Constrained Weighted DEA Method Based on Volume Under Surface: A Case Study in Large Industrial Sectors

Data envelopment analysis (DEA) model has been widely applied for estimating efficiency scores of decision making units (DMUs) and is especially used in many applications in transportation. In this paper, a novel common weight credibility DEA (CWCDEA) model is proposed to evaluate DMUs considering uncertain inputs and outputs. To develop a credibility DEA model, a credibility counterpart constraint is suggested for each constraint of DEA model. Then, the weights generated by the credibility DEA (CDEA) model are considered as ideal solution in a multi-objective DEA model. To solve the multi-objective DEA model, a goal programming model is proposed. The goal programming model minimized deviations from the ideal solutions and found the common weights of inputs and outputs. Using the common weights generated by goal programming model, the final efficiency scores for decision making are calculated. The usefulness and applicability of the proposed approach have been shown using a data set in the airline industry.

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.

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.

This chapter presents work on the use of an artificial intelligence technique to cluster stratified samples of container terminals derived from Data Envelopment Analysis (DEA). This technique is Kohonen’s self-organizing map (SOM; (Kohonen, 1995)). Data envelopment analysis measures the relative efficiency of comparable entities called Decision Making Units (DMUs) essentially performing the same task using similar multiple inputs to produce similar multiple outputs ((Charnes et al., 1978)). The purpose of DEA is to empirically estimate the so-called efficient frontier based on the set of available DMUs. DEA provides the user with information about the efficient and inefficient units, as well as the efficiency scores and reference sets for inefficient units. The results of the DEA analysis, especially the efficiency scores, are used in practical applications as performance indicators. There are many problems associated with applying the DEA in some applications. One problem is that the improvement projection for inefficient units in DEA analysis is concrete relative to its efficiency score. This means, in DEA, relative performance of any DMU can be contrasted only to the efficient DMUs that register unit efficiency score. There is no influence on the performance of efficient DMUs by presence or absence of inefficient DMUs. Therefore, the classical DEA does not actually provide a direct means to rank DMUs based on their relative degrees of efficiency or inefficiency ((Sharma & Yu, 2010)). The second problem is that the DEA models assume that all DMUs are homogenous and identical in their operations ((Seiford, 1994)). Since various applications have heterogeneous DMUs and there is a high request to evaluate these applications under the DEA due to its acceptance as a performance measurement in different kind of business, we have to modify the DEA to work with these applications. If the heterogeneous DMUs are assessed by DEA without any modifications, the DEA yields a biased performance scores and inaccurate analyses. For example, the resources (land, equipment, and labor) of container terminals varies across the world, which requires to be evaluated in term of its common input characterstics. An essential requirement in analyzing these container terminals is to build a fair referencing system for each container terminal to manage and provide a solid plan that improves all inefficient terminals and supports all efficient terminals. This system can not be assessed under the standard DEA due to the non-homogenous nature of these container terminals in terms of their operations, different standards of equipments, infrastructure, and variety in quay length and area size. These factors will yield unfair benchmarking evaluation 5

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.

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.

This study presents a DEA model without the conventional non-Archimedian infinitesimal E. This article also introduces a new DEA efficiency measure. Incorporating slacks in inputs and shortages in outputs, the new DEA measure expresses the relative efficiency of decision making units more properly than traditional one. 1 Introduction and Historical Background In their ingenious paper (lOJ, Charnes, Cooper and Rhodes introduced a fractional pro­ gramming method to measure the relative efficiency of a Decision Making Unit (DMU), which was solved by transforming the fractional programming into a linear programming problem via the Charnes-Cooper scheme (6J. The method was referred to as DEA (Da.ta En­ velopment Analysis). The DEA model proposed in (10J maintained an assumption; all the weighting values to inputs and outputs were assumed to be nonnegative. In the subsequent short communication (11), Charnes et. al. changed their DEA problems and required that the weights be strictly positive. Thus, t.he introduction of the non-Archimedian in­ finitesimal e was anticipated to distinguish bet.ween nonnegative and positive values. ( This problem was already discussed in (10J implicitly.) Although the subsequent discussions can be found in (5), (7), and (12), and the role of e has become unclear and weakened, it is still frequently used in the literature (e.g., (4),(8)) and in particular, in some cases of compu­ tational situations, values such as e = 10- 5 ,10- 6 (single precision) or e = 10- 12 (double precision) are conveniently employed to substitute for the non-Archimedian infinitesimal e. However, the approach may produce a theoretically contradicting issue. That is, we cannot uniquely determine what is the best~. Different e values yield different DEA re­ sults. Therefore, we need a completely e-free development of DEA from both theoretical and computational points of view. This article is organized as follows. Section 2 defines an input oriented DEA model based on the production possibility set. Its dual corresponds to the Charnes-Cooper­ Rhodes (CCR) model with the weights to inputs and outputs as variables. Then, we define a DMU as slackless if, for every optimal solution to the DEA model, it has no slack in inputs and no shortages in outputs. By a theorem of the alternative or the strong theorem of complemantary slackness, it will be proved that for a slackless DMU there is a strictly positive weight solution in the corresponding CCR model. Subsequently, for a DMU with non-zero slacks in an optimal solution to the DEA model, there exist no positive weight solutions in the CCR model. Section 3 defines the max-slack solution and shows a procedure to find it. The max-slack solution can be used for deciding whether the DMU is slackless or not. Then, we propose a method for finding positive weights for slackless DMUs. Thus, all jobs of the CCR model can be successfully achieved with no recourse to e. Section 4 introduces a new measure of relative efficiency, based on the max-slack solution, which

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.

This study aimed to measure the efficiency scores of 75 dairy buffalo farms in the province of Nueva Ecija, Central Luzon, Philippines, using an input-oriented, variable-return-to-scale Data Envelopment Analysis (DEA) model. The farmer-informants or decision-making units (DMUs) were categorized as smallholders, family modules, and semi-commercial in operations. Personal interviews using structured questionnaires were done to gather various information on the socio-economic and management practices of the DMUs. Output in the form of volume and value of milk produced and inputs such as quantities and costs of biologics, feeds, forage, and labor were also collected and evaluated among individual DMUs. The efficiency scores were computed using PIM-DEA software, which identified fully efficient DMUs lying on the frontier line (scores of 1.0) and those enveloped by it (inefficient DMUs with scores of less than 1.0). The overall mean Technical Efficiency (TE), Allocative Efficiency (AE), and Economic Efficiency (EE) scores among the DMUs were 0.80, 0.81, and 0.65, respectively. Most of the inefficient DMUs were in the smallholder category. In sum, smallholder DMUs classified under low and moderate TE clusters should reduce their inputs by 53.31% and 40.01%, respectively, to become fully efficient. Likewise, higher lambda values among efficient peer DMUs indicate the best practice frontiers that the inefficient peer DMUs can benchmark with. Extension and advisory services can help promote the best management practices of the frontiers to improve the TE, AE, and EE of the inefficient DMUs.

We study in this paper the performance of Hospitals in Lebanon. Using the nonparametric method Data Envelopment Analysis (DEA), we are able to measures relative efficiency of Hospitals in Lebanon. DEA is a technique that uses linear programming and it measures the relative efficiency of similar type of organizations termed as Decision Making Units (DMUs). In this study, due to the lack of individual data on hospital level, each DMU refers to a qada in Lebanon where the used data represent the aggregation of input and outputs of different hospitals within the qada. In DEA, the inclusion of more number of inputs and /or outputs results in getting a more number of efficient units. Therefore, selecting the appropriate inputs and outputs is a major factor of DEA results. Therefore, we use here the Principal Component Analysis (PCA) in order to reduce the data structure into certain principal components which are essential for identifying efficient DMUs. It is important to note that we have used the basic BCC-input model for the entire analysis. We considered 24 DMUs for the study, using DEA on original data; we got 17 DMUs out of 24 DMUs as efficient. Then we considered 1 PC for inputs and 1 PC for output with almost 80 percent variances, resulting in 3 DMUs as efficient and 21 as inefficient. Using 1 PC for input and 2 PCs for output with 90 percent variance for both input and output, we got 9 DMUs as efficient and 15 DMUs as inefficient. Finally, we have attempted to identify the efficient units with 2 PCs and for 2 PCs for input and outputs with variance more than 95 percent, resulting in 10 efficient DMUs and 14 inefficient DMUs. In Principal Component analysis, if the variance lies between 80 percent to-90 percent it is judged as a meaningful one. It is concluded that Principal Component Analysis plays an important role in the reduction of input output variables and helps in identifying the efficient DMUs and improves the discriminating power of DEA.

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.

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.

Evaluation method based on ranking in data envelopment analysis

Traditional data envelopment analysis (DEA) models find the most desirable weights for each decision-making unit (DMU) in order to estimate the highest efficiency score as possible. These efficiency scores are then used for ranking the DMUs. The main drawback is that the efficiency scores based on weights obtained from the standard DEA models ignore other feasible weights; this is due to the fact that DEA may have multiple solutions for each DMU. To overcome this problem, Salo and Punkka (2011) deemed each DMU as a “Black Box” and developed models to obtain the efficiency bounds for each DMU over sets of all its feasible weights. In many real world applications, there are DMUs that have a two-stage production system. In this paper, we extend the Salo and Punkka’s (2011) model to a more common and practical case considering the two-stage production structure. The proposed approach calculates each DMU’s efficiency bounds for the overall system as well as efficiency bounds for each subsystem/substage. An application for nonlife insurance companies has been discussed to illustrate the applicability of the proposed approach and show the usefulness of this method.