Non-radial Data Envelopment Analysis Model Research Articles

Evaluation of undergraduate academic programs through data envelopment analysis and time-to-degree estimates at Spanish public universities

This article proposes nonparametric and parametric methods for conducting meaningful evaluations of academic programs. In particular, it proposes the use of data envelopment analysis (DEA) along with regression analysis for the evaluation of Spanish public universities' undergraduate curricula. Unlike the radial DEA models, which assume an equiproportional expansion of all outputs to achieve efficiency, the current study also relies on the use of non-radial DEA models for assessing the efficiency of Spanish public universities. A non-radial DEA measure (the so-called Russell measure) allows for unlike proportional augmentations in each positive output. In this study, non-radial DEA measures allow us to identify different levels of inefficiency for each output considered (social sciences and non-social sciences degrees). Specifically, the results show that the inefficiency in the production of scientific and technical degrees is greater than that in the production of humanities and social sciences degrees, although there are differences among institutions. Bachelor's degree production time is also estimated, and a duration analysis explains the time to degree. A worrying result is the "excessive" time it takes for a university to produce four-year undergraduate degree programs. The mean graduation time is 5.7 years. The Cox proportional hazards regression shows that a shorter time to graduation is associated with higher teaching quality as well as a higher faculty-to-student ratio. Parametric survival analysis using a lognormal distribution with gamma frailty also verifies these latter results.

A hybrid returns to scale-DEA model for sustainable efficiency evaluation of urban transportation systems

The urban transportation network has an undeniable role in addressing the economic, social and environmental issues caused by the traffic. Transportation managers seek to use the existing facilities and capacities in an optimal way to increase customer satisfaction. Therefore, it is necessary to develop an approach to evaluate the performance of the urban transportation system to provide service to citizens effectively. This study develops an approach based on the extended version of the data envelopment analysis (DEA) model to measure the nonradial efficiency and super-efficiency of metro-stations considering the sustainability concept. The developed non-radial DEA model considers the hybrid returns to scale the form of technology by combining constant and variable returns to scale assumptions to improve its applicability to identify efficient and inefficient stations. This DEA model also incorporates the non-discretionary inputs and different types of outputs (i.e. undesirable, negative and non-negative) to improve discrimination power and the ability to interpret the results. The findings help decision-makers identify super-efficient stations as a benchmark for future planning and finding the best location to construct metro-stations. Furthermore, this research enables managers to optimally use the resources to increase the transferred passengers, reduce customer dissatisfaction and optimise the annual profit.

A bootstrapping dynamic two-stage SBM model: An application to assess industrial water use and health risk systems

Despite the great number of applications of bootstrapping data envelopment analysis (DEA) with a one-stage structure, there are limited attempts for approximating the distribution of the DEA estimator considering the two-stage structure across multiple periods. This research develops the dynamic two-stage non-radial DEA model based on smoothed bootstrap and subsampling bootstrap. Then, we run the proposed models on assessing the efficiency of China's industrial water use and health risk (IWUHR) systems and compare them with the bootstrapping results on standard radial network DEA. The results are as follows. (1) The proposed non-radial DEA model based on smoothed bootstrap can adjust original over-estimated and under-estimated values. (2) China's IWUHR system has good performance, and its HR stage performs better than the IWU stage for 30 provinces from 2011 to 2019. The poor performance of the IWU stage in Jiangxi and Gansu needs to be noticed. The provincial differences of the detailed bias-corrected efficiencies expand in the later period. (3) The rankings of IWU efficiency in the three regions are in agreement with that of HR efficiency: eastern, western, and central regions in this order. Particular attention should be paid to the downward trend of the bias-corrected IWUHR efficiency in the central region.

Environmental efficiency assessment of Dublin Port using two-stage non-radial DEA model

The operation of a port is of critical economic importance because of its role in international trade. However, increased operations increase the port's environmental impact and contribute to climate change and global warming. Dublin Port is one of the busiest ports in Ireland, and throughput is expected to increase as the economy continues to grow. Achieving a balance between growing economic activity and reducing environmental impacts is critical to a sustainable future. The efficiency of the port considering operation, economic, and environmental factors can be evaluated using the well-known nonparametric model of Data Envelopment Analysis (DEA). In this study, a novel two-stage non-radial DEA model is used to evaluate the environmental efficiency of Dublin Port considering landward and seaward operations. The proposed two-stage model DEA isolates the efficiency of the two port sides and calculates the overall efficiency. The model minimizes Dublin Port's annual CO2 emissions by reducing a combination of variables that can be realistically controlled by engineering and policy measures. The analysis was extended to account for possible variations in a number of key environmental output factors to compensate for the lack of real-world data availability. The study found that the number of terminals and capital expenditures have significant impacts on the port's environmental efficiency. Small adjustments or reductions in key indicators can improve Dublin Port's efficiency. This methodology can be applied to other ports in growing economies that use similar indicators to assess their environmental efficiency.

A Modified-Range Directional Measure for Assessing the Sustainability of Suppliers by DEA/UTASTAR

Sustainability in the supply chain means considering environmental, social, and economic practices. Conventional data envelopment analysis (DEA) models deal with desirable, discretionary, and nonnegative data. However, there might be undesirable outputs, nondiscretionary factors, and negative data. On the other hand, some criteria can be considered as outputs and inputs. These factors are named as the dual-role criteria. The objective of this paper is to develop a non-radial DEA model for dealing with negative data in the presence of undesirable, non-discretionary, and dual-role factors in weight restrictions context. The ordinal regression method, UTASTAR, is performed to define priorities in terms of criteria. The capabilities of the proposed method are compared with other methods. A case study is presented in which the best sustainable suppliers of SAPCO are selected. To check the importance of dual-role variables, two extra cases are considered.

Robust non-radial data envelopment analysis models under data uncertainty

Russell measure (RM) and enhanced Russell measure (ERM) are popular non-radial measures for efficiency assessment of decision-making units (DMUs) in data envelopment analysis (DEA). Input and output data of both original RM and ERM are assumed to be deterministic. However, this assumption may not be valid in some situations because of data uncertainty arising from measurement errors, data staleness, and multiple repeated measurements. Interval DEA (IDEA) has been proposed to measure the interval efficiencies from the optimistic and pessimistic viewpoints while the robustness of the assessment is questionable. This paper draws on a class of robust optimisation models to surmount uncertainty with a high degree of robustness in the RM and ERM models. The contribution of this paper is fivefold; (1) we develop new robust non-radial DEA models to measure the robust efficiency of DMUs under data uncertainty, which are adjustable based upon conservatism levels, (2) we use Monte-Carlo simulation in an attempt to identify an appropriate range for the budget of uncertainty in terms of the highest conformity of ranking results, (3) we introduce the concept of the price of robustness to scrutinise the effectiveness and robustness of the proposed models, (4) we compare the developed robust models in this paper with other existing approaches, both radial and non-radial models, and (5) we explore an application to assess the efficiency of the Master of Business Administration (MBA) programmes where data uncertainties influence the quality and reliability of results.

Comparison of Different Methods for Estimation of Returns to Scale in Nonradial Data Envelopment Analysis Models

Comparison of Different Methods for Estimation of Returns to Scale in Nonradial Data Envelopment Analysis Models

Operational Performance of Banks: Frontier-Based Data Envelopment Analysis with Undesirable Output

The current banking scenario marks the rising level of non-performing loans (NPLs), which negatively impacts the operational performance of banks. There is a need for an operating performance model that integrates the NPLs into the measurement of operational efficiency to provide the overall performance profile for Indian banks. The study applies a non-radial data envelopment analysis model developed by Tone (2001) and incorporates NPLs as undesirable output. The study draws empirical insights on operational performance for Indian banks for a recent five-year period. With the adoption of the non-orientation approach of the developed model, the significant contribution of the study is related to mean factor efficiency analysis, which allows the identification of inefficient sources causing operational inefficiency within banks. The robustness test result throws light on efficiency differences between two ownership categories of banks. Implications of empirical findings suggest that the regulators devise measures to control the level of NPLs to help improve the operational efficiency of the Indian banking system.

Measuring operational and quality-adjusted efficiency of Chilean water companies

The path to a sustainable management of the urban water cycle requires the assessment of both operational and quality-adjusted efficiency in a unified manner. This can be done by the use of non-radial Data Envelopment Analysis models. This study used Range Adjusted Measure models to evaluate the operational, quality-adjusted, and operational & quality-adjusted efficiency (O&QAE) scores of the Chilean water industry including water leakage and unplanned interruptions as undesirable outputs. It was found that on average water utilities presented large O&QAE scores over time. The mean O&QAE score was 0.964 which means that water utilities could further reduce costs and undesirable outputs by 3.6% on average, while trying to expand the scale of operation. This finding suggests that excellent quality-adjusted efficiency at an efficient expenditure could be feasible. It was also evidenced that customer density, mixed water resources, and ownership influenced the O&QAE of Chilean water companies.

Integrating group frontier and metafrontier directional distance functions to evaluate the efficiency of production units

Over the last decade, many studies have adopted the data envelopment analysis (DEA)-type metafrontier framework to relax the constraint of technological heterogeneity. In conventional metafrontier analyzes, either radial or nonradial DEA models are used in two separate DEA efficiency analyzes. The results of a metafrontier analysis may be biased if this approach is adopted in a nonradial DEA model. One possible problem is that the value of the technology gap ratio is greater than one because the technology gaps to be estimated for decision-making units (DMUs) under different technology groups relative to the metatechnology have no connection between group frontiers and metafrontiers. Furthermore, the direction of projection of each DMU onto the metafrontier is totally independent of the direction to the efficiency frontier of the respective group frontier. Our proposed integration of group technology and metatechnology constraints into a union model offers a possible solution to the existing metafrontier problem and provides more robust metafrontier results regardless of whether radial or nonradial DEA models are used. Four numerical examples and one empirical application are demonstrated, and the results appear to support the use of our proposed model.

Eco-efficiency and Eco-productivity assessments of the states in the United States: A two-stage Non-parametric analysis

This study implements radial and non-radial Data Envelopment Analysis (DEA) models to assess eco-efficiency and eco-productivity of the 50 states in the United States in 2018. The models are based on three inputs (capital stock, employment, and energy consumption), a single desirable output (real gross domestic product) and a single undesirable output variable (CO2 emissions). The radial DEA models reveal that at least 32 states are operated efficiently. Five states perform at the most optimal scale size, whereas 17 states have considerable potential to boost their productive efficiencies by enlarging available resources, and 28 states are overinvested in their input variables given their current output levels. The non-radial DEA models show that, overall, the states’ capital efficiency is very high, whereas energy and emission efficiencies are very low. The states’ eco-productivity is relatively higher than the eco-efficiency levels. In the second stage of the analysis, non-parametric statistical tests and Tobit regressions are conducted for further investigation. According to the non-parametric statistical test, high capital stock, labor force, and energy usage do not affect the states’ productive efficiency. However, states with low carbon dioxide emissions have significantly higher eco-efficiency and eco-productivity levels. The Tobit regression results illustrate that nuclear power and renewable energy consumption significantly affect the states’ relative efficiencies.

Improving information reliability of non-radial value efficiency analysis: An additive slacks based measure approach

The value efficiency approach is one possible way of incorporating information preferences into performance analysis of Decision-Making Units (DMUs). In this paper, we propose a novel geometric interpretation of value efficiency while plugging it into radial and non-radial DEA (Data Envelopment Analysis) models under the assumption of variable returns to scale. In addition, this novel geometric interpretation of value efficiency is extended to Additive Slacks-Based Measure (ASBM) modeling. This is achieved by linearization of non-radial DEA models using multi-objective programming. Performance of such proposed approaches in terms of reliability and discriminatory power are compared through a case study involving Finish bank branches. Research implications are then derived and conclusions are drawn.

Eco-efficiency assessment of municipal solid waste services: Influence of exogenous variables.

Improving the eco-efficiency of municipalities in the provision of municipal solid waste (MSW) services is fundamental in the context of a circular economy. This study evaluates the eco-efficiency of a sample of Spanish municipalities, integrating the total cost as input, recyclable waste as desirable output, and unsorted waste as undesirable output. Following a pioneering approach, the weighted Russell directional distance model (a non-radial data envelopment analysis model) was employed, which allowed us to obtain a global inefficiency score and individual inefficiency scores for each variable integrated in the model. In the second stage of analysis, the potential factors affecting the previously computed inefficiency scores were investigated. The results indicated that one third of the municipalities evaluated were eco-efficient in the provision of MSW services with the total cost being the variable in which the municipalities exhibited the best performance. Moreover, the size of the municipalities, population served, population density, tourism, and availability of containers for separative collection of paper, glass, and plastic significantly affect the eco-efficiency of the municipalities. The findings of this study provide detailed information to support decision-making for the policy makers to improve the eco-efficiency of the municipalities in managing MSW.

Financing manufacturers for investing in Industry 4.0 technologies: internal financing vs. External financing

Supply chain finance (SCF) as a crucial approach plays a key role in improving commitment, trust, financial flows, and profitability in a supply chain (SC). Many industrial organisations finance their SC through two resources: internal financing (buyer) and external financing (bank). The main objective of this paper is to develop an advanced data envelopment analysis (DEA) model for measuring the sustainability of financing resources of Industry 4.0 technologies. To do so, for the first time a non-radial DEA model in the presence of both zero inputs and ratio data is proposed. In this paper, the sustainability factors, including economic, environmental, and social factors are incorporated into the proposed approach. The developed DEA model, for the first time, is applied in SCF. The results show the most sustainable financial resource for investing in Industry 4.0 technologies. Also, the inputs and outputs’ inefficiencies are determined.

A Review of Data Envelopment Analysis in Airline Efficiency: State of the Art and Prospects

The rapid development of the aviation industry has brought about the deterioration of the climate, which makes airline efficiency become a hot issue of social concern. As an important nonparametric method, Data Envelopment Analysis (DEA), has been widely applied in efficiency evaluation. This paper examines 130 papers published in the period of 1993–2020 to summarize the literature involving the special application of DEA models in airline efficiency. The paper begins with an overall review of the existing literature, and then the radial DEA, nonradial DEA, network DEA, dynamic DEA, and DEA models with undesirable outputs applied in airline efficiency are introduced. The main advantages and disadvantages of the above models are summarized, and the drivers of airline efficiency are analyzed. Finally, the literature review ends up with future research directions and conclusions.

A New Model to Analyze the Efficiency of a Multilevel Drug Supply Network for Hospitals

It is of special importance to procure medicines as strategic commodities. The purpose of this study is to manage a drug supply network using a non-radial data envelopment analysis (DEA) model. This study is conducted in private hospitals in Tehran. In this regard, a drug supply chain at three levels of suppliers, distributors, and consumers (pharmacies and hospitals) is examined. Indicators and limitations of the network are identified and then the appropriate model is formulated using mathematical equations on the basis of a non-radial DEA model. In order to validate the proposed model, data related to 30 hospitals during 2019 and 2020 is evaluated. According to this model, 5 hospitals had efficient supply networks and 25 hospitals had deficient supply networks. The proposed new model is able to evaluate the multilevel supply network and intermediate components in hospitals. The problems of the drug supply network are due to the increase in demands for the time period under consideration and the existence of inconsistencies in the drug supply chain in hospitals, which has led to an increase in inefficient hospitals.

Energy efficiency analysis in public hospitals: an application of radial and non-radial data envelopment analysis models

Energy efficiency analysis in public hospitals: an application of radial and non-radial data envelopment analysis models

Chinese liquor company management efficiency from a social responsibility perspective: a two stage dynamic directional distance function

Because the liquor industry is an important industry in China, alcohol companies have greater social responsibilities when upgrading their production processes to improve efficiencies. Two main data envelopment analysis (DEA) methods have been used for efficiency analyses: radial models, such as CCR (Charnes, Cooper, Rhodes) and BCC (Banker, Charnes, Cooper) and non-radial methods such as SBM (slacks-based model); however, both have disadvantages. The radial DEA model ignores the non-radial slacks and the non-radial DEA model ignores the characteristics of the same proportion in the radial DEA model. Therefore, this research used a dynamic two-stage directional distance function (DDF) model to analyse the production efficiencies of Chinese listed liquor companies from 2016 to 2018 by evaluating each company’s poverty alleviation input efficiencies, business operations efficiencies, and their social responsibility efficiencies, which was based on their wastewater treatment efficiencies. To overcome the disadvantages in traditional data envelopment models, the DDF model consisted of both input and output direction vectors, the indicator values for which indicated their relative importance or priorities. The analyses found that the indicator efficiencies at most liquor companies had declined, with the poverty alleviation indicator efficiencies being generally lower than the wastewater treatment indicator efficiencies. Several policy and management recommendations are given to improve the overall corporate efficiency and social responsibility in the Chinese liquor industry.

A slacks-based measure approach for efficiency decomposition in multi-period two-stage systems

Two-stage production systems are often encountered in many real applications where the production process is divided into two processes. In contrast to the conventional data envelopment analysis (DEA) models, two-stage DEA models take the operations of the internal processes into account. A number of studies have used two-stage DEA models in order to evaluate the performance of decision making units (DMUs) having a network structure. In this paper, we use a non-radial DEA model called the network slacks-based measure (NSBM) model to measure the efficiency of a system with a multi-period two-stage structure. Then we describe the properties of the proposed model in details. Moreover, we shall decompose the overall efficiency of the system over a number of time periods as a weighted average of the efficiency in each period. The efficiency of the stages, in respect to the entire periods shall be decomposed in terms of the weighted average efficiency of the stages in each period. Finally, the real data of Mellat bank branches in Tehran extracted from extant literature is used to illustrate the proposed approach.

Supporting better practice benchmarking: A DEA-ANN approach to bank branch performance assessment

The quest for best practices may lead to an increased risk of poor decision-making, especially when aiming to attain best practice levels reveals that efforts are beyond the organization’s present capabilities. This situation is commonly known as the “best practice trap”. Motivated by such observation, the purpose of the present paper is to develop a practical methodology to support better practice benchmarking, with an application to the banking sector. In this sense, we develop a two-stage hybrid model that employs Artificial Neural Network (ANN) via integration with Data Envelopment Analysis (DEA), which is used as a preprocessor, to investigate the ability of the DEA-ANN approach to classify the sampled branches of a Greek bank into predefined efficiency classes. ANN is integrated with a family of radial and non-radial DEA models. This combined approach effectively captures the information contained in the characteristics of the sampled branches, and subsequently demonstrates a satisfactory classification ability especially for the efficient branches. Our prediction results are presented using four performance measures (hit rates): percent success rate of classifying a bank branch’s performance exactly or within one class of its actual performance, as well as just one class above the actual class and just one class below the actual class. The proposed modeling approach integrates the DEA context with ANN and advances benchmarking practices to enhance the decision-making process for efficiency improvement.