Additive Data Envelopment Analysis Model Research Articles

Efficient targets and reference sets in selectively convex technologies

Conventional models of data envelopment analysis (DEA) typically assume that the underlying production technology is a convex set. It is known that such assumption may be clearly unsubstantiated in certain cases. Examples include studies in which some inputs or outputs are stated as proportions or percentages, or are represented by categorical measures. Excluding such “problematic” inputs and outputs from the assumption of convexity while assuming the latter for the remaining measures leads to the notion of selective convexity. Further examples of selectively convex technologies include technologies parameterized by an environmental factor and technologies in which only the input or output sets are convex. In this paper, we consider the identification of efficient targets and reference sets of decision making units in a selectively convex technology, which has not yet been explored in the literature. We show that, for such technologies, the conventional method based on the solution of the additive DEA model may not correctly identify the reference sets and needs an adjustment.

Measurement and evaluation of multi-function parallel network hierarchical DEA systems

Many organisations are composed of multiple departments connected either in series or in parallel, which may be further decomposed into a number of functions arranged in a hierarchical structure. Several researchers have successfully used appropriate Data Envelopment Analysis (DEA) modelling techniques to assess complex structures. However, to our knowledge, no-one has yet examined the case of measuring and evaluating a parallel network structure combined with a hierarchical one. This paper discusses the development of a multi-function parallel system with embedded hierarchical network structures. A linear additive decomposition DEA model and a non-linear multiplicative aggregation DEA model are proposed as alternatives to evaluate the operating performance of such a structure. The system, the sub-systems, and the efficiencies of their internal units, as well as their relationships, are identified. The system efficiency of the additive model is shown to be greater than or equal to that of the multiplicative model. To verify the applicability of our proposed models, we consider a hypothetical example of the measurement and evaluation of the performances of several Business Schools across a number of universities. Other envisaged areas of application of our structure could include supporting the evaluation of the supply chain management of a firm, or the determination of the most desirable ship design considering maintenance issues.

Performance evaluation of emergency department physicians using robust value‐based additive efficiency model

AbstractWe propose a novel variant of the value‐based additive data envelopment analysis model. It conducts a comprehensive robustness analysis of efficiency outcomes for all feasible input and output weights using mathematical programming and the Monte Carlo simulation. We also introduce the original procedures for selecting a common vector of weights and an approach for investigating the stability of results in a multiscenario setting. The presented framework is applied to evaluate the performance of emergency department physicians using data from the Children's Hospital of Eastern Ontario in Ottawa. Our focus is on the physicians' performance when dealing with groups of patients' complaints related to abdominal pain and constipation, fever, extremity injury, head injury, and laceration/puncture. The obtained results emphasize the strong dependence of the physicians' performances on the selected weight vectors. However, they prove helpful in pointing out overall good performers who can serve as universal benchmarks or niche performers being markedly better in providing care to a given complaint group. They also offer a basis for developing an improvement plan for the underperforming physicians, identifying the priorities for a practice‐oriented model, and recognizing the most challenging patients' complaints.

Developing a new integrated artificial immune system and fuzzy non-discretionary DEA approach

As a useful performance evaluation and decision-making tool, data envelopment analysis (DEA) has been proven to be an excellent data-oriented efficiency analysis method when there are multiple inputs and outputs. However, when working with large datasets, DEA requires more time to solve and calculate the optimal values for each decision-making unit (DMU). To close this methodological gap, this study proposes a new integrated fuzzy nondiscretionary DEA (FNDEA) model and artificial immune system (AIS) to predict and find the optimal values of DMUs. In so doing, we first modify an FNDEA model to classify the set of all DMUs into efficient and inefficient, and immune system (AIS) is used to predict and find the optimal values of DMUs. Then, a modified fuzzy nondiscretionary additive DEA model, which is designed as a middle chain, is used for sensitivity analysis of inefficient DMUs to determine their target outputs, which are called antigens. Finally, we try to reduce the distance between these two steps in order to predict the optimal values (with nearest distance to antigens) of inefficient DMUs and improve their efficiency by using a combined AIS and FNDEA model called the FNDEA–AIS approach. To illustrate the advantages of the proposed FNDEA–AIS approach, a dataset from 24 Iranian forest management units is collected; the results indicated that our new FNDEA–AIS approach (in comparison with other well-established performance prediction techniques) exhibits better convergent validity and high correlation with low error rate to predict optimal values of inefficient DMUs. The main conclusion is that our new applied method, developed for the first time herein, provides a suitable improvement over previously developed methods, such as artificial neural networks (ANNs), to detect inefficiency and to improve the overall performance when analyzing different types of real-life problems.

A novel artificial intelligent approach: comparison of machine learning tools and algorithms based on optimization DEA Malmquist productivity index for eco-efficiency evaluation

Purpose Cement as one of the major components of construction activities, releases a tremendous amount of carbon dioxide (CO2) into the atmosphere, resulting in adverse environmental impacts and high energy consumption. Increasing demand for CO2 consumption has urged construction companies and decision-makers to consider ecological efficiency affected by CO2 consumption. Therefore, this paper aims to develop a method capable of analyzing and assessing the eco-efficiency determining factor in Iran’s 22 local cement companies over 2015–2019. Design/methodology/approach This research uses two well-known artificial intelligence approaches, namely, optimization data envelopment analysis (DEA) and machine learning algorithms at the first and second steps, respectively, to fulfill the research aim. Meanwhile, to find the superior model, the CCR model, BBC model and additive DEA models to measure the efficiency of decision processes are used. A proportional decreasing or increasing of inputs/outputs is the main concern in measuring efficiency which neglect slacks, and hence, is a critical limitation of radial models. Thus, the additive model by considering desirable and undesirable outputs, as a well-known DEA non-proportional and non-radial model, is used to solve the problem. Additive models measure efficiency via slack variables. Considering both input-oriented and output-oriented is one of the main advantages of the additive model. Findings After applying the proposed model, the Malmquist productivity index is computed to evaluate the productivity of companies over 2015–2019. Although DEA is an appreciated method for evaluating, it fails to extract unknown information. Thus, machine learning algorithms play an important role in this step. Association rules are used to extract hidden rules and to introduce the three strongest rules. Finally, three data mining classification algorithms in three different tools have been applied to introduce the superior algorithm and tool. A new converting two-stage to single-stage model is proposed to obtain the eco-efficiency of the whole system. This model is proposed to fix the efficiency of a two-stage process and prevent the dependency on various weights. Converting undesirable outputs and desirable inputs to final desirable inputs in a single-stage model to minimize inputs, as well as turning desirable outputs to final desirable outputs in the single-stage model to maximize outputs to have a positive effect on the efficiency of the whole process. Originality/value The performance of the proposed approach provides us with a chance to recognize pattern recognition of the whole, combining DEA and data mining techniques during the selected period (five years from 2015 to 2019). Meanwhile, the cement industry is one of the foremost manufacturers of naturally harmful material using an undesirable by-product; specific stress is given to that pollution control investment or undesirable output while evaluating energy use efficiency. The significant concentration of the study is to respond to five preliminary questions.

Bankruptcy Prediction with the Use of Data Envelopment Analysis: An Empirical Study of Slovak Businesses

The paper deals with methods of predicting bankruptcy of a business with the aim of choosing a prediction method which will have exact results. Existing bankruptcy prediction models are a suitable tool for predicting the financial difficulties of businesses. However, such tools are based on strictly defined financial indicators. Therefore, the Data Envelopment Analysis (DEA) method has been applied, as it allows for the free choice of financial indicators. The research sample consisted of 343 businesses active in the heating industry in Slovakia. Analysed businesses have a significant relatively stable position in the given industry. The research was based on several studies which also used the DEA method to predict future financial difficulties and bankruptcies of studied businesses. The estimation accuracy of the Additive DEA model (ADD model) was compared with the Logit model to determine the reliability of the DEA method. Also, an optimal cut-off point for the ADD model and Logit model was determined. The main conclusion is that the DEA method is a suitable alternative for predicting the failure of the analysed sample of businesses. In contrast to the Logit model, its results are independent of any assumptions. The paper identified the key indicators of the future success of businesses in the analysed sample. These results can help businesses to improve their financial health and competitiveness.

Additive integer-valued data envelopment analysis with missing data: A multi-criteria evaluation approach.

Traditional data envelopment analysis (DEA) models assume that all the inputs and outputs data are available. However, missing data is a common problem in data analysis. Although several scholars have developed techniques to conduct DEA with missing data, these techniques have some disadvantages. A multi-criteria evaluation approach is proposed to measure the efficiency of decision making units (DMUs) with missing data. In this approach, analysts first estimate the upper and lower bounds of DMUs’ efficiency using the proposed I-addIDEA-U models (interval additive integer-valued DEA models with undesirable outputs) that can be applied to address integer-valued variables and undesirable outputs. Then, DMUs’ “relative” efficiency is evaluated using the proposed “Halo + Hot deck” DEA method (if there is no correlation between variables) or regression DEA techniques (if there is a correlation between variables). Finally, the multi-index comprehensive evaluation method is applied to determine which scenario (the lower bound of efficiency, the “relative” efficiency, or the upper bound of efficiency) should be selected. With a case study, it is shown that the proposed multi-criteria evaluation approach is more effective than traditional approaches such as the mean imputation DEA method, the deletion DEA method, and the dummy entries DEA method.

Supplier selection: comparison of DEA models with additive and reciprocal data

Supplier evaluation is one of the most important fields of application for data envelopment analysis (DEA). Criteria may include negative data in both input and output factors. Data translation can solve this problem, but interpretation is not evident from the literature. Use of an additive model is one method of managing the problem of negative data. This paper addresses this issue in relation to the supplier ranking problem. It describes the development of a ranking with cross-efficiency that incorporates negative data into the additive model. The additive model we describe is compared with previously used DEA models in which data is replaced with reciprocal values when necessary. We present a supplier-evaluation-related example of this case. After the efficiency evaluation, a supplier ranking system is constructed. To do this, we use the cross-efficiencies obtained from the additive model. Aggregate efficiencies help display the suppliers in descending order of efficiency. Finally, the paper compares self- and peer-appraisal indicators for reciprocal and additive DEA models.

An integrated efficiency evaluation of China stock market

Several studies employ data envelopment analysis (DEA) in the area of portfolio optimization or stock market efficiency evaluation, however, they have not extended two-stage network DEA to further decompose the efficiency of firms on the stock market and understand the origin of performance. Because of China’s rising role in global stock market, the current research utilizes the sample of 140 firms extracted from China CSI 300 Index from 2012 to 2016 and proposes an additive two-stage network DEA model to evaluate the performance of China listed firms derived from production and financial production process with fundamental and technical analysis approaches. Analytic hierarchy process and second order cone programming are developed to determine the weights and to solve the nonlinear problem in the additive efficiency decomposition model. In addition to, future data estimated from regression analysis is applied in the DEA model to predict the performance. The main findings are as follows: The production process is more important in defining the overall efficiency of a firm on the stock market; There are significant differences in the distribution of efficiencies among various group industries; The health care, information technology or energy industry has a predicted outstanding performance in general.

Using a Choquet integral-based approach for incorporating decision-maker’s preference judgments in a Data Envelopment Analysis model

In a world in permanent (r)evolution that revolves around money, seeking new ways to contain costs, better allocate resources, and, overall, improve performance is a constant across all fields. Hence, the use of computational methods based on operational research and statistical science is crucial for achieving an appropriate combination of efficiency and effectiveness, especially in domains where the decision-making process is a complex task. This is where Data Envelopment Analysis (DEA) comes in. However, as a non-parametric and, usually, purely objective technique, DEA makes up for what it lacks in incorporating preference information with flexibility and adaptability, which is particularly important in areas where the decision-makers’ judgments are crucial. This work proposes a cutting-edge and original approach to fill in this knowledge gap by linking DEA and multiple criteria decision-making with an additive DEA model that takes into account criteria interactivity, by using an inference methodology to determine their weights, and decision-makers’ preference information incorporation, by taking advantage of the Choquet multiple criteria preference aggregation model. Thus, this approach was applied to a case study of performance assessment of Portuguese National Healthcare Service secondary healthcare providers across robustness-testing perspectives, generating credible weights stemmed from the decision-maker’s judgments and yielding acceptable and valid results.

Additive Integer-Valued DEA Models With Fuzzy Undesirable Outputs: Closest Benchmarking Targets and Super-Efficiency

Many production activities generate undesirable outputs apart from desirable outputs. In addition, the data related to undesirable outputs may be fuzzy (imprecise) in some cases. Based on the fuzzy data theory, we propose a group of additive integer-valued data envelopment analysis (DEA) models with fuzzy undesirable outputs. The advantages of the proposed models are as follows: (1) they enable decision-makers to evaluate the efficiency of decision making units (DMUs) with integer-valued variables and fuzzy undesirable outputs; (2) they can be easily solved without any transformation because they are linear programming models; (3) they are better than radial DEA models as they can identify inefficiencies in all the selected inputs and outputs. Particularly, minimum distance-based additive integer-valued DEA models with fuzzy undesirable outputs are developed in this paper to find the closest benchmarking targets for inefficient DMUs, and additive super-efficiency integer-valued DEA models with fuzzy undesirable outputs are presented to differentiate and rank efficient DMUs. The validity of the proposed models is examined by an empirical application in the pallet rental industry.

A common-weights approach for efficiency evaluation in fuzzy data envelopment analysis with undesirable outputs: Application in banking industry

Data Envelopment Analysis (DEA) is a non-parametric approach based on linear programming for evaluating the performance of decision making units (DMUs) with multiple inputs and multiple outputs. The lack of the ability to generate the actual weights, not considering the impact of undesirable outputs in the evaluation process and the measuring of efficiencies of DMUs based upon precise observations are three main drawbacks of the conventional DEA models. This paper proposes a novel approach for finding the common set of weights (CSW) to compute efficiencies in DEA model with undesirable outputs when the data are represented by fuzzy numbers. The proposed approach is based on fuzzy arithmetic which formulates the fuzzy additive DEA model as a linear programing problem and gives fuzzy efficiencies of all DMUs based on resulting CSW. We demonstrate the applicability of the proposed model with a simple numerical example. Finally, in the context of performance management, an application of banking industry in Iran is presented for analyzing the influence of fuzzy data and depicting the impact of undesirable outputs over the efficiency results.

Benchmarking and Performance Evaluation Towards the Sustainable Development of Regions in Taiwan: A Minimum Distance-Based Measure with Undesirable Outputs in Additive DEA

Sustainable development (SD) governance for a better society has received considerable attention. The development of a robust benchmarking and performance evaluation approach is a matter of growing concern to accelerate the progress in achieving SD. In this study, a minimum distance-based additive data envelopment analysis model with window analysis is proposed to attain the closest benchmarking target in the presence of undesirable outputs. This novel extension not only focuses on the construction of a composite indicator to shed light on the efficiency of each decision-making unit but also provides convincing and realizable suggestions for improving efficiency. This study benchmarks the SD efficiency across 19 administrative regions of Taiwan covering the period from 2011 to 2016. The empirical results reveal that the average SD efficiency of Taiwan has experienced a gradual deterioration over the last 3 years, and the primary sources of regional SD inefficiency may vary with industrial structure. Potential directions of improvement for reinforcing sustainable practices in Taiwan are also discussed. The findings can provide local governments with holistic insights into the sources that degrade SD performance and further contribute to improving SD solutions by recommending appropriate policies to achieve a more sustainable society.

Two-stage additive integer-valued data envelopment analysis models

PurposeThe purpose of this paper is to propose a modified model in multi-stage processes when there are intermediate measures between the stages and in this sense, the new efficiency scores are more accurate. Conventional data envelopment analysis (DEA) models disregard the internal structures of peer decision-making units (DMUs) in evaluating their relative efficiency. Such an approach would cause managers to lose important DMU information. Therefore, in multistage processes, traditional DEA models encounter problems when intermediate measures are used for efficiency evaluation.Design/methodology/approachIn this study, two-stage additive integer-valued DEA models were proposed. Three models were proposed for measuring inefficiency slacks in each stage and in the system as a whole.FindingsThree models were proposed for measuring inefficiency slacks in each stage and in the system as a whole.Originality/valueThe advantage of the proposed models for multi-stage systems is that they can accurately determine the stages with the greatest weaknesses/strengths. By introducing an applied case in the Iranian power industry, the paper demonstrated the applications and advantages of the proposed models.

Multi-period additive efficiency measurement in data envelopment analysis with non-positive and undesirable data

The conventional data envelopment analysis (DEA) models make an assumption of non-negativity in the inputs and outputs data of the decision making units (DMUs) under analysis. In this paper, we present a non-radial measure of efficiency of DMUs by establishing a multi-period additive DEA model taking into consideration both desirable and undesirable inputs and outputs with positive and non-positive values. The proposed efficiency model possesses the requisite features of translation invariance and unit independence, obligatory when dealing with negative values in the data set. Furthermore, this paper contributes with the proposal of a multi-period additive super-efficiency DEA model to discriminate the performance of efficient decision making units. Finally, we present an efficiency evaluation 37 countries worldwide on economic parameters to demonstrate the applicability and efficacy of the proposed models.

Efficiency evaluation of parallel interdependent processes systems: an application to Chinese 985 Project universities

Data envelopment analysis (DEA) has been widely applied in measuring the efficiency of homogeneous decision-making units. Network DEA, as an important branch of DEA, was built to examine the internal structure of a system, whereas traditional DEA models regard a system as a ‘black box’. However, only a few previous studies on parallel systems have considered the interdependent relationship between system components. In recent years, parallel interdependent processes systems commonly exist in production systems because of serious competition among organisations. Thus, an approach to measure the efficiency of such systems should be proposed. This paper builds an additive DEA model to measure a parallel interdependent processes system with two components which have an interdependent relationship. Then, the model is applied to analyse the ‘985 Project’ universities in China, and certain policy implications are explained.

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

AbstractThis 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.

Eco-efficiency measurement and improvement of Chinese industry using a new closest target method

PurposeThe purpose of this paper is to measure Chinese industries’ eco-efficiency during 2006-2013. The Chinese industry attained rapid achievement in recent decades, but meanwhile, overconsumption of energy and environmental pollution have become serious problems. To solve these problems, many research studies used the data envelopment analysis (DEA) to measure the Chinese industry’s eco-efficiency. However, because the target set by these works is usually the furthest one for a province to be efficient, it may hardly be accepted by any province.Design/methodology/approachThis paper builds a new “closest target method” based on an additive DEA model considering the undesirable outputs. This method is a mixed-integer programming problem which can measure the ecological efficiency of provinces and more importantly guide the province to perform efficiently with minimum effort.FindingsThe results show that the eco-efficiency of Chinese provinces increased at the average level, but the deviations remained at a larger value. Compared to the “furthest” target methods, the targets by the approach proposed by this study are more acceptable for a province to improve its performance on both economy and environment counts.Originality/valueThis study is the first attempt to introduce the closest targets concept to measure the eco-efficiency and set the target for each provincial industry in China.

Equivalent solutions to additive two-stage network data envelopment analysis

In the additive approach of two-stage network data envelopment analysis (DEA), the non-linear DEA model is transformed into a parametric linear model and then solved by computing a series of linear programs. Lim and Zhu (2013; Integrated data envelopment analysis: Global vs. local optimum.European Journal of Operational Research, 229(1), 276–278) and Ang and Chen (2016; Pitfalls of decomposition weights in the additive multi-stage DEA model. Omega, 58, 139–153) propose two parametric linear approaches to solve additive two-stage network DEA model. The current study shows that the two approaches are equivalent and use the same parameter in searching for the global optimal solution.

Sustainability Evaluation of Railways in China Using a Two-Stage Network DEA Model with Undesirable Outputs and Shared Resources

This paper constructs an additive two-stage network DEA (data envelopment analysis) model with consideration of undesirable outputs and shared inputs. Following the triple bottom line standard of sustainability, we calculate both the overall and sub-stage sustainability performance of railway transportation in China from 2002 to 2013, from the aspects of economy, environment and society. The results show that the overall sustainability of China’s railway presents a character of first declining, then rising and declining again. Moreover, the railway sustainability of China’s eastern areas are much better than that of the western and central areas, and the gap has become much larger since 2009. As for the sub-stage efficiency, neither the production stage nor the service stage of the railway is efficient in sustainability, and the efficiency of the production stage is lower than that of service stage and plays a greater impact on the overall sustainability. Therefore, in order to improve the overall sustainability of China’s railways, it is essential to improve the level of railway engineering construction and develop technological innovations in railway production.