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.     

Radial data envelopment analysis models with mixed orientation of input and output

This paper discusses parametric solutions and envelopment formulations of radial data envelopment analysis (DEA) models with mixed orientation of input and output. These solutions geometrically but not numerically lie between the two usual solutions from input and output orientations. The consequent results provide alternative optimal solutions between those from input‐ and output‐oriented CCR models for constant returns to scale DEA models and optimal scale efficiency in addition to technical efficient solutions from input‐ and output‐oriented BCC models for variable returns to scale DEA models.     

New analytical hierarchical process/data envelopment analysis methodology for ranking decision‐making units

The analytical hierarchical process/data envelopment analysis (AHP/DEA) methodology for ranking decision‐making units (DMUs) has some problems: it illogically compares two DMUs in a DEA model; it is not compatible with DEA ranking in the case of multiple inputs/multiple outputs; and it leads to weak discrimination in cases where the number of inputs and outputs is large. In this paper, we propose a new two‐stage AHP/DEA methodology for ranking DMUs that removes these problems. In the first stage, we create a pairwise comparison matrix different from AHP/DEA methodology; the second stage is the same as AHP/DEA methodology. Numerical examples are presented in the paper to illustrate the advantages of the new AHP/DEA methodology.     

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.     

An integrated data envelopment analysis and free disposal hull framework for cost-efficiency measurement using rough sets

Traditional cost-efficiency analysis methods require exact and precise values for inputs, outputs and input prices. However, this is not the case in many real-life applications. This study proposes a rough cost-efficiency approach to the problem of ranking efficient decision making units (DMUs). Based on rough set theory, a nonparametric methodology for cost-efficiency analysis is developed. The merits of this methodology include computational ease and the capacity to incorporate data uncertainty. Furthermore, it applies to both convex data envelopment analysis (DEA) and non-convex free disposal hull (FDH) technologies under different returns-to-scale assumptions. A numerical example and a real-life case study in the Japanese banking industry demonstrate the applicability of the proposed framework. In particular, the rankings of the DMUs resulting from the proposed models are compared with those obtained using the maximum technical efficiency loss index.     

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.     

Right and left returns to scales in data envelopment analysis: Determining type and measuring value

This study identifies types and values of right and left returns to scales (RTSs) of efficient decision making units (DMUs) in data envelopment analysis (DEA). In this research, we first introduce a new approach to estimate types of right and left returns to scales of efficient DMUs and then, values of right and left returns to scales of these DMUs are measured by presenting two new DEA models.     

A computational study of DEA with massive data sets

Data envelopment analysis (DEA) is computationally intensive. This work answers conclusively questions about computational performance and scale limits of the standard LP-based procedures currently used. Examples of DEA problems with up to 15K entities are documented and it is not hard to imagine problem size increasing as new more sophisticated applications are found for DEA. This work reports on a comprehensive computational study involving DEA problems with up to 100K DMUs. We explore the impact of different LP algorithms including interior point methods as well as accelerators such as advanced basis starts and DEA specific enhancements such as “restricted basis entry” (RBE). Our results demonstrate that solution times behave close to quadratically and that massive problems can be solved efficiently. We propose ideas for extending DEA into a data mining tool.     

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.     

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.     

Using N-D method to solve multi-response problem in Taguchi

Using Taguchi method to achieve a robust experimental design in the study of product quality is an important issue. The Taguchi method is to seek the best factors/levels combination with lowest societal cost solution to achieve customers requirements. However, the Taguchi method can only be used to optimize the single-response problem; it cannot be used to optimize the multi-response problem. This paper submits an optimal procedure, N-D method (Artificial Neural Network and Data Envelopment Analysis), by using artificial neural networks (ANNs) and data envelopment analysis (DEA) to achieve the optimization of multi-response problem. Two case studies in Su and Tong (1997) and Tong and Su (1997) are resolved by the proposed N-D method. The result deriving from the proposed N-D method indicates that it offers an efficient and feasible solution in the multi-response problems.This revised version was published in June 2005 with corrected page numbers.     

A stochastic cross‐efficiency data envelopment analysis approach for supplier selection under uncertainty

This paper addresses one of the key objectives of the supply chain strategic design phase, that is, the optimal selection of suppliers. A methodology for supplier selection under uncertainty is proposed, integrating the cross‐efficiency data envelopment analysis (DEA) and Monte Carlo approach. The combination of these two techniques allows overcoming the deterministic feature of the classical cross‐efficiency DEA approach. Moreover, we define an indicator of the robustness of the determined supplier ranking. The technique is able to manage the supplier selection problem considering nondeterministic input and output data. It allows the evaluation of suppliers under uncertainty, a particularly significant circumstance for the assessment of potential suppliers. The novel approach helps buyers in choosing the right partners under uncertainty and ranking suppliers upon a multiple sourcing strategy, even when considering complex evaluations with a high number of suppliers and many input and output criteria.     

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.     

Fuzzy rough DEA model: A possibility and expected value approaches

Uncertainty is certain in the world of uncertainty. Measuring the performance of any entity in such an uncertain environment is unavoidable. Fuzzy rough data envelopment analysis (FRDEA) provides a room to evaluate the relative efficiency of homogenous entities, widely known as decision making units (DMUs) in the data envelopment analysis (DEA) literature. This paper attempts to create a fuzzy rough DEA model by integrating the classical DEA, fuzzy set theory, and rough set theory, which apparently provide a way to accommodate the uncertainty. Moreover, in contrast to the probability approach, this paper provides a pavement to measure the relative efficiency of any given DMUs in line with the possibility approach along with the fuzzy rough expected value operator.     

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.     

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.     

Indian thermal power plant challenges and remedies via application of modified data envelopment analysis

This paper evaluates the performance of coal‐fired thermal power plants in India for the year 2008–2009 using data envelopment analysis (DEA); subdividing the power plants into three categories depending on their scale—small, medium, and large. The classical DEA model is analyzed to identify the efficient ones from the whole gamut of plants run by various organizations of the central government, state government, and private sector. Slack analysis is carried out to explore the specific areas that need to be focused on, in quantitative terms, for the overall efficiency improvement. Further efficiency evaluation is extended from a single criterion‐based conventional approach to a multiple criteria oriented approach, and the resulting DEA models are more efficient and flexible in many aspects, particularly in discriminant and weight analysis. Results of multicriteria DEA (MCDEA) are substantiated with cross‐efficiency analysis by deploying the weights obtained by the MCDEA in the cross‐efficiency analysis. On the basis of the insights provided by the outcome of the analysis, both qualitative and quantitative measures are proposed for improvement of the plant performances. The result of this analysis may assist the management of the power plants to introspect and review their systems and processes for optimal use of resources. The methodology adopted in the present work can also be employed for deeper understanding of power plants in other parts of India as well as in other countries.     

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.     

Negative data in DEA: Recognizing congestion and specifying the least and the most congested decision making units

One of the important concepts of data envelopment analysis (DEA) is congestion. A decision making unit (DMU) has congestion if an increase (decrease) in one or more input(s) of the DMU leads to a decrease (increase) in one or more its output(s). The drawback of all existing congestion DEA approaches is that they are applicable only to technologies specified by non-negative data, whereas in the real world, it may exist negative data, too. Moreover, specifying the strongly and weakly most congested DMUs is a very important issue for decision makers, however, there is no study on specifying these DMUs in DEA. These two facts are motivations for creating this current study. Hence, in this research, we first introduce a DEA model to determine candidate DMUs for having congestion and then, a DEA approach is presented to detect congestion status of these DMUs. Likewise, we propose two integrated mixed integer programming (MIP)-DEA models to specify the strongly and weakly most congested DMUs. Note that the proposed approach permits the inputs and outputs that can take both negative and non-negative magnitudes. Also, a ranking DEA approach is introduced to rank the specified congested DMUs and identify the least congested DMU. Finally, a numerical example and an empirical application are presented to highlight the purpose of this research.     

Performance optimization of integrated job-driven and resilience factors by means of a quantitative approach

Job-driven factors affect overall productivity and describe the characteristics influencing human performance. Resilience engineering (RE) is the capability of systems and groups to cope with disturbances and disruptions to enhance their performance. This study employs data envelopment analysis (DEA) approach to optimize the overall performance of a ceramic tile company by considering resilience and job-driven factors. The required data were collected via a standard questionnaire whose reliability was examined by statistical methods. In this regard, sensitivity analysis was performed to determine the most important factors. DEA results showed that job stress, job burnout, and management commitment play a central role in the investigated system. The overall results indicated that job-driven factors have a higher weight than resilience factors. This is one of the first studies that concurrently examine job-driven and resilience factors. Second, the present study uses DEA method in a ceramic tile manufacturer to achieve optimum performance. Third, the weights of all factors are computed for optimum redesign and re-engineering. Fourth, decision-makers may identify weak areas and strong points of their systems with respect to job-driven and resilience factors.