Developing an Input Oriented Data Envelopment Analysis Model with Fuzzy Uncertainty in Variables

A traditional DEA (data envelopment analysis) model is useful for estimating the best performances for a successful and a more efficiency DMU (decision-making unit). This study uses a traditional DEA model to estimate the efficiency score of bank z in Taiwan and get a good efficiency score based on the 2006 data, however the bank z was taken over by the government in early 2007. In illustrating this paradox phenomenon, the study reconsiders the tradition DEA model by contributing a worst-practice frontier under a traditional DEA model. Findings: the bank z is located on the intersection of the worst-practice frontier and the traditional DEA model frontier. This study provides a critical determinant of a bank’s failure that a bank has a location such as the bank z.

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) allows evaluation of the relative efficiencies of similar entities, known as decision making units (DMUs), which consume the same types of resources and offer similar types of products. It is known that under certain circumstances, when the number of DMUs does not meet the DEA Golden Rule, that is, this number is not sufficiently large compared to the total number of inputs and outputs, traditional DEA models often yield solutions that identify too many DMUs as efficient. In fact, this weak discrimination power and unrealistic weight distribution presented by DEA models remain a major challenge, leading to the development of models to improve this performance, such as: multiple criteria data envelopment analysis (MCDEA), bi-objective multiple criteria data envelopment analysis, goal programming approaches to solve weighted goal programming (WGP–MCDEA) and extended–MCDEA. This paper proposes a new MCDEA model which is based on goal programming, with and without super efficiency concepts, and presents test results that show its advantages over the above cited models. A set of problems from the literature and real-world applications are used in these tests. The results show that the new MCDEA model provides better discrimination of DMUs in all tested problems, and provides a weight dispersion that is statistically equal to that obtained by other MCDEA models. An additional feature of the proposed model is that it allows the identification of the input and output variables that are most important to the problem, to make it easier for the decision maker to improve the efficiency of the DMUs involved. This is very useful in practice, because in general, the available resources are scarce, so it is a further advantage of the proposed MCDEA model over the others tested.

Purpose The purpose of this paper is to provide an outline of the major contributions in the literature on the determination of the least distance in data envelopment analysis (DEA). The focus herein is primarily on methodological developments. Specifically, attention is mainly paid to modeling aspects, computational features, the satisfaction of properties and duality. Finally, some promising avenues of future research on this topic are stated. Design/methodology/approach DEA is a methodology based on mathematical programming for the assessment of relative efficiency of a set of decision-making units (DMUs) that use several inputs to produce several outputs. DEA is classified in the literature as a non-parametric method because it does not assume a particular functional form for the underlying production function and presents, in this sense, some outstanding properties: the efficiency of firms may be evaluated independently on the market prices of the inputs used and outputs produced; it may be easily used with multiple inputs and outputs; a single score of efficiency for each assessed organization is obtained; this technique ranks organizations based on relative efficiency; and finally, it yields benchmarking information. DEA models provide both benchmarking information and efficiency scores for each of the evaluated units when it is applied to a dataset of observations and variables (inputs and outputs). Without a doubt, this benchmarking information gives DEA a distinct advantage over other efficiency methodologies, such as stochastic frontier analysis (SFA). Technical inefficiency is typically measured in DEA as the distance between the observed unit and a “benchmarking” target on the estimated piece-wise linear efficient frontier. The choice of this target is critical for assessing the potential performance of each DMU in the sample, as well as for providing information on how to increase its performance. However, traditional DEA models yield targets that are determined by the “furthest” efficient projection to the evaluated DMU. The projected point on the efficient frontier obtained as such may not be a representative projection for the judged unit, and consequently, some authors in the literature have suggested determining closest targets instead. The general argument behind this idea is that closer targets suggest directions of enhancement for the inputs and outputs of the inefficient units that may lead them to the efficiency with less effort. Indeed, authors like Aparicio et al. (2007) have shown, in an application on airlines, that it is possible to find substantial differences between the targets provided by applying the criterion used by the traditional DEA models, and those obtained when the criterion of closeness is utilized for determining projection points on the efficient frontier. The determination of closest targets is connected to the calculation of the least distance from the evaluated unit to the efficient frontier of the reference technology. In fact, the former is usually computed through solving mathematical programming models associated with minimizing some type of distance (e.g. Euclidean). In this particular respect, the main contribution in the literature is the paper by Briec (1998) on Hölder distance functions, where formally technical inefficiency to the “weakly” efficient frontier is defined through mathematical distances. Findings All the interesting features of the determination of closest targets from a benchmarking point of view have generated, in recent times, the increasing interest of researchers in the calculation of the least distance to evaluate technical inefficiency (Aparicio et al., 2014a). So, in this paper, we present a general classification of published contributions, mainly from a methodological perspective, and additionally, we indicate avenues for further research on this topic. The approaches that we cite in this paper differ in the way that the idea of similarity is made operative. Similarity is, in this sense, implemented as the closeness between the values of the inputs and/or outputs of the assessed units and those of the obtained projections on the frontier of the reference production possibility set. Similarity may be measured through multiple distances and efficiency measures. In turn, the aim is to globally minimize DEA model slacks to determine the closest efficient targets. However, as we will show later in the text, minimizing a mathematical distance in DEA is not an easy task, as it is equivalent to minimizing the distance to the complement of a polyhedral set, which is not a convex set. This complexity will justify the existence of different alternatives for solving these types of models. Originality/value As we are aware, this is the first survey in this topic.

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.

Data envelopment analysis (DEA) has been commonly used in the energy saving of enterprise plants. Nevertheless, when the traditional DEA model analyzes the effectiveness of decision-making units (DMUs), over 1/3 of the DMUs’ efficiency values are 1, so the traditional DEA model cannot distinguish the cons and pros of the DMUs. And although the DEA cross-model(DEACM) is able to differentiate the cons as well as pros of the effective DMUs, it can’t obtain the improvement direction of the ineffective DMUs. Therefore, an energy saving and management method based on an improved DEACM, which can use the higher efficiency distinction to identify the efficiency state of the DMUs, is proposed in this paper. Meanwhile, the improvement direction of the ineffective DMU can be found by the self-evaluation of the improved DEACM. Finally, the improved DEACM is utilized to save and manage the energy configuration of the PTA solvent system in the industrial process. The experimental results reveal that the practicality and effectiveness of the proposed method are verified, and in addition, the efficiency discrimination is well. Moreover, the proposed model can find the direction of the quantitative targets of energy saving to improve the energy efficiency of PTA production.

Information technology (IT) is defined as the obtainment, procedure, storage and propagation of sounding, drawing, and textual information by combining microelectronics-based computing and telecommunications. Nowadays, IT is starting to spread further from the conventional personal computer and network technologies to integrations of other fields of technology such as the use of cell phones, televisions, automobiles, etc. In other words, IT has penetrated in daily life of human beings and become one part of the whole society. The importance of IT has become momentous. Therefore, to understand the performance of efficiency and productivity of the IT firms is critical for managers as well as for personal investors. Until now, there are very few researches tried to analyze final performance of the IT firms. As a result, this research intends to use traditional Data Envelopment Analysis (DEA) CCR or BCC models to evaluate the performance of IT firms. The Decision Making Units (DMUs) on this research are chosen from IT firms in S&P 500. However, the traditional DEA models are not fair models from the aspect of improper weight derivations. Thus, this paper intends to analyze the efficiency of IT firms in S&P 500 efficiencies by using multiple objective programming (MOP) based Data Envelopment Analysis (DEA). In a MOP based DEA approach, DMUs will be evaluated based on an equal standard and the results will be evaluated more fairly. The world’s leading IT firms in S&P 500 will be evaluated based on publicly available financial reports of the fiscal year 2010. In addition, the newly developed MOP can improve the traditional DEA’s unfair weights problems and benchmark the efficiency of IT firms in S&P 500 correctly. In the empirical study, the MOP based DEA demonstrated that F5 Networks should be the communications equipment companies of IT worthwhile to be invested. In the future, performance evaluation results can be served as foundations for investment strategies definition.KeywordsInformation Technology (IT)Standard and Poor’s 500 indexPerformance EvaluationData Envelopment Analysis (DEA)Multiple Objective Programming (MOP)

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.

Data envelopment analysis (DEA) with considering the best condition for each decision making unit (DMU) assesses the relative efficiency for it and divides a homogenous group of DMUs into two categories: efficient and inefficient, but traditional DEA models can not rank efficient DMUs. Although some models were introduced for ranking efficient DMUs, Franklin Lio & Hsuan peng (2008), proposed a common weights analysis (CWA) approach for ranking them. These DMUs are ranked according to the efficiency score weighted by the common set of weights and shadow prices. This study shows there are some cases that shadow prices of efficient DMUs are equal, hence this method is not applicable for ranking them. Next, we propose a new method for ranking units with equal shadow prices.

The primary objective of this research is to develop more reliable portfolios by accurately calculating risk and return, emphasizing a secure asset weighting strategy. We employ the DEA bootstrap method and the SPP-CVaR (Stop-Profit Point-Conditional Value at Risk) methodology to achieve this objective. Previous scholarly research often lacks a robust statistical foundation for evaluating asset performance, particularly regarding sustainability, as traditional approaches rely on single data samples. Additionally, many studies fail to account for the relevance of risk and return until the investor exits the market. We introduce a new approach focusing on exit time to evaluate sustainable investments to address this gap. We employ data envelopment analysis (DEA) to assess the performance of these assets, comparing results from both the DEA bootstrap method and traditional DEA models. Our DEA models incorporate SPP-CVaR (Conditional Value at Risk) as a measure of risk and mean return as the output variable, both calculated until the investor exits the market. Traditional DEA models have limitations in statistical interpretation, so we enhance our analysis with the DEA bootstrap method. This method involves resampling data to create multiple samples, offering a distribution of performance measures for each asset and providing a more comprehensive understanding of asset performance and uncertainty. By comparing the bootstrap and results of conventional methods, we demonstrate the advantages of using statistical techniques to evaluate and compare financial assets. The SPP-CVaR is calculated by deriving and converting the risk-neutral density, simulating price paths, and identifying stop-profit points. We then analyze the exit time and price distributions to compute the SPP-CVaR for each stop-profit point. The value of this study lies in its integration of sustainability analysis with risk measures, helping investors build profitable and ethically aligned portfolios. By providing a detailed assessment of an asset's sustainability profile, our approach assists investors in making informed decisions that align with their financial and ethical goals.

The appreciative democratic voice of DEA: A case of faculty academic performance evaluation

Efficiency evaluation based on data envelopment analysis in the big data context

Background:The Integrated Child Development Services (ICDS) scheme was launched in 1975 for the improvement in maternal and child health and nutrition. The services under ICDS are implemented through Anganwadi centers (AWCs) and are delivered by Anganwadi workers (AWWs) at grassroots level. To evaluate the efficiency of all AWCs located in the field practice area of the medical college in North India, using data envelopment analysis (DEA) technique.Materials and Methods:A cross-sectional study was conducted in the catchment area of rural health training center. Each of the 15 AWCs was considered a decision-making unit (DMU), and physical structure and logistics were included as input variables; and percentage of beneficiaries receiving supplementary nutrition and health checkups were included as output variables. DEA technique was used to calculate the efficiency score for each DMU with the help of DEAOS free online software.Results:DMU 14th was found to be most efficient (100%) and DMU second was the least efficient (45%). DMU 13 and 14 demonstrated a level of performance that is superior to all other DMUs. DMU 13th and 14th were, therefore, considered 100% efficient. DEA analysis showed that total output increases and/or input reductions were required for making the inefficient DMUs efficient.Conclusion:Most of the AWCs were inefficient and an improvement in the infrastructure and logistics is likely to improve the efficiency of AWCs.

One of the weak points of DEA (Data Envelopment Analysis) models indicated in literature[1,2] is their sensitivity to variable measurement errors. The occurrence of data interference, whichis the basis of the productivity analysis, may distort the classification of the units and may causemisjudgement of their effectiveness.In the article the results of simulation concerning the DEA models sensitivity to occurrence andfeatures of random element in the monitored variables describing the model are presented.The set of thirty DMU (Decision Making Units) described by the means of three inputvariables, two output variables and one environmental variable was analysed. On the basis of thedetermined initial value of all the kinds of variables for each DMU, their relative effectiveness andtheir ranking were determined. Then, the value of each variable was interfered randomly with thenoise with normal distribution N(m,σ) and once again relative effectiveness and ranking of DMUwere determined. The calculation was done repeatedly, taking into account different levels ofvariance. The simulation carried out in the described manner was the basis for the assessment ofthe stability of the classification with the occurrence of measurement errors.On the basis of the research, the limits of DEA models resistance to the occurrence of errors inthe data that are used for productivity analysis were determined.In the authors’ opinion, the proposals in the article may be recognised as a vital input for thedevelopment of the methodology of comparative productivity analysis by the means of DEAmodels.

One of the major concerns in healthcare management is the optimal allocation of staffing and resources. The global crisis created by the COVID-19 Pandemic has created extreme strains both on the staffing and the resources available to the healthcare systems. It has geometrically added to the number of patients seeking health services. In addition, the Pandemic has dramatically increased the rate of mortality in the hospitals in an unprecedented way. Therefore, in this research, in order not to sacrifice the quality of the services provided, we have used Data Envelopment Analysis (DEA) model to determine the efficiency of the emergency departments in the hospitals and the possible improvements that could be made to them. As traditional DEA models do not seek to reduce the undesirable outputs and increase the undesirable inputs, in addition to determining the efficiency of decision making units (DMU) despite some undesirable input components, the effect of these units on performance is investigated. To this end, considering the problem assumptions, first, a set of proper production possibilities is defined. Finally, a new method is introduced to determine the system’s performance in the presence of some undesirable input components. The impact of undesirable components on determining efficiency is specified, and a real example is provided consisting of emergency rooms in 30 hospitals, in which five desirable inputs and four desirable outputs along with one undesirable input are considered. The example is solved using the presented model, and the efficiency scores are determined.