable weight sets to be used in computing cross-evaluation. An advantage of this new method is that each obtained weight set can reflect the relative strengths of the efficient DMU under consideration. Moreover, the method also attempts to preserve the original classificatory result of DEA, and in addition this method produces much less zero weights than DEA in our computational results.     

Equivalences between Data Envelopment Analysis and the theory of redundancy in linear systems

This paper establishes how the non-parametric frontier estimation methodology of Data Envelopment Analysis (DEA) and the classical problem of detecting redundancy in a system of linear inequalities are connected. We present an analysis of the sets generated in two of DEA's models from where the empirical efficient production frontier is established from the point of view of polyhedral set theory. This yields convenient alternative characterizations of these sets which provide new insights about their properties. We use these insights to show how these polyhedral sets connect DEA to redundancy in linear systems. This means that DEA can benefit from a rich and well-established collection of computational and theoretical results which apply directly from redundancy in linear systems.     

Benchmark optimization and attribute identification for improvement of container terminals

The aim of this paper is to optimize the benchmarks and prioritize the variables of decision-making units (DMUs) in data envelopment analysis (DEA) model. In DEA, there is no scope to differentiate and identify threats for efficient DMUs from the inefficient set. Although benchmarks in DEA allow for identification of targets for improvement, it does not prioritize targets or prescribe level-wise improvement path for inefficient units. This paper presents a decision tree based DEA model to enhance the capability and flexibility of classical DEA. The approach is illustrated through its application to container port industry. The method proceeds by construction of multiple efficient frontiers to identify threats for efficient/inefficient DMUs, provide level-wise reference set for inefficient terminals and diagnose the factors that differentiate the performance of inefficient DMUs. It is followed by identification of significant attributes crucial for improvement in different performance levels. The application of this approach will enable decision makers to identify threats and opportunities facing their business and to improve inefficient units relative to their maximum capacity. In addition, it will help them to make intelligent investment on target factors that can improve their firms’ productivity.     

A double-frontier approach for measuring market imperfection

This paper proposes a new methodology for evaluating the market imperfection and the bargaining power of each agent acting on a given market. The new methodology is an extension of DEA to the two frontiers case with respect to a privileged direction. A particular attention is paid to the treatment of bidirectional free disposability. This model is motivated by the analysis of survey data consisting of a set of contracts described in the space of price and attributes.     

A new data envelopment analysis method for priority determination and group decision making in the analytic hierarchy process

The DEAHP method for weight deviation and aggregation in the analytic hierarchy process (AHP) has been found flawed and sometimes produces counterintuitive priority vectors for inconsistent pairwise comparison matrices, which makes its application very restrictive. This paper proposes a new data envelopment analysis (DEA) method for priority determination in the AHP and extends it to the group AHP situation. In this new DEA methodology, two specially constructed DEA models that differ from the DEAHP model are used to derive the best local priorities from a pairwise comparison matrix or a group of pairwise comparison matrices no matter whether they are perfectly consistent or inconsistent. The new DEA method produces true weights for perfectly consistent pairwise comparison matrices and the best local priorities that are logical and consistent with decision makers (DMs)’ subjective judgments for inconsistent pairwise comparison matrices. In hierarchical structures, the new DEA method utilizes the simple additive weighting (SAW) method for aggregation of the best local priorities without the need of normalization. Numerical examples are examined throughout the paper to show the advantages of the new DEA methodology and its potential applications in both the AHP and group decision making.     

A distance-based measure of super efficiency in data envelopment analysis: an application to gas companies

Conventional data envelopment analysis (DEA) assists decision makers in distinguishing between efficient and inefficient decision making units (DMUs) in a homogeneous group. Standard DEA models can not provide more information about efficient units. Super-efficiency DEA models can be used in ranking the performance of efficient DMUs and overcome this obstacle. Because of the possible infeasibility, the use of super efficiency models has been restricted. This research proposes a methodology to determine a distance-based measure of super-efficiency. The proposed methodology overcomes the infeasibility problem of the existing ranking methodologies. The applicability of the proposed model is illustrated in the context of the analysis of gas companies?? performance.     

Separating managerial inefficiency and external conditions in data envelopment analysis

In this paper, we highlight the importance of appropriately dealing with non-controllable inputs in technical efficiency evaluations by using DEA. In order to do this, the two most important options that exclusively use DEA methodology for the incorporation of these variables – the one-stage model by Banker and Morey [Operations Research 34(4) (1986a) 513] and the three-stage method developed by Fried and Lovell [Searching the Zeds, Working paper presented at II Georgia Productivity Workshop, 1996] – are compared both methodologically and empirically. At the same time, we propose a modification to the latter model which allows us to improve its results and interpretation. The education sector has been selected for the empirical application, the reason being that it has the desirable feature that, in the productive process, the students' socio-economic and family status (a non-controllable input) has a direct influence on the school results.The results obtained show the superiority of the multi-stage approach. It is argued that the model developed by Banker and Morey does not deal appropriately with inefficient units, as producer's behaviour in this model does not reflect the objective situation faced by such DMUs.     

Data envelopment analysis for environmental assessment: Comparison between public and private ownership in petroleum industry

Environmental assessment recently becomes a major policy issue in the world. This study discusses how to apply Data Envelopment Analysis (DEA) for environmental assessment. An important feature of the DEA environmental assessment is that it needs to classify outputs into desirable (good) and undesirable (bad) outputs because private and public entities often produce not only desirable outputs but also undesirable outputs as a result of their production activities. This study proposes the three types of unification for DEA environmental assessment by using non-radial DEA models. The first unification considers both an increase and a decrease in the input vector along with a decrease in the direction vector of undesirable outputs. This type of unification measures “unified efficiency”. The second unification considers a decrease in an input vector along with a decrease in the vector of undesirable outputs. This type of unification is referred to as “natural disposability” and measures “unified efficiency under natural disposability”. The third unification considers an increase in an input vector but a decrease in the vector of undesirable outputs. This type of unification is referred to as “managerial disposability” and measures “unified efficiency under managerial disposability”. All the unifications increase the vector of desirable outputs. To document their practical implications, this study has applied the proposed approach to compare the performance of national oil firms with that of international oil firms. This study identifies two important findings on the petroleum industry. One of the two findings is that national oil companies under public ownership outperform international oil companies under private ownership in terms of unified (operational and environmental) efficiency and unified efficiency under natural disposability. However, the performance of international oil companies exhibits an increasing trend in unified efficiency. The other finding is that national oil companies need to satisfy the environmental standard of its own country while international oil companies need to satisfy the international standard that is more restricted than the national standards. As a consequence, international oil companies outperform national oil companies in terms of unified efficiency under managerial disposability.     

Validating DEA as a ranking tool: An application of DEA to assess performance in higher education

There is a general interest in ranking schemes applied to complex entities described by multiple attributes. Published rankings for universities are in great demand but are also highly controversial. We compare two classification and ranking schemes involving universities; one from a published report, ‘Top American Research Universities’ by the University of Florida's TheCenter and the other using DEA. Both approaches use the same data and model. We compare the two methods and discover important equivalences. We conclude that the critical aspect in classification and ranking is the model. This suggests that DEA is a suitable tool for these types of studies.     

Evaluation of rejected cases in an acceptance system with data envelopment analysis and goal programming

Some DEA models have been proposed for acceptance or rejection based on a set of cases that have been previously classified. Also, a modified DEA-type linear programming model has been proposed to determine whether a new case must be accepted or rejected, depending on its location on, above, or below the sample frontier. However, these models assume that all attributes that characterize a case are discretionary. This paper extends these results by proposing a model that includes discretionary and non-discretionary attributes (inputs), and more important, a goal program which resembles a modified additive model to determine which characteristics must be changed (and by how much) in order to accept an initially rejected case. A real application is provided to illustrate the potential of the proposed ideas.     

Input–output substitutability and strongly monotonic p-norm least distance DEA measures

In DEA, there are two frameworks for efficiency assessment and targeting: the greatest and the least distance framework. The greatest distance framework provides us with the efficient targets that are determined by the farthest projections to the assessed decision making unit via maximization of the p-norm relative to either the strongly efficient frontier or the weakly efficient frontier. Non-radial measures belonging to the class of greatest distance measures are the slacks-based measure (SBM) and the range-adjusted measure (RAM). Whereas these greatest distance measures have traditionally been utilized because of their computational ease, least distance projections are quite often more appropriate than greatest distance projections from the perspective of managers of decision-making units because closer efficient targets may be attained with less effort. In spite of this desirable feature of the least distance framework, the least distance (in) efficiency versions of the additive measure, SBM and RAM do not even satisfy weak monotonicity. In this study, therefore, we introduce and investigate least distance p-norm inefficiency measures that satisfy strong monotonicity over the strongly efficient frontier. In order to develop these measures, we extend a free disposable set and introduce a tradeoff set that implements input–output substitutability.     

具有阶段最终产出的链式网络DEA模型

针对具有阶段最终产出的链式网络提出了阶段最终产出为期望产出和非期望产出的概念并建立了相应的网络模型.给出了网络决策单元的网络DEA有效性与阶段DEA有效性的关系,给出了判别的充分必要条件.可以判断当网络决策单元不为网络DEA有效时,它在哪个阶段出现了无效率的情况.