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As returns to scale (RTS) describes the long run connection of the changes of outputs relative to increases in the inputs, the purpose of this study is to answer the following questions: If the proportionate changes exist in the inputs, what is the rate of changes in outputs with respect to the inputs’ variations in the two-stage networks over the long term? How can the authors investigate quantitative RTS in the two-stage networks? In other words, the purpose of this research is to introduce a different approach to estimate the performance, RTS and scale economies (SE) in network structures.

This paper proposes a novel non-radial approach based on data envelopment analysis to analyze the performance and to investigate RTS and SE in two-stage processes.

The findings show that the range adjusted measure (RAM)/RTS approach can identify reference sets for overall systems and each stage. In addition, the models presented in this paper can classify decision-making units and determine the increasing/decreasing trends of RTS.

The majority of previous RTS studies have been examined in black-box structures and have been discussed in a radial framework. Therefore, in this study, RTS and SE in the two-stage networks are dealt with using an extended RAM approach. Actually, the efficiency and RTS for each stage and the overall model are calculated using the proposed technique.

A growing body of evidence points to the influence of location and allocation decisions on the structure of healthcare networks. The authors introduced a three-level hierarchical facility location model to minimize travel time in the healthcare system under uncertainty.

Most healthcare networks are hierarchical and, as a result, the linkage between their levels makes it difficult to specify the location of the facilities. In this article, the authors present a hybrid approach according to data envelopment analysis and robust programming to design a healthcare network. In the first phase, the efficiency of each potential location is calculated based on the non-radial range-adjusted measure considering desirable and undesirable outputs based on a number of criteria such as the target area's population, proximity to earthquake faults, quality of urban life, urban decrepitude, etc. The locations deemed suitable are then used as candidate locations in the mathematical model. In the second phase, based on the proposed robust optimization model, called light robustness, the location and allocation decisions are adopted.

The developed model is evaluated using an actual-world case study in District 1 of Tehran, Iran and relevant results and different sensitivity analyses were presented as well. When the percentage of referral parameters changes, the value of the robust model's objective function increases.

The contributions of this article are listed as follows: Considering desirable and undesirable criteria to selecting candidate locations, providing a robust programming model for building a service network and applying the developed model to an actual-world case study.

The purpose of this paper is to provide an outline of the major contributions in the literature on the determination of the least distance in data envelopment analysis (DEA). The focus herein is primarily on methodological developments. Specifically, attention is mainly paid to modeling aspects, computational features, the satisfaction of properties and duality. Finally, some promising avenues of future research on this topic are stated.

DEA is a methodology based on mathematical programming for the assessment of relative efficiency of a set of decision-making units (DMUs) that use several inputs to produce several outputs. DEA is classified in the literature as a non-parametric method because it does not assume a particular functional form for the underlying production function and presents, in this sense, some outstanding properties: the efficiency of firms may be evaluated independently on the market prices of the inputs used and outputs produced; it may be easily used with multiple inputs and outputs; a single score of efficiency for each assessed organization is obtained; this technique ranks organizations based on relative efficiency; and finally, it yields benchmarking information. DEA models provide both benchmarking information and efficiency scores for each of the evaluated units when it is applied to a dataset of observations and variables (inputs and outputs). Without a doubt, this benchmarking information gives DEA a distinct advantage over other efficiency methodologies, such as stochastic frontier analysis (SFA). Technical inefficiency is typically measured in DEA as the distance between the observed unit and a “benchmarking” target on the estimated piece-wise linear efficient frontier. The choice of this target is critical for assessing the potential performance of each DMU in the sample, as well as for providing information on how to increase its performance. However, traditional DEA models yield targets that are determined by the “furthest” efficient projection to the evaluated DMU. The projected point on the efficient frontier obtained as such may not be a representative projection for the judged unit, and consequently, some authors in the literature have suggested determining closest targets instead. The general argument behind this idea is that closer targets suggest directions of enhancement for the inputs and outputs of the inefficient units that may lead them to the efficiency with less effort. Indeed, authors like Aparicio et al. (2007) have shown, in an application on airlines, that it is possible to find substantial differences between the targets provided by applying the criterion used by the traditional DEA models, and those obtained when the criterion of closeness is utilized for determining projection points on the efficient frontier. The determination of closest targets is connected to the calculation of the least distance from the evaluated unit to the efficient frontier of the reference technology. In fact, the former is usually computed through solving mathematical programming models associated with minimizing some type of distance (e.g. Euclidean). In this particular respect, the main contribution in the literature is the paper by Briec (1998) on Hölder distance functions, where formally technical inefficiency to the “weakly” efficient frontier is defined through mathematical distances.

All the interesting features of the determination of closest targets from a benchmarking point of view have generated, in recent times, the increasing interest of researchers in the calculation of the least distance to evaluate technical inefficiency (Aparicio et al., 2014a). So, in this paper, we present a general classification of published contributions, mainly from a methodological perspective, and additionally, we indicate avenues for further research on this topic. The approaches that we cite in this paper differ in the way that the idea of similarity is made operative. Similarity is, in this sense, implemented as the closeness between the values of the inputs and/or outputs of the assessed units and those of the obtained projections on the frontier of the reference production possibility set. Similarity may be measured through multiple distances and efficiency measures. In turn, the aim is to globally minimize DEA model slacks to determine the closest efficient targets. However, as we will show later in the text, minimizing a mathematical distance in DEA is not an easy task, as it is equivalent to minimizing the distance to the complement of a polyhedral set, which is not a convex set. This complexity will justify the existence of different alternatives for solving these types of models.

As we are aware, this is the first survey in this topic.

Operational performance is critical for the banking sector for both managers and other stakeholders as it strongly affects the overall performance of the banking system. Traditional performance measures such as ratio analysis encountered certain shortcomings. At this juncture, data envelopment analysis (DEA) approaches are increasingly applied in bank efficiency studies. However, basic DEA models ignored the interactions between consecutive terms and focused primarily on measuring performance independently for each study period. All this is required to develop an operational performance model that can enable the long-term decision model.

An attempt has been made to develop a dynamic DEA within a non-radial category to measure interconnection activities considering non-performing loans as an undesirable link. This study uses the Indian banking dataset from 2015 to 2019. The study's research design directs three directions: ‘comparison of the dynamic DEA with the traditional static DEA model, areas of inefficiencies that are investigated for each factor using the factor efficiency index and the robustness results highlighting the performance difference between bank categories.'

Comparing with static DEA results, the study confirms that the dynamic model best measures long-term operational performance due to the linkage between consecutive terms. The efficiency analysis concludes that the input factor that requires the most improvement is ‘fixed assets' and ‘deposits'. The output factor that needs the most progress is ‘non-interest income'. The robustness of the developed model is proven by ownership categories present within the Indian banking system. At a significance level of 10%, the result of both the separate and dynamic model for privately owned banks is significantly better than that of publicly owned banks.

This paper proposes an operational efficiency model for Indian banks in line with undesirable output. The mean factor efficiency analysis related to non-radial DEA modelling enhances managerial flexibilities in determining improvement initiatives.

Due to its high leverage nature, a bank suffers vitally from the credit risk it inherently bears. As a result, managing credit is the ultimate responsibility of a bank. In this chapter, we examine how efficiently banks manage their credit risk via a powerful tool used widely in the decision/management science area called data envelopment analysis (DEA). Among various existing versions, our DEA is a two-stage, dynamic model that captures how each bank performs relative to its peer banks in terms of value creation and credit risk control. Using data from the largest 22 banks in the United States over the period of 1996 till 2013, we have identified leading banks such as First Bank systems and Bank of New York Mellon before and after mergers and acquisitions, respectively. With the goal of preventing financial crises such as the one that occurred in 2008, a conceptual model of credit risk reduction and management (CRR&M) is proposed in the final section of this study. Discussions on strategy formulations at both the individual bank level and the national level are provided. With the help of our two-stage DEA-based decision support systems and CRR&M-driven strategies, policy/decision-makers in a banking sector can identify improvement opportunities regarding value creation and risk mitigation. The effective tool and procedures presented in this work will help banks worldwide manage the unknown and become more resilient to potential credit crises in the 21st century.

The purpose of this paper is to estimate energy efficiency of 132 countries from 2007 to 2014 according to their performance, categorizing the nations into similar groups.

Data envelopment analysis model based on Goal Programming and then K-Means clustering algorithm are used to determine the efficiency and clustering the nations based on their efficiency performances.

The results of the study reveal that developing low-income countries could lead to high energy-efficiency scores, and countries with different development and income levels can become efficient in the field of energy consumption. Following the nations during a seven-year period also indicates that the changes in energy-related indicators such as renewable energy consumption and energy productivity are the main drivers to move a country between clusters.

The present study aimed to investigate whether similar nations with similar energy efficiency level in a cluster are similar in their development and income level, and changing the energy consumption pattern during the seven-year period could move the countries from a cluster to another one.

The purpose of this paper is to present a holistic approach for measuring overall bank efficiency and its decomposition in intermediation and operating efficiencies.

Recently developed two-stage network data envelopment analysis model by Liang et al. (2008) has been used for obtaining intermediation and operational efficiencies along with overall bank efficiency. The bootstrapped truncated regression algorithm as proposed by Simar and Wilson (2007) has been employed to explore the influential determinants of intermediation and operating efficiencies.

The empirical results reveal that the operating inefficiency is the dominant source of overall bank inefficiency in Indian banking sector. Another interesting finding is that public sector banks are more efficient than private banks in the intermediation stage of production process, while private banks are more efficient in the operating stage of production process. Finally, the results of bootstrapped truncated regression show that variations in intermediation efficiency are explained by bank size, liquidity position, directed lending and intermediation cost, while inter-bank differences in operating efficiency are influenced by profitability and income diversification.

The most significant practical implication that has been derived from the research findings is that at the industry level, overall efficiency enhancement needs improvement both in terms of resource-utilization and income-generating abilities of the banks. However, the relatively easy way to achieve higher bank efficiency is to improve the efficiency of banks in generating incomes from interest and fee-based sources.

This paper is the first to provide a comprehensive assessment of performance of Indian banks by examining the efficiency of individual banks considering both the intermediation and operating approaches simultaneously.

Assessing inputs and outputs is a significant aspect of taking decisions while there are complex and multistage processes in many examinations. Due to the presence of interval performance measures in various real-world studies, the purpose of this study is to address the changes of interval inputs of two-stage processes for the perturbations of interval outputs of two-stage systems, given that the overall efficiency scores are maintained.

Actually, an interval inverse two-stage data envelopment analysis (DEA) model is proposed to plan resources. To illustrate, an interval two-stage network DEA model with external interval inputs and outputs and also its inverse problem are suggested to estimate the upper and lower bounds of the entire efficiency and the stages efficiency along with the variations of interval inputs.

An example from the literature and a real case study of the banking industry are applied to demonstrate the introduced approach. The results show the proposed approach is suitable to estimate the resources of two-stage systems when interval measures are presented.

To the best of the authors’ knowledge, there is no study to estimate the fluctuation of imprecise inputs related to network structures for the changes of imprecise outputs while the interval efficiency of network processes is maintained. Accordingly, this paper considers the resource planning problem when there are imprecise and interval measures in two-stage networks.

The 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.

This 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.

The 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.

This 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.

For strategic and competitive insights, the purpose of this paper is to measure and benchmark the comparative operating efficiencies of Association of Southeast Asian Nations’ (ASEAN) major airlines and present a new interpretation along with managerial implications.

This research statistically tests returns to scale and the equality of mean efficiencies for 15 ASEAN airlines covering the period 2010-2014. The disaggregate input efficiency of ASEAN airlines is computed by comparing the target and actual inputs.

The disaggregate input efficiency of ASEAN airlines shows that aircraft efficiency is the lowest, operating cost efficiency is better, and available seat efficiency is the best.

This paper applies data envelopment analysis models, disaggregated input efficiency measures, and bootstrapping approaches to compute the operational efficiency of ASEAN airlines. Strategic suggestions are made to improve the operational efficiency of ASEAN airlines.