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.     

A study of optimal weights of Data Envelopment Analysis - Development of a context-dependent DEA-R model

The weight is one of the main issues of Data Envelopment Analysis (DEA), and relevant theoretical research indicates that many DEA mathematical models include redundant restraints on weight, resulting in underestimated efficiency, pseudo inefficiency, and difficulty in representing specific Input/Output relationships. This study proposes a context-dependent DEA-R model to address shortcomings resulting from redundant restraints on the weights of an efficient decision making unit (DMU), and converts the optimal weight to analyze the influences of redundant restraints on weights. The evaluation results of Taiwan medical centers show that the efficiency of the DMU is underestimated and pseudo inefficiency may occur due to redundant restraints on weight. Moreover, optimal weights are used as variables to conduct cluster analysis in order to determine the information of the weights. The results of cluster analysis indicate that it can assist DMUs in understanding the relationships between DMUs, and contribute to the development of a unique survival strategy for hospitals.     

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 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.     

A DEA‐based method of allocating the fixed cost as a complement to the original input

This paper focuses on the problem of how to divide a fixed cost as a complement to an original input among decision‐making units (DMUs) equitably. Using the data envelopment analysis (DEA) technique, this paper concerns the problem from the perspective of efficiency analysis. It is found that not all DMUs can become efficient under common weights if a low enough fixed cost is assigned. Therefore, the global modified additive DEA (MAD) model is introduced. By optimizing the global MAD‐efficiency, a new allocation method and the corresponding algorithm to ensure the uniqueness of the allocation result is designed. The proposed method can be used under both constant returns to scale and variable returns to scale for nonnegative data; it is suitable for the situation where the costs play a great role in the production of DMUs. Numerical results show the validity and advantages of our method.     

Online banking performance evaluation using data envelopment analysis and principal component analysis

This paper presents a hybrid approach to conducting performance measurements for Internet banking by using data envelopment analysis (DEA) and principal components analysis (PCA). For each bank, DEA is applied to compute an aggregated efficiency score based on outputs, such as web metrics and revenue; and inputs, such as equipment, operation cost and employees. The 45 combinations of DEA efficiencies of the studied banks are calculated, and used as a ranking mechanism. PCA is used to apply relative efficiencies among the banks, and to classify them into different groups in terms of operational orientations, i.e., Internet banking and cost efficiency focused orientations. Identification of operational fitness and business orientation of each firm, in this way, will yield insights into understanding the weaknesses and strengths of banks, which are considering moving into Internet banking.     

Duality and efficiency computations in the cost efficiency model with price uncertainty

The calculation of cost efficiency requires complete and accurate information on the input prices at each decision making unit (DMU). In practice, however, exact knowledge of the relevant prices is difficult to come by, and prices may be subject to variation in the short term. To estimate the cost efficiency while taking price uncertainty into account, cone-ratio DEA models incorporating the available price information as weight restrictions can be applied. However, the literature lacks a clear explanation regarding the exact relationships between these two models. In this paper, through a duality study, we establish both the theoretical properties of these relationships and the characteristics of their efficiency solutions between cone-ratio DEA models and CE models, assuming there are imprecise price data. Based on the duality study, we also develop a new approach and design a lexicographic order algorithm to estimate the lower bounds of the cost efficiency measure. Our computational experiments indicate that the proposed models are robust and that the proposed algorithm is computationally simple.     

A study of the relative efficiency of Chinese ports: a financial ratio‐based data envelopment analysis approach

Abstract: This research examines the relative efficiency of 11 major Chinese ports by using an innovative adopted version of Data Envelopment Analysis (DEA). DEA is a non‐parametric approach to weigh the inputs/outputs and measure the relative efficiency of decision‐making units. This paper adopts an output‐oriented version of DEA based on financial ratios in which no inputs are utilized. The new adopted DEA model provides a rounded judgement on port efficiency taking into consideration multiple financial ratios simultaneously and combining them into a single measure of efficiency. The mathematical model is solved for every port, and the relative efficiency of each port is determined. The results of DEA show that the higher a port's efficiency ratio in relation to the corresponding ratio of another port, the higher the efficiency of this port. Finally, suggestions based on the data analysis are provided for managerial decision makers to improve the areas needed for port operating efficiency.     

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.     

A Review of Energy-Related Cost Issues and Prediction Models in Cloud Computing Environments

With the expansion of cloud computing, optimizing the energy efficiency and cost of the cloud paradigm is considered significantly important, since it directly affects providers’ revenue and customers’ payment. Thus, providing prediction information of the cloud services can be very beneficial for the service providers, as they need to carefully predict their business growths and efficiently manage their resources. To optimize the use of cloud services, predictive mechanisms can be applied to improve resource utilization and reduce energy-related costs. However, such mechanisms need to be provided with energy awareness not only at the level of the Physical Machine (PM) but also at the level of the Virtual Machine (VM) in order to make improved cost decisions. Therefore, this paper presents a comprehensive literature review on the subject of energy-related cost issues and prediction models in cloud computing environments, along with an overall discussion of the closely related works. The outcomes of this research can be used and incorporated by predictive resource management techniques to make improved cost decisions assisted with energy awareness and leverage cloud resources efficiently.     

Increasing discrimination of DEA evaluation by utilizing distances to anti-efficient frontiers

This paper develops three DEA performance indicators for the purpose of performance ranking by using the distances to both the efficient frontier and the anti-efficient frontier to enhance discrimination power of DEA analysis. The standard DEA models and the Inverted DEA models are used to identify the efficient and anti-efficient frontiers respectively. Important issues like possible intersections of the two frontiers are discussed. Empirical studies show that these indicators indeed have much more discrimination power than that of standard DEA models, and produce consistent ranks. Furthermore, three types of simulation experiments under general conditions are carried out in order to test the performance and characterization of the indicators. The simulation results show that the averages of both the Pearson and Spearman correlation coefficients between true efficiency and indicators are higher than those of true efficiency and efficiency scores estimated by the BCC model when sample size is small.     

An integrated fuzzy regression-data envelopment analysis algorithm for optimum oil consumption estimation with ambiguous data

This study introduces an integrated fuzzy regression (FR) data envelopment analysis (DEA) algorithm for oil consumption estimation and optimization with uncertain and ambiguous data. This is quite important as oil consumption estimations deals with several uncertainties due to social, economic factors. Furthermore, DEA is integrated with FR because there is no clear cut as to which FR approach is superior for oil consumption estimation. The standard indicators used in this paper are population, cost of crude oil, gross domestic production (GDP) and annual oil production. Fifteen popular and most cited FR models are considered in the algorithm. Each FR model has different approach and advantages. The input data is divided into train and test data. The FR models have been tuned for all their parameters according to the train data, and the best coefficients are identified. Center of Average Method for defuzzification output process is applied. For determining the rate of error of FR models estimations, the rate of defuzzified output of each model is compared with its actual rate consumption in test data. The efficiency of 15 FR models is examined by the output-oriented Data Envelopment Analysis (DEA) model without inputs by considering three types of relative error: RMSE, MAE and MAPE. The applicability and superiority of the proposed algorithm is shown for monthly oil consumption of Canada, United States, Japan and Australia from 1990 to 2005.     

Two-stage DEA: An application to major Brazilian banks

Although banking has been widely studied using standard DEA (Data Envelopment Analysis) models and its variations, these models do not in fact account for the internal structure relative to measures characterizing banking operations performance. In this paper, efficiency in Brazilian banking is measured using a two-stage process. In the first stage, called cost efficiency, number of branches and employees are used to attain a certain level of administrative and personnel expenses per year. In the second stage, called productive efficiency, these expenses allow the consecution of two important net outputs: equity and permanent assets. The network-DEA centralized efficiency model is adopted here to optimize both stages simultaneously. Results indicate that Brazilian banks are heterogeneous, with some focusing on cost efficiency and others on productive efficiency. Furthermore, cost efficiency is explained by M&A and size, while productive efficiency is explained by M&A and public status. Policy implications for the Brazilian banking sector are also derived.     

A comparison of DEA and the stochastic frontier model using panel data

Two competing approaches for the measurement of efficiency are the stochastic frontier model and data envelopment analysis (DEA). Previous research has established that the two models applied to cross‐sectional data are both adversely affected by measurement error. While the cross‐sectional stochastic frontier model does not effectively handle statistical noise, panel data models do. This is true because additional information from multiple time periods is incorporated into the estimation. A panel data DEA model that uses averaged data has been shown to effectively smooth out measurement error. In this paper, we compare the panel data models using simulated data.     

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.     

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.     

Modeling fuzzy data envelopment analysis by parametric programming method

Data envelopment analysis (DEA) is a methodology for measuring the relative efficiency of decision making units (DMUs) consuming the same types of inputs and producing the same types of outputs. This paper studies the DEA models with type-2 data variations. In order to deal with the existed type-2 fuzziness, we propose the mean reduction methods for type-2 fuzzy variables. Based on the mean reductions of the type-2 fuzzy inputs and outputs, we formulate a new class of fuzzy generalized expectation DEA models. When the inputs and outputs are mutually independent type-2 triangular fuzzy variables, we discuss the equivalent parametric forms for the constraints and the generalized expectation objective, where the parameters characterize the degree of uncertainty of the type-2 fuzzy coefficients so that the information cannot be lost via our reduction method. For any given parameters, the proposed model becomes nonlinear programming, which can be solved by standard optimization solvers. To illustrate the modeling idea and the efficiency of the proposed DEA model, we provide one numerical example.     

Measurement efficiency and productivity in SAS/OR

This paper explores the use of the optimisation procedures in SAS/OR software with application to the measurement of efficiency and productivity of decision-making units (DMUs) using data envelopment analysis (DEA) techniques. DEA was originally introduced by Charnes et al. [J. Oper. Res. 2 (1978) 429] is a linear programming method for assessing the efficiency and productivity of DMUs. Over the last two decades, DEA has gained considerable attention as a managerial tool for measuring performance of organisations and it has widely been used for assessing the efficiency of public and private sectors such as banks, airlines, hospitals, universities and manufactures. As a result, new applications with more variables and more complicated models are being introduced.Further to successive development of DEA a non-parametric productivity measure, Malmquist index, has been introduced by Fare et al. [J. Prod. Anal. 3 (1992) 85]. Employing Malmquist index, productivity growth can be decomposed into technical change and efficiency change.On the other hand, the SAS is a powerful software and it is capable of running various optimisation problems such as linear programming with all types of constraints. To facilitate the use of DEA and Malmquist index by SAS users, a SAS/MALM code was implemented in the SAS programming language. The SAS macro developed in this paper selects the chosen variables from a SAS data file and constructs sets of linear-programming models based on the selected DEA. An example is given to illustrate how one could use the code to measure the efficiency and productivity of organisations.     

Target setting with minimum improving costs in data envelopment analysis: A mixed integer linear programming approach

This study addresses a problem called cost‐minimizing target setting in data envelopment analysis (DEA) methodology. The problem is how to make an inefficient decision‐making unit efficient by allocating to it as few organizational resources as possible, assuming that the marginal costs of reducing inputs or increasing outputs are known and available, which is different from previous furthest and closest DEA targets setting methods. In this study, an existed cost minimizing target setting heuristics approach based on input‐oriented model is examined to show that there exist some limitations. This study develops a simple mixed integer linear programming to determine the desired targets on the strongly efficient frontier based on non‐oriented DEA model considering the situation in the presence of known marginal costs of reducing inputs and increasing outputs simultaneously. Some experiments with the simulated datasets are conducted, and results show that the proposed model can obtain more accurate projections with lower costs compared with those from furthest and closest target setting approaches. Besides, the proposed model can be realistic and efficient in solving cost‐minimizing target setting problem.