Fuzzy efficiency measures in fuzzy DEA/AR with application to university libraries

The primary objective of comparing libraries is to make the top management of the libraries aware that the libraries are not functioning as expected and hence their request for funds and resources to improve performance should be supported. Since larger universities require larger libraries to satisfy higher demand, we concentrate on the comparison of university libraries of different university size in terms of the number of faculty and students. While it is different from the conventional constant ratio method, this approach allows for non-proportionality between the library size and the university size. In other words, the library size need not increase at the same pace as the university. To compare the twenty-four university libraries in Taiwan, we developed a data envelopment analysis (DEA) model based on the concept of Pareto optimality to calculate a score for each library as the basis for comparison. Thus this study by taking into account the size of the university and non-proportionality yields a more informative and meaningful result than previous studies because very small or very large libraries do not have a disproportionate impact.

Relative efficiency of decision making units producing homogeneous outputs can be estimated by data envelopment analysis (DEA) which is a non-parametric technique. Sometimes, different types of efficiencies such as technical (relative) efficiency and effectiveness of services in transport services, or other commodities which cannot be stored, need to be measured simultaneously to fully capture these services’ overall efficiency because of different dimensions of these two measurements. The integrated data envelopment analysis (IDEA) approach simultaneously measures these two efficiency measurements. But can deterministic models be developed to solve the problems that have a different level of uncertainty? The extension of the IDEA approach from deterministic to uncertain situations, where interval numbers illustrate observations, has been proposed in this study. The extension principle is utilised to develop a pair of two-level mathematical programs to compute the upper and lower bounds of the interval service effectiveness (SE) and technical efficiency (TE). The example of intercity bus companies in Iran is applied to illustrate how to calculate the TE, SE, technical effectiveness (TET), and how to derive their relationship when the data is interval.

This study aimed to measure the efficiency scores of 75 dairy buffalo farms in the province of Nueva Ecija, Central Luzon, Philippines, using an input-oriented, variable-return-to-scale Data Envelopment Analysis (DEA) model. The farmer-informants or decision-making units (DMUs) were categorized as smallholders, family modules, and semi-commercial in operations. Personal interviews using structured questionnaires were done to gather various information on the socio-economic and management practices of the DMUs. Output in the form of volume and value of milk produced and inputs such as quantities and costs of biologics, feeds, forage, and labor were also collected and evaluated among individual DMUs. The efficiency scores were computed using PIM-DEA software, which identified fully efficient DMUs lying on the frontier line (scores of 1.0) and those enveloped by it (inefficient DMUs with scores of less than 1.0). The overall mean Technical Efficiency (TE), Allocative Efficiency (AE), and Economic Efficiency (EE) scores among the DMUs were 0.80, 0.81, and 0.65, respectively. Most of the inefficient DMUs were in the smallholder category. In sum, smallholder DMUs classified under low and moderate TE clusters should reduce their inputs by 53.31% and 40.01%, respectively, to become fully efficient. Likewise, higher lambda values among efficient peer DMUs indicate the best practice frontiers that the inefficient peer DMUs can benchmark with. Extension and advisory services can help promote the best management practices of the frontiers to improve the TE, AE, and EE of the inefficient DMUs.

A fuzzy modeling for fuzzy portfolio optimization

A characteristic of data envelopment analysis (DEA) is to allow individual decision-making units (DMUs) to select the factor weights that are the most advantageous for them in calculating their efficiency scores. This flexibility in selecting the weights, on the other hand, deters the comparison among DMUs on a common base. In order to rank all the DMUs on the same scale, this paper proposes a compromise solution approach for generating common weights under the DEA framework. The efficiency scores calculated from the standard DEA model are regarded as the ideal solution for the DMUs to achieve. A common set of weights which produces the vector of efficiency scores for the DMUs closest to the ideal solution is sought. Based on the generalized measure of distance, a family of efficiency scores called ‘compromise solutions’ can be derived. The compromise solutions have the properties of unique solution and Pareto optimality not enjoyed by the solutions derived from the existing methods of common weights. An example of forest management illustrates that the compromise solution approach is able to generate a common set of weights, which not only differentiates efficient DMUs but also detects abnormal efficiency scores on a common base.

Traditional DEA models allow individual decision-making units (DMUs) to arbitrarily determine the weights of all variables to calculate their efficiencies. This flexibility in selecting the weights is a great advantage for many DMUs, but it also brings some defects such as non-uniqueness of weights sets and the appearance of zero-value weights. Different sets of weights to calculate efficiencies violate the requirement that DMUs should be compared on the same base, leading to the efficiency ranking being not accepted by decision-makers. In this paper, we provide a DEA-based approach for obtaining DMUs’ efficiencies, which assumes that DMUs are collective rationality and its objective is to maximise the satisfaction degrees of all the DMUs. Then, we provide a maxmin model and two corresponding algorithms for generating the common set of weights (CSW). Lastly, the proposed approach is applied to the ranking of 17 forest districts and is compared with other methods.

ASPAC Conference on Library Science and University Libraries in Taiwan

Data Envelopment Analysis (DEA) is a nonparametric approach to evaluating the relative efficiency of decision making units (DMUs) that use multiple inputs to produce multiple outputs. An assumption underlying DEA is that all the data assume the form of specific numerical values. In some applications, however, the data may be imprecise. For instance, some of the data may be known only within specified bounds, while other data may be known only in terms of ordinal relations. DEA with imprecise data or, more compactly, the Imprecise Data Envelopment Analysis (IDEA) method developed in this paper permits mixtures of imprecisely- and exactly-known data, which the IDEA models transform into ordinary linear programming forms. This is carried even further in the present paper to comprehend the now extensively employed Assurance Region (AR) concepts in which bounds are placed on the variables rather than the data. We refer to this approach as AR-IDEA, because it replaces conditions on the variables with transformations of the data and thus also aligns the developments we describe in this paper with what are known as cone-ratio envelopments in DEA. As a result, one unified approach, referred to as the AR-IDEA model, is achieved which includes not only imprecise data capabilities but also assurance region and cone-ratio envelopment concepts.

Data Envelopment Analysis (DEA) models with weight restrictions (WRs) have proven valuable for benchmarking and target setting. Although the DEA literature has explored the incorporation of managerial preferences and value judgments regarding the relative worth of inputs and outputs, as well as the establishment of targets in benchmarking contexts, little attention has been devoted to target setting under restricted DEA models. Moreover, despite the significant advances offered by minimum distance models for target establishment, limited research has addressed benchmarking improvement plans that integrate expert opinions and prior knowledge. Some studies have examined minimum distance models constrained to the efficient Assurance Region (AR) frontier, primarily by extending the concept of closest targets under WR. In contrast, this paper develops improvement plans that deviate minimally from the closest target projection obtained from the original, unrestricted DEA model—termed the reference target. This reference target is considered an acceptable “peer” since it requires the least effort for a decision making unit (DMU) to reach optimal performance before incorporating WR. To this end, we developed a mixed-integer linear programming (MILP) model under the assumption of Variable Returns to Scale in DEA. The proposed approach is illustrated through an application to benchmarking the tourism performance of localities in Córdoba, Argentina. The results reveal realistic and achievable improvement plans for the analyzed localities, ensuring that both global efforts are managed and expert-imposed restrictions are satisfied.

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.

Data Envelopment Analysis (DEA) technique is considered one of the most appropriate tool for assessing performance through calculating the technical efficiencies of a collection of related comparable organizations in transforming inputs into outputs. The conventional DEA methods require accurate measurement of both the inputs and outputs. However, the observed values of the input and output data in real-world problems are sometimes imprecise or vague, i.e. fuzzy. Imprecise evaluations may be the result of unquantifiable, incomplete and non-obtainable information. From the literature of fuzzy DEA applications, most if not all developed models considered all input and output variables as fuzzy, through adopting either the traditional DEA model or the output version of the model, and solved using the α-level approach. Accordingly, the main aim of this paper is to develop a Fuzzy Input Oriented DEA Model that considers a mix of both fuzzy and deterministic output and/or input variables to be solved using the α-cut approach. The developed model algorithm is divided into three stages; it starts by defining the membership function for the fuzzy variables (assumed triangular), then finding the α-cuts for the fuzzy variables, and finally calculating the relative efficiency for each decision making unit (DMU). The model is demonstrated through an illustrative example.

Data envelopment analysis (DEA) is a tool for measuring the relative efficiency of decision-making units (DMUs) that perform similar tasks. One of the uses of the DEA is the establishment of benchmarks for inefficient DMUs. These benchmarks play the role of target for inefficient DMUs. However, traditional DEA (TDEA) models fail to rank the efficient DMUs, and as a result, they cannot determine a benchmark for the inefficient DMUs. To overcome this shortcoming, this paper proposes virtual network DEA (NDEA) approach. The proposed method not only ranks the whole inefficient and efficient DMUs but also establishes a virtual benchmark called ideal DMU. The case study demonstrates the applicability of the proposed model.

Productivity and economic efficiency analysis has entered a new phase, since the data envelopment analysis (DEA) introduced a nonparametric method of measuring technical and allocative efficiency. The DEA efficiency models have three most interesting features, which have fostered numerous applications in several disciplines, for example, microeconomics, operations research, and econometrics. The first feature is the specification and estimation of a multi-output multi-input production frontier, which can be estimated without any price information. Second, the production frontiers can be estimated for public sector decision making units (DMUs) with observed input and output data only and every DMU can be compared in terms of its relative efficiency in respect of the whole group comprising all DMUs. Third, if the market data in the form of output and input prices are available, then the DEA model can be used to compute overall cost efficiency and allocative efficiency. Thus a cost frontier can be estimated along with a productive frontier. In a cost frontier, output technical inefficiency indicates the amount by which a firm or DMU can increase output, holding cost constant and input technical inefficiency captures the amount by which a firm can reduce costs, holding output constant.KeywordsData Envelopment AnalysisMutual FundData Envelopment Analysis ModelBalance Growth PathIndustrial OrganizationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

A key issue within the emissions trading system is how tradable emissions permits (TEPs) are initially allocated among a set of entities. This study proposes an approach based on the proportional allocation concept to allocate TEPs among a set of decision making units (DMUs). We firstly deduce a TEP allocation set based on the rule that the TEPs allocated to DMUs should be proportional to their environmental contribution. We then obtain the allocation intervals of DMUs from the set, expressing the allocation as the convex combination between the upper and the lower bound. Finally, we define the satisfaction degree as the coefficient of the convex combination, and propose an algorithm based on the max‐min fairness of satisfaction degrees to obtain a unique TEP allocation plan. To illustrate our approach, we provide the example of how TEPs are allocated among 30 provincial administrative regions in China. Our findings indicate that our allocation method can be helpful for achieving a saving in energy consumption and reducing emissions. In addition, from the data envelopment analysis perspective, the TEP allocation set can ensure that both each individual DMU and the organization as a whole become efficient under a common set of variable weights.

Data envelopment analysis (DEA) is a non-parametric technique for measuring the efficiency of decision making units (DMU) with exact input and output terms. So far, a number of DEA models with interval data have been developed. The radial DEA model such as CCR or BCC model with interval data are well known as basic DEA models with interval data. However, these radial DEA models have some defects. In this study, we develop a new approach based upon the slacks-based measurement (SBM) of super-efficiency model for dealing with interval data in DEA. The SBM super-efficiency DEA model can not only discriminate the performance of efficient DMUs from inefficient ones, but can distinguish between the efficient DMUs. In addition, this model can overcome the drawback that the super-efficiency model can be infeasible under variable returns to scale (VRS) assumption. An illustrative example is provided to verify the idea of this paper and show its potential application and validity.