A common weight credibility data envelopment analysis model for evaluating decision making units with an application in airline performance

This study evaluates three different types of data envelopment analysis (DEA) models by applying them to measure China’s energy efficiency. The efficacy of DEA in efficiency measurement is the primary reason why DEA has gained significant attentions from researchers across the world. The primary benefits of DEA include its ability to provide both efficiency scores and improvement targets for decision making units (DMUs) under measurement. The improvement targets suggest several ways to improve inefficient DMUs’ efficiency. An improvement target that is close to the DMU under measurement is considered to be easy-to-achieve in DEA. However, in previous studies, most conventional DEA models used for China’s efficiency measurement provided a far improvement targets that cannot be achieved immediately and would require several years. Thus, a least-distance DEA model that can provide a closer improvement target is used in this study. Furthermore, a conventional DEA model and a ratio type DEA model are used to study and compare the performances. All three DEA models are applied to the measurement of China’s energy efficiency in 1997, 2002, 2007, and 2012. The differences in the efficiency scores and improvement targets provided by the three models have been reviewed in this paper. Although the results show different improvement targets, it can be inferred that reducing the overall energy consumption and increasing the GDP are still two effective measures for inefficient provinces, districts, and cities according to the experimental results.

Pan, Z.-H.; Jiao, X.-Y.; Conradt, T.; Ding, X.-M., and Wang, H.-Y., 2019. Performance evaluation of groundwater overdraft recovery units in north and coastal China based on DEA models. In: Gong, D.; Zhu, H., and Liu, R. (eds.), Selected Topics in Coastal Research: Engineering, Industry, Economy, and Sustainable Development. Journal of Coastal Research, Special Issue No. 94, pp. 1–5. Coconut Creek (Florida), ISSN 0749-0208.Groundwater overdraft has affected sustainable development, especially in North and Coastal China, since the 1960s. The Chinese government instituted the Pilot Project of Groundwater Overexploitation Control (PPGOC) in Hebei Province during 2014 to 2016. This project introduced a set of hydrological, agricultural and administrative activities to recover the aquifer in the pilot area. In order to evaluate the effects of these activities on the groundwater status, a series of Data Envelopment Analysis (DEA) models are assembled as a model group and applied to calculate the relative performance of groundwater recovery units, i.e. the recovery efficiency in 49 counties or Decision-Making Units (DMUs). It is shown that the DEA model group can be used to evaluate the recovery efficiency, improve the performance of units not on the DEA frontier via radial and slack movement, and study the possibility of cost reduction. The result shows that 20 DMUs formed the frontier, which is the collective of the efficient DMUs, and that another 29 DMUs require efficiency improvement. The high efficiency of certain DMUs is related to the location and farmers' responses, which indicates that groundwater overdraft recovery is a technical problem that also has something to do with social and economic development and comprehensive governance. The model group can be used as a reference in the forthcoming implementation of aquifer recovery in groundwater overdraft zones in North and Coastal China.

A robust data envelopment analysis model with different scenarios

Traditional data envelopment analysis (DEA) models require the values for all inputs and outputs should be known exactly. However, it is essential to take into account the presence of qualitative factors of inputs and outputs in a real evaluation problem. By referring to the cloud theory and conventional interval DEA model, this paper develops a new fuzzy DEA model called Cloud DEA (C-DEA) model to deal with qualitative factors. Through three digital parameters (Ex, En, He), the fuzziness and randomness of qualitative factors are integrated in a unified way. Based on cloud generator and alpha-level sets, qualitative information and fuzzy data are converted into interval data, respectively, and are incorporated into the interval DEA models. It shows in a numerical example that the C-DEA model has many advantages over the conventional DEA methodology and can be used to evaluate the relative efficiency of decision making units (DMUs) under uncertainty.

Inadequate results may arise in some instances of DEA model applications. For example, a data envelopment analysis (DEA) model may show ‘a notoriously inefficient unit’ as an efficient one. In addition, too many efficient units may appear in some DEA models. An elegant and subtle approach was proposed to deal with these problems, which is based on incorporating domination cones in DEA models. Yu, Wei and Brockett suggested the generalized DEA (GDEA) model that unifies and extends most of the well-known DEA models based on using domination cones. In this paper, we propose a model that is more general than the GDEA model, on the one hand, as it covers situations that the GDEA model cannot describe. On the other hand, our model enables one to construct step-by-step any model from the family of the GDEA models by incorporating artificial units and rays in the space of inputs and outputs in the Banker, Charnes, Cooper (BCC) model, which makes the process of model construction visible and more understandable. Moreover, we show that any GDEA model can be approximated by some BCC model.

Cross-efficiency evaluation based on ideal and anti-ideal decision making units

In this paper we consider the Variable Returns to Scale (VRS) Data Envelopment Analysis (DEA) model. In a DEA model each Decision Making Unit (DMU) is classified either as efficient or inefficient. Changes in inputs or outputs of any DMU can alter its classification, i.e. an efficient DMU can become inefficient and vice versa. The goal of this paper is to assess changes in inputs and outputs of an extreme efficient DMU that will not alter its efficiency status, thus obtaining the region of efficiency for that DMU. Namely, a DMU will remain efficient if and only if after applying changes this DMU stays in that region. The representation of this region is done using an iterative procedure. In the first step an extended DEA model, whereby a DMU under evaluation is excluded from the reference set, is used. In the iterative part of the procedure, by using the obtained optimal simplex tableau we apply parametric programming, thus moving from one facet to the adjacent one. At the end of the procedure we obtain the complete region of efficiency for a DMU under consideration.

The field of data envelopment analysis (DEA) has evolved rapidly since its introduction to decision-making science 40 years ago. DEA has since attracted the attention of many researchers because of its unique characteristic to measure the efficiency of multiple-input and multiple-output decision-making units (DMUs) without assigning prior weight to the input and output, unlike most available decision analysis tools. The body of research has resulted in a huge amount of literature and diverse DEA models with very many different approaches. DEA classifies all units under assessment into two groups: efficient with a 100% efficiency score and inefficient with a less than 100% efficiency score. This ability is considered both a strength and a weakness of the standard DEA model because, although it allows DEA to evaluate the efficiency of any dataset, it lacks the power to rank all DMUs, by giving full efficiency scores to many efficient units. This issue has attracted many researchers to investigate the weak discrimination power of classical DEA models, resulting in a subfield of research that focuses on DEA ranking. This thesis focuses on the development of the conventional DEA model, and an attempt has been made to study models that are considered as improved models, or approaches that bring a better ranking field, that may bring more accurate evaluation than the original DEA. After studying DEA ranking models, the thesis presents various models under the optimistic and pessimistic DEA ranking approaches. The first and fundamental contribution are the optimistic and pessimistic free disposal hull (FDH) models. In this study, authentic optimistic and pessimistic DEA models without convexity are developed from both input and output orientation. Further into the research investigation, extended models have been proposed, by combining the conventional and FDH ranking models with other different approaches in the literature. Chapter 4 of this thesis presents three extended FDH models: an FDH slack-based model, an FDH superefficiency model, and a dual frontier without infeasibility super-efficiency FDH model. Chapter 5 shows the development of extended models when virtual DMUs are considered. Improved virtual DMU models and improved FDH virtual DMU models are proposed in order to develop the DEA ranking ability from both optimistic and pessimistic approaches. The final model is an optimistic and pessimistic forecasting approach using regression analysis. The forecasting model can be used by decision makers to determine the resources needed for future planning to build an efficient new unit with reference to the current DMU set.

The field of data envelopment analysis (DEA) has evolved rapidly since its introduction to decision-making science 40 years ago. DEA has since attracted the attention of many researchers because of its unique characteristic to measure the efficiency of multiple-input and multiple-output decision-making units (DMUs) without assigning prior weight to the input and output, unlike most available decision analysis tools. The body of research has resulted in a huge amount of literature and diverse DEA models with very many different approaches. DEA classifies all units under assessment into two groups: efficient with a 100% efficiency score and inefficient with a less than 100% efficiency score. This ability is considered both a strength and a weakness of the standard DEA model because, although it allows DEA to evaluate the efficiency of any dataset, it lacks the power to rank all DMUs, by giving full efficiency scores to many efficient units. This issue has attracted many researchers to investigate the weak discrimination power of classical DEA models, resulting in a subfield of research that focuses on DEA ranking. This thesis focuses on the development of the conventional DEA model, and an attempt has been made to study models that are considered as improved models, or approaches that bring a better ranking field, that may bring more accurate evaluation than the original DEA. After studying DEA ranking models, the thesis presents various models under the optimistic and pessimistic DEA ranking approaches. The first and fundamental contribution are the optimistic and pessimistic free disposal hull (FDH) models. In this study, authentic optimistic and pessimistic DEA models without convexity are developed from both input and output orientation. Further into the research investigation, extended models have been proposed, by combining the conventional and FDH ranking models with other different approaches in the literature. Chapter 4 of this thesis presents three extended FDH models: an FDH slack-based model, an FDH superefficiency model, and a dual frontier without infeasibility super-efficiency FDH model. Chapter 5 shows the development of extended models when virtual DMUs are considered. Improved virtual DMU models and improved FDH virtual DMU models are proposed in order to develop the DEA ranking ability from both optimistic and pessimistic approaches. The final model is an optimistic and pessimistic forecasting approach using regression analysis. The forecasting model can be used by decision makers to determine the resources needed for future planning to build an efficient new unit with reference to the current DMU set.

PurposeThe purpose of this paper is to present a stochastic p-robust data envelopment analysis (DEA) model for decision-making units (DMUs) efficiency estimation under uncertainty. The main contribution of this paper consists of the development of a more robust system for the estimation of efficiency in situations of inputs uncertainty. The proposed model is used for the efficiency measurement of a commercial Iranian bank.Design/methodology/approachThis paper has been arranged to launch along the following steps: the classical Charnes, Cooper, and Rhodes (CCR) DEA model was briefly reviewed. After that, the p-robust DEA model is introduced and then calculated the priority weights of each scenario for CCR DEA output oriented method. To compute the priority weights of criteria in discrete scenarios, the analytical hierarchy analysis process (AHP) is used. To tackle the uncertainty of experts’ opinion, a synthetic technique is applied based on both robust and stochastic optimizations. In the sequel, stochastic p-robust models are proposed for the estimation of efficiency, with particular attention being paid to DEA models.FindingsThe proposed method provides a more encompassing measure of efficiency in the presence of synthetic uncertainty approach. According to the results, the expected score, relative regret score and stochastic P-robust score for DMUs are obtained. The applicability of the extended model is illustrated in the context of the analysis of an Iranian commercial bank performance. Also, it is shown that the stochastic p-robust DEA model is a proper generalization of traditional DEA and gained a desired robustness level. In fact, the maximum possible efficiency score of a DMU with overall permissible uncertainties is obtained, and the minimal amount of uncertainty level under the stochastic p-robustness measure that is required to achieve this efficiency score. Finally, by an example, it is shown that the objective values of the input and output models are not inverse of each other as in classical DEA models.Originality/valueThis research showed that the enormous decrease in maximum possible regret makes only a small addition in the expected efficiency. In other words, improvements in regret can somewhat affect the expected efficiency. The superior issue this kind of modeling is to permit a harmful effect to the objective to better hedge against the uncertain cases that are commonly ignored.

To solve the problem that activity-based management (ABM) method is difficult in quantitative logistics cost evaluation, a data envelopment analysis (DEA) model for logistics cost evaluation based on activity analysis is developed in this paper. The practice of logistics ABM is scarce in China, as a result, itpsilas difficult to acquire activities costs data of other enterprises. So, time intervals of logistics activities are considered as decision-making units (DMUs) in the DEA model. DMUspsila efficiencies and optimal virtual DMUs are determined by solution of DEA model developed in this paper. In this paper, numerical examples are also given to illustrate the application of the above model. The results show that the above evaluation method is objective and accurate, and not only the efficiency of logistics activity can be evaluated, but also optimal structure of logistics activity cost can be obtained. Therefore, this method gives the improved route of logistics activity, and is very practical.

The data envelopment analysis (DEA) model is extensively used to estimate efficiency, but no study has determined the DEA model that delivers the most precise estimates. To address this issue, we advance the Monte Carlo simulation-based data generation process proposed by Kohl and Brunner (2020). The developed process generates an artificial dataset using the Translog production function (instead of the commonly used Cobb Douglas) to construct well-behaved scenarios under variable returns to scale (VRS). Using different VRS DEA models, we compute DEA efficiency scores with artificially generated decision-making units (DMUs). We employ five performance indicators followed by a benchmark value and ranking as well as statistical hypothesis tests to evaluate the quality of the efficiency estimates. The procedure allows us to determine which parameters negatively or positively influence the quality of the DEA estimates. It also enables us to identify which DEA model performs the most efficiently over a wide range of scenarios. In contrast to the widely applied BCC (Banker-Charnes-Cooper) model, we find that the Assurance Region (AR) and Slacks-Based Measurement (SBM) DEA models perform better. Thus, we endorse the use of AR and SBM models for DEA applications under the VRS regime.

Airport efficiency is an important issue for each country. The classical DEA models use different input and output weights in each decision making unit (DMU) that seems not reasonable. We present a multiple objectives based Data Envelopment Analysis (DEA) model which can be used to improve discriminating power of DEA method and generate a more reasonable input and out weights. The traditional DEA model is first replaced by a multiple objective linear program (MOLP) that a set of Pareto optimal solutions is obtained by genetic algorithm. We then choose a set of common weights for inputs and outputs within the Pareto solutions. A gap analysis is included in this study that can help airports understand their gaps of performances to aspiration levels. For this new proposed model based on MOLP it is observed that the number of efficient DUMs is reduced, improving the discrimination power. Numerical example from real-world airport data is provided to show some advantages of our method over the previous methods.

Purpose – The purpose of this paper is to build a novel data envelopment analysis (DEA) model to evaluate the efficiencies of decision making units (DMUs). Design/methodology/approach – Using the Choquet integrals as aggregating tool, the authors give a novel DEA model to evaluate the efficiencies of DMUs. Findings – It extends DEA model to evaluate the DMU with interactive variables (inputs or outputs), the classical DEA model is a special form. At last, the authors use the numerical examples to illustrate the performance of the proposed model. Practical implications – The proposed DEA model can be used to evaluate the efficiency of the DMUs with multiple interactive inputs and outputs. Originality/value – This paper introduce a new DEA model to evaluate the DMU with interactive variables (inputs or outputs), the classical DEA model is a special form.

Traditional data envelopment analysis (DEA) models select weights specific for every decision making unit (DMU) in a way that maximize the performance of each DMU. With the DEA models, the inputs and outputs of each DMU are evaluated with the different set of weights that are not common. Importances of weights of the inputs and outputs not to happen same for every DMU. This is advantageous for some DMUs, while for other DMUs it is disadvantageous. Another drawback is that in the DEA performance calculations, for some inputs and outputs, it selects very small or zero weights. A very small near zero or zero weight probably means that an important criterion will not be considered in the performance calculation. Together with above, another defect is the same efficiency score (1/100) are given to all efficient DMUs. This prevents full ranking of DMUs. One way for eliminate the disadvantages which mentioned above is to use same set of weights during calculation of the performance of all DMUs. The weights of the Andersen-Petersen super efficiency model were used as stepping stone in this new common set of weights (CSWs) generation algorithm. This new algorithm will be apply to the well-known data of a real-world problem in litarature.