Alternative mixed integer linear programming models for identifying the most efficient decision making unit in data envelopment analysis

A mixed integer linear model for selecting the best decision making unit (DMU) in data envelopment analysis (DEA) has recently been proposed by Foroughi [Foroughi, A. A. (2011a). A new mixed integer linear model for selecting the best decision making units in data envelopment analysis. Computers and Industrial Engineering, 60(4), 550–554], which involves many unnecessary constraints and requires specifying an assurance region (AR) for input weights and output weights, respectively. Its selection of the best DMU is easy to be affected by outliers and may sometimes be incorrect. To avoid these drawbacks, this paper proposes three alternative mixed integer linear programming (MILP) models for identifying the most efficient DMU under different returns to scales, which contain only essential constraints and decision variables and are much simpler and more succinct than Foroughi’s. The proposed alternative MILP models can make full use of input and output information without the need of specifying any assurance regions for input and output weights to avoid zero weights, can make correct selections without being affected by outliers, and are of significant importance to the decision makers whose concerns are not DMU ranking, but the correct selection of the most efficient DMU. The potential applications of the proposed alternative MILP models and their effectiveness are illustrated with four numerical examples.     

Comments on finding the most efficient DMUs in DEA: An improved integrated model

This paper improves the integrated DEA model proposed for finding the most efficient DMUs introduced by Amin and Toloo, [Amin, Gholam R., Toloo, M. (2007). Finding the most efficient DMUs in DEA: An improved integrated model. Computers & Industrial Engineering, 52(2), 71–77]. The paper shows the problem of using the integrated DEA model and presents an improved integrated DEA model for determining a single efficient unit. Also the paper indicates the property of the improvements mathematically and a numerical example shows the usefulness and intelligibility of the study.     

Improved data envelopment analysis models for evaluating interval efficiencies of decision-making units

In a recent article, Wang et al. [Wang, N. S., Yi, R. H., & Wang, W. (2008). Evaluating the performances of decision-making units based on interval efficiencies. Journal of Computational and Applied Mathematics, 216, 328–343] proposed a pair of interval data envelopment analysis (DEA) models for measuring the overall performances of decision-making units (DMUs) with crisp data. In this paper, we demonstrate that interval DEA models face problems in determining the efficiency interval for each DMU when there are zero values for every input. To remedy this drawback, we propose a pair of improved interval DEA models which make it possible to perform a DEA analysis using the concepts of the best and the worst relative efficiencies. Two numerical examples will be examined using the improved interval DEA models. One of the examples is a real-world application about 42 educational departments in one of the branches of the Islamic Azad University in Iran that shows the advantages and applicability of the improved approach in real-life situations.     

The voting analytic hierarchy process method for discriminating among efficient decision making units in data envelopment analysis

Making optimal use of available resources has always been of interest to humankind, and different approaches have been used in an attempt to make maximum use of existing resources. Limitations of capital, manpower, energy, etc., have led managers to seek ways for optimally using such resources. In fact, being informed of the performance of the units under the supervision of a manager is the most important task with regard to making sensible decisions for managing them. Data envelopment analysis (DEA) suggests an appropriate method for evaluating the efficiency of homogeneous units with multiple inputs and multiple outputs. DEA models classify decision making units (DMUs) into efficient and inefficient ones. However, in most cases, managers and researchers are interested in ranking the units and selecting the best DMU. Various scientific models have been proposed by researchers for ranking DMUs. Each of these models has some weakness(es), which makes it difficult to select the appropriate ranking model. This paper presents a method for ranking efficient DMUs by the voting analytic hierarchy process (VAHP). The paper reviews some ranking models in DEA and discusses their strengths and weaknesses. Then, we provide the method for ranking efficient DMUs by VAHP. Finally we give an example to illustrate our approach and then the new method is employed to rank efficient units in a real world problem.     

Ranking efficient decision-making units in data envelopment analysis using fuzzy concept

This paper introduces a new mathematical method for improving the discrimination power of data envelopment analysis and to completely rank the efficient decision-making units (DMUs). Fuzzy concept is utilised. For this purpose, first all DMUs are evaluated with the CCR model. Thereafter, the resulted weights for each output are considered as fuzzy sets and are then converted to fuzzy numbers. The introduced model is a multi-objective linear model, endpoints of which are the highest and lowest of the weighted values. An added advantage of the model is its ability to handle the infeasibility situation sometimes faced by previously introduced models.     

Cross efficiency evaluation method based on weight-balanced data envelopment analysis model

In this paper, the cross efficiency evaluation method, regarded as a DEA extension tool, is firstly reviewed for its utilization in identifying the Decision Making Unit (DMU) with the best practice and ranking the DMUs by their respective cross-efficiency scores. However, we then point out that the main drawback of the method lies in non-uniqueness of cross-efficiency scores resulted from the presence of alternate optima in traditional DEA models, obviously making it become less effective. Aiming at the research gap, a weight-balanced DEA model is proposed to lessen large differences in weighted data (weighted inputs and weighted outputs) and to effectively reduce the number of zero weights for inputs and outputs. Finally, we use two examples of the literature to illustrate the performance of this approach and discuss some issues of interest regarding the choosing of weights in cross-efficiency evaluations.     

A method using weight restrictions in data envelopment analysis for ranking and validity issues in decision making

In this article we introduce a comprehensive yet efficient approach based on data envelopment analysis (DEA) with restricted multipliers for accountable and understandable multiple attribute decision making (MADM). Information system (IS) appraisals are motivated and used for illustrating the proposed methodology. Results show that the given DEA based approach can easily and significantly increase the information frame of the decision maker by identifying disparate rankings and by affirming the stability and validity of ranking outcomes. The given validity concept is contrary to the directions given in the main body of research and can also be used to question ranking outcomes of classic MADM methods.     

A unified model for detecting efficient and inefficient outliers in data envelopment analysis

Data envelopment analysis (DEA) uses extreme observations to identify superior performance, making it vulnerable to outliers. This paper develops a unified model to identify both efficient and inefficient outliers in DEA. Finding both types is important since many post analyses, after measuring efficiency, depend on the entire distribution of efficiency estimates. Thus, outliers that are distinguished by poor performance can significantly alter the results. Besides allowing the identification of outliers, the method described is consistent with a relaxed set of DEA axioms. Several examples demonstrate the need for identifying both efficient and inefficient outliers and the effectiveness of the proposed method. Applications of the model reveal that observations with low efficiency estimates are not necessarily outliers. In addition, a strategy to accelerate the computation is proposed that can apply to influential observation detection.     

Measuring the relative performance for leading fabless firms by using data envelopment analysis

IC Design (fabless) is critical for the global semi-conductor industry. The total revenue of all global fabless firms in 2003 was about US$20 billion, with the top 30 firms earning accounting for 96% of the market share. To examine the leaders in the field, this research analyzes the relative performances of those top 30 fabless firms. Fabless firms are often evaluated based on subjective judgments, and an overall scheme to measure the performance involving objective, multi-input and multi-output criteria is yet to be established. There is also a need for identifying and determining suggestions of how specific firms could improve their performance. Data Envelopment Analysis (DEA) method has been employed in this paper to satisfy the above needs. Using the input and output data of 2003, this study used the DEA method to build a model to evaluate the performance of those global top 30 fabless firms. The current research used four efficiency models: CCR, A&P, BCC, and Cross-Efficiency. To offer a comparison of efficiencies and associated discussions, an analysis of the Scale-Return is provided. Finally, the performance of various fabless firms in 2003 is analyzed. According to the CCR and A&P models, the results showed that the top ten Decision Management Units (DMUs) achieved better operation performance among the 30 leading global fabless firms.     

Benchmarking of service quality with data envelopment analysis

This paper proposes a data envelopment analysis (DEA) approach to measurement and benchmarking of service quality. Dealing with measurement of overall service quality of multiple units with SERVPERF as multiple-criteria decision-making (MCDM), the proposed approach utilizes DEA, in particular, the pure output model without inputs. The five dimensions of SERVPERF are considered as outputs of the DEA model. A case study of auto repair services is provided for the purpose of illustration. The current practice of benchmarking of service quality with SERVQUAL/SERVPERF is limited in that there is little guidance to whom to benchmark and to what degree service quality should be improved. This study contributes to the field of service quality benchmarking by overcoming the above limitations, taking advantage of DEA’s capability to handle MCDM problems and provide benchmarking guidelines.     

A robust optimization approach for imprecise data envelopment analysis

Crisp input and output data are fundamentally indispensable in traditional data envelopment analysis (DEA). However, the input and output data in real-world problems are often imprecise or ambiguous. Some researchers have proposed interval DEA (IDEA) and fuzzy DEA (FDEA) to deal with imprecise and ambiguous data in DEA. Nevertheless, many real-life problems use linguistic data that cannot be used as interval data and a large number of input variables in fuzzy logic could result in a significant number of rules that are needed to specify a dynamic model. In this paper, we propose an adaptation of the standard DEA under conditions of uncertainty. The proposed approach is based on a robust optimization model in which the input and output parameters are constrained to be within an uncertainty set with additional constraints based on the worst case solution with respect to the uncertainty set. Our robust DEA (RDEA) model seeks to maximize efficiency (similar to standard DEA) but under the assumption of a worst case efficiency defied by the uncertainty set and it’s supporting constraint. A Monte-Carlo simulation is used to compute the conformity of the rankings in the RDEA model. The contribution of this paper is fourfold: (1) we consider ambiguous, uncertain and imprecise input and output data in DEA; (2) we address the gap in the imprecise DEA literature for problems not suitable or difficult to model with interval or fuzzy representations; (3) we propose a robust optimization model in which the input and output parameters are constrained to be within an uncertainty set with additional constraints based on the worst case solution with respect to the uncertainty set; and (4) we use Monte-Carlo simulation to specify a range of Gamma in which the rankings of the DMUs occur with high probability.     

Fuzzy data envelopment analysis and its application to location problems

In this paper, fuzzy DEA (data envelopment analysis) models are proposed for evaluating the efficiencies of objects with fuzzy input and output data. The obtained efficiencies are also fuzzy numbers that reflect the inherent ambiguity in evaluation problems under uncertainty. An aggregation model for integrating fuzzy attribute values is provided in order to rank objects objectively. Using the proposed method, a case study involving a restaurant location problem is analyzed in detail. Rent of establishment, traffic amount, level of security, consumer consumption level and competition level are identified as the primary factors in determining an ideal location for a Japanese-style rotisserie restaurant. Based on field investigation, the uncertain information on primary factors is represented by fuzzy numbers. Using the fuzzy aggregation model, the best location of restaurant is determined. The case study shows that fuzzy DEA models can be quite useful for solving business problems under uncertainty.     

An interactive application of data envelopment analysis in microcomputers

This article describes a general-purpose microcomputer code for data envelopment analysis (DEA) that incorporates four different DEA models in the form of a user-friendly, menu-driven structure.Research financially supported by Dean's Professorship, College of Business, the Ohio State University.     

Efficiency persistence of bank and thrift CEOs using data envelopment analysis

We examine the performance of chief executive officers (CEOs) of US banks and thrifts. We apply data envelopment analysis (DEA) to measure the performance of CEOs on a yearly basis over the 1997–2004 period, and find evidence that best-practice CEOs who have a DEA efficiency score of one are rewarded with higher compensation compared to under-performing CEOs who have a DEA efficiency score greater than one. We find DEA efficiency score to be a highly significant predictor of CEO compensation, even after adjusting for firm size. In addition, we find that DEA efficiency scores of CEOs have decreased over the observation period. We also find that best-practice CEOs tend to be persistent on a yearly basis, but we find little evidence of multi-period persistence. The results of this study can serve as a benchmark for CEOs wishing to evaluate their performance relative to their peers, and as a new measure of CEO performance.     

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.     

A data envelopment analysis method for optimizing multi-response problem with censored data in the Taguchi method

Taguchi method is an efficient method used in off-line quality control in that the experimental design is combined with the quality loss. This method including three stages of systems design, parameter design, and tolerance design has been deeply discussed in Phadke [Quality engineering using robust design (1989)]. It is observable that most industrial applications solved by Taguchi method belong to single-response problems. However, in the real world more than one quality characteristic should be considered for most industrial products, i.e. most problems customers concern about are multi-response problems. As a result, Taguchi method is not appropriate to optimize a multi-response problem. At present, it is still necessary to rely on the engineering judgment to optimize the multi-response problem; therefore uncertainty will be increased during the decision-making process. On the other hand, due to some uncontrollable causes occurring, only a portion of experiment can be completed so that the censored data will be produced. Traditional approaches for analysis of censored data are computationally complicated. In order to overcome above two shortages, this article proposes an effective procedure on the basis of the neural network (NN) and the data envelopment analysis (DEA) to optimize the multi-response problems. A case study of improving the quality of hard disk driver in Su and Tong [ Total Quality Management 8 (1997) 409] is resolved by the proposed procedure. The result indicates that it yields a satisfactory solution.     

A mixed integer optimisation model for data classification

In this work, a mixed integer linear programming (MILP) model is proposed for the multi-class data classification problem using a hyper-box representation. The latter representation is particularly suitable for capturing disjoint data regions. The objective function used is the minimisation of the total number of misclassified data samples. In order to improve the training and testing accuracy of our approach, an iterative solution procedure is developed to assign potential multiple boxes to each single class. Finally, the applicability of the proposed approach is demonstrated through a number of illustrative examples. According to the computational results obtained, the proposed optimisation-based approach is competitive in terms of prediction accuracy when compared with various standard classifiers.     

Common weights data envelopment analysis with uncertain data: A robust optimization approach

One of the primary issues on data envelopment analysis (DEA) models is the reduction of weights flexibility. There are literally several studies to determine common weights in DEA but none of them considers uncertainty in data. This paper introduces a robust optimization approach to find common weights in DEA with uncertain data. The uncertainty is considered in both inputs and outputs and a suitable robust counterpart of DEA model is developed. The proposed robust DEA model is solved and the ideal solution is found for each decision making units (DMUs). Then, the common weights are found for all DMUs by utilizing the goal programming technique. To illustrate the performance of the proposed model, a numerical example is solved. Also, the proposed model of this paper is implemented by using some actual data from provincial gas companies in Iran.     

Uncertain network data envelopment analysis with undesirable outputs to evaluate the efficiency of electricity power production and distribution processes

In this paper, a customized network data envelopment analysis model is developed to evaluate the efficiency of electric power production and distribution processes. In the production phase, power plants consume fuels such as oil and gas to generate the electricity. In the distribution phase, regional electricity companies transmit and distribute the electricity to the customers in houses, industries, and agriculture. Although, the electricity is assumed to be a clean type of energy, several types of emissions and pollutions are produced during electricity generation. The generated emissions are considered as an undesirable output. A customized network data envelopment analysis (NDEA) approach is proposed to evaluate the efficiency of these processes Each decision making unit (DMU) includes two serially connected sub-DMUs, i.e., production and distribution stages. The models are extended using interval data to address the considerable uncertainty in the problem. The efficiency scores of main process, and each sub-process are determined. The final ranking of DMUs and sub-DMUs are achieved using a multi-attribute decision making (MADM) method. The whole approach is applied in a real case study in electrical power production and distribution network with 14 DMUs. The proposed approach has the following innovations in comparison with existing methods: (1) Both production and distribution process are evaluated in a unique model; (2) Undesirable outputs and uncertainty of data are considered in proposed approach; (3) Properties of proposed models are discussed through several theorems; (4) The efficiencies of production and distribution phases are determined distinctively; (5) A full ranking approach is proposed; (6) A real case study of electrical power production and distribution network is surveyed. The results of proposed approach are adequate and interesting. This approach can be customized for application in similar systems such as water production-supply management, Oil and fuel production–distribution systems, and supply chains.