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An attractive feature of standard data envelopment analysis (DEA) is that decision-making units (DMUs) are put in their best possible light. This is accomplished by not imposing any restrictions on how the inputs and outputs can be weighted together. Unfortunately, this flexibility also has drawbacks. The underlying best practice production structure is typically very complex, which can make it difficult to understand efficiency evaluations. This flexibility may also motivate DMUs to pick specialized input‒output combinations simply to appear more efficient, particularly in applications where they are rewarded based on their DEA performance. In this paper, we therefore propose an approach that retains the fundamental principles of DEA while reducing flexibility in the evaluations. Our approach entails performing ex post k-centroid clustering of DMUs according to their input‒output mix patterns. The resulting mixed-integer programming problem seeks to put the centroids (as prototypes of their generated clusters) in their best possible light. This clustering enables us to work with a less complex underlying technology, which simplifies the evaluations and enhances their interpretability. Furthermore, it limits the possibility of DMUs inflating their performance by selecting extreme input‒output combinations. We demonstrate our approach with a simple numerical example and a complex data set involving Brazilian electricity distribution companies, providing clear and realistic illustrations of its application., An attractive feature of standard data envelopment analysis (DEA) is that decision-making units (DMUs) are put in their best possible light. This is accomplished by not imposing any restrictions on how the inputs and outputs can be weighted together. Unfortunately, this flexibility also has drawbacks. The underlying best practice production structure is typically very complex, which can make it difficult to understand efficiency evaluations. This flexibility may also motivate DMUs to pick specialized input‒output combinations simply to appear more efficient, particularly in applications where they are rewarded based on their DEA performance. In this paper, we therefore propose an approach that retains the fundamental principles of DEA while reducing flexibility in the evaluations. Our approach entails performing ex post k-centroid clustering of DMUs according to their input‒output mix patterns. The resulting mixed-integer programming problem seeks to put the centroids (as prototypes of their generated clusters) in their best possible light. This clustering enables us to work with a less complex underlying technology, which simplifies the evaluations and enhances their interpretability. Furthermore, it limits the possibility of DMUs inflating their performance by selecting extreme input‒output combinations. We demonstrate our approach with a simple numerical example and a complex data set involving Brazilian electricity distribution companies, providing clear and realistic illustrations of its application.An attractive feature of standard data envelopment analysis (DEA) is that decision-making units (DMUs) are put in their best possible light. This is accomplished by not imposing any restrictions on how the inputs and outputs can be weighted together. Unfortunately, this flexibility also has drawbacks. The underlying best practice production structure is typically very complex, which can make it difficult to understand efficiency evaluations. This flexibility may also motivate DMUs to pick specialized input‒output combinations simply to appear more efficient, particularly in applications where they are rewarded based on their DEA performance. In this paper, we therefore propose an approach that retains the fundamental principles of DEA while reducing flexibility in the evaluations. Our approach entails performing ex post k-centroid clustering of DMUs according to their input‒output mix patterns. The resulting mixed-integer programming problem seeks to put the centroids (as prototypes of their generated clusters) in their best possible light. This clustering enables us to work with a less complex underlying technology, which simplifies the evaluations and enhances their interpretability. Furthermore, it limits the possibility of DMUs inflating their performance by selecting extreme input‒output combinations. We demonstrate our approach with a simple numerical example and a complex data set involving Brazilian electricity distribution companies, providing clear and realistic illustrations of its application.

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

The Strategic Framework for European Cooperation in Education and Training (ET 2020) aimed to promote the exchange of best practices among the Member States. This paper assesses the performance evolution of European countries in terms of the common objectives for the education sector. The framework used to evaluate European education systems is based on constructing a composite indicator adopting a “benefit-of-the-doubt” approach. The evaluation of performance change over time is done using a Global Malmquist Index. Sigma and beta convergence of EU countries are also explored using non-parametric frontier techniques. The results are analysed for the period 2009–2018 and discussed in light of the goals envisaged and the national policies adopted. The results revealed a trend of improvement in the performance of education systems in most European countries in the period analysed. Although most European countries moved closer to the European best practice frontier over time, as confirmed by the values of sigma-convergence, a few countries are still lagging considerably below their peers, as revealed by the existence of divergence in beta.

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 analyses, either radial or nonradial DEA models are used in two separate DEA efficiency analyses. 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 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.

In this paper, we focus on a two-level production and distribution planning problem in the field of supply chain management, and examine the situations where the leader does not fully know the manufacturing technologies of the follower. In such a situation, the parameters representing the manufacturing technologies cannot be explicitly used to formulate the follower’s production planning problem. To overcome this difficulty, we propose formulations that implicitly express manufacturing technologies by using the input-output data observed from the production activities of the follower, incorporating the idea of data envelopment analysis (DEA). Assuming that the follower has multiple production facilities, we consider two possibilities of the observable input-output data and formulate two corresponding production planning problems; firstly, that only the input-output data aggregated for all the production facilities can be observed collectively, and secondly, that the input-output data for each of the production facilities can be observed separately. To clarify the validity of these DEA approaches, we compare them with the conventional formulation with technological coefficients using a numerical example.

In recent years, implementation of pay-for-performance (P4P) programmes in health care has become a worldwide initiative. However, most P4P programmes incorporate systems of Performance Indicators (PI) without accounting for trade-offs between indicators. This article has two objectives: (1) to develop a Data Envelopment Analysis (DEA) methodology for performance assessment of primary care providers; and (2) to propose an innovative methodology for P4P contracting based on the DEA assessment results. To achieve the first objective, we modify the standard DEA model to account for the necessary relations between the weights attributed to each PI and domain of performance and to account for the effect of the relevant environmental variables. To achieve the second objective, we combine relative and absolute performance assessments in the elaboration of several bases for reward, and then we link these assessments to a system of graduated rewards. A benchmarking programme is also proposed to contribute to the dissemination of best practices. This article contributes to the literature by proposing an enhanced methodology for performance assessment of primary care providers which can form the basis for P4P rewards planning. The applicability and advantages of the proposed methodology are illustrated with data from Portugal, but it can easily be adapted to different sets of PIs or domains, making it relevant for performance assessment and for P4P reward setting in other contexts and countries. info:eu-repo/semantics/publishedVersion

This paper introduces a modelling framework which combines Data Envelopment Analysis and Markov Chains into an integrated decision aid. Markov Chains are typically used in contexts where a system (e.g. staff profile in a large organisation) is at the start of the planning horizon in a given state, and the aim is to transform the system to a new state by the end of the horizon. The planning horizon can involve several steps and the system transits to a new state after each step. The transition probabilities from one step to the next are influenced by both organisational and external (non-organisational) factors. We develop our generic methodology using as a vehicle the homogeneous Markov manpower planning system. The paper recognizes a gap in existing Markovian manpower planning methods to handle stochasticity and optimization in a more tractable manner and puts forward an approach to harness the power of DEA to fill this gap. In this context, the Decision Maker (DM) can specify potential anticipated future outcomes (e.g. personnel flows) and then use DEA to identify additional feasible courses of action through convexity. These feasible strategies can be evaluated according to the DM's judgement over potential future states of nature and then employed to guide the organisation in making interventions that would affect transition probabilities to improve the probability of attaining the ultimate state desired for the system. The paper includes a numerical illustration of the suggested approach, including data from a manpower planning model previously addressed using classical Markov modelling.

Firms have become increasingly customer-centric, implying that customers, rather than products, are treated as the most important asset of a firm. The switch to customer-centric strategies also implies that firms are collecting an enormous amount of customer-related data. The purpose of this paper is to propose a DEA-based methodology to determine the contribution of customer segments to firm value. We show the practical usefulness of our methodology through an application to Activity Based Costing (ABC) data collected from a large European telecom provider, which offers fixed telephone, mobile telephone, digital television and internet subscriptions. Our analysis reveals that the average cost reduction potential across all customer segments amounts to 1.26% of the total controllable costs, which represents approximately EUR 5 million when expressed in monetary terms. We also document substantial variation in the cost reduction potential across customer segments.

Funding Information: We wish to thank the reviewers for useful suggestions and comments, which greatly improved our paper. Publisher Copyright: © 2021 The Authors Our paper focuses on a robustness analysis of efficiency scores in the context of Data Envelopment Analysis (DEA) assuming interval scale data, as defined in A. Dehnokhalaji, P. J. Korhonen, M. Köksalan, N. Nasrabadi and J. Wallenius, “Efficiency Analysis to incorporate interval scale data”, European Journal of Operational Research 207 (2), 2010, pp. 1116–1121. We first show that the definition of the efficiency score used in our paper is a well-defined measure according to Aparicio and Pastor (J. Aparicio and J. T. Pastor, “A well-defined efficiency measure for dealing with closest targets in DEA”, Applied Mathematics and Computation 219 (17), 2013, pp. 9142–9154.). Next, we characterize how robust the efficiency scores are with respect to improvements and deteriorations of inputs and outputs. We illustrate our analysis with two examples: a simple numerical example and a more complex example using real-world data.

To help enhancing affordability and availability in the U.S. individual health insurance markets, we evaluate whether expanding interstate markets is associated with efficiency improvement, and the potentials of “Medicaid for All” and “Medicare for All”. This research aims to provide insights and evidence for data-driven decision making in reforming individual health insurance markets and optimizing individual health insurance operations. We employ traditional, non-oriented slack-based, order-α partial frontier, bootstrapped bias-corrected, and modified context-dependent data envelopment analysis (DEA) models, as well as generalized linear, Tobit, and residual inclusion regression models. We find that higher competition or expansion is not associated with higher consumer efficiency or societal efficiency. Our results also indicate that, in minimizing premiums or expenses given enrollment and utilization of medical services, individual health plans are less efficient than Medicaid managed care plans, but more efficient than Medicare Advantage plans. Our findings imply that, for individual plans, expanding interstate markets is not accompanied with lower premiums or expenses without the sacrifice of medical services. This research suggests that it should be advisable to structure individual health insurance markets following the Medicaid managed care model but not the Medicare Advantage model. To “Medicaid-ize” individual markets, we propose to structure the individual coverage in two layers: a conditionally subsidized Medicaid managed care program with mandatory essential benefits, and an unsubsidized “Medicaid Supplement” program for optional additional coverages.

Data envelopment analysis is a technique widely used to measure the relative efficiency of a set of decision making units and for ranking alternatives based on the measured efficiency. When there are data that need to be estimated, a group of experts is consulted. The opinions of the experts can be aggregated at either the data level, based on which the efficiency is calculated, or the efficiency level, where the efficiencies calculated from the data provided by individual experts are aggregated. However, the results may not be consistent, which leads to a puzzling situation as which result to follow. In this paper, a method of determining appropriate weights by which the opinions of the experts can be used to calculate the efficiency of alternatives is proposed. One radial model and one slacks-based measure (SBM) model are constructed based on this idea. It is shown that, for both models the results obtained from aggregating the opinions at the data level and at the efficiency level are the same. The final efficiencies are thus reliable. A case of a robot selection problem for a manufacturing company in Taiwan is used for the purpose of illustration. The results show that the radial efficiency is dependent on the non-Archimedean number and will overstate the performance of the robot. The SBM efficiency, which does not have this drawback, is more reliable than the radial efficiency to be used for ranking. A robot is suitably selected based on the SBM efficiency.

Within the framework of data envelopment analysis (DEA) methodology, the problem of determining the closest targets on the efficient frontier is receiving increased attention from both academics and practitioners. In the literature, the number of approaches to this problem are increasing, most of which are based on the computation of closest targets. Some of the existing approaches satisfy the important property of strong monotonicity. However, they tend to either propose a complex conceptual framework and multi-stage procedure or change the original definition of Holder distance functions. Clearly, these approaches cannot be solved easily when there are many “extreme” efficient units with multiple inputs and multiple outputs. To solve this problem, we consider the notion of the extended facet production possibility set (EFPPS). In particular, we propose a Mixed Integer Linear Program (MILP) to find the closest efficient targets and that is related to a measure that satisfies the strong monotonicity property. Additionally, in this paper, the proposed approach is applied to real data from 38 universities involved in China's 985 university project.

Classical efficiency studies on data envelopment analysis (DEA) consider all its inputs and outputs are desirable factors and real valued-data. Additionally, the DEA models only focus either on input-oriented projection minimizing inputs for an inefficient decision making unit (DMU) while keeping outputs at their maximum level, or output-oriented projection maximizing outputs under the present level of input consumption. To simultaneously deal with input excesses and output shortfalls maximizing both projections, this paper proposes a bi-objective DEA model in the context of undesirable factors and mixed integer requirements. These factors and requirements were integrated into the objective function and constraints of the existing bi-objective models. In addition, the proposed model estimates the returns to scale of DMUs that depends on the projections of input reduction and output augmentation. The applicability and usefulness of the proposed model were tested using the dataset of 39 Spanish airports retrieved from the literature. Besides, the proposed model was compared with the three existing bi-objective DEA models in the literature to test its validity.

In this paper we propose hinging hyperplanes (HHs) as a flexible nonparametric representation of a concave or an S-shaped production function. We derive the HHs using expressions with focus on the distinction between hinge location and the bending along each hinge. We argue that the HHs approximation can be estimated using a fixed endogenous determined partitioning of the input space. Assuming a homothetic production function allows us to separate the S-shape scaling law and the underlying core function. We propose an estimation procedure where two HHs function approximations of the core function and the scaling law are estimated simultaneously. A closed form expression of the inverse of the piecewise linear inverse scaling law is proposed and proved. We stress the known result that the HHs formulation is equivalent to the Canonical Piecewise-Linear representation of a piecewise linear function and exploit the result that the HHs formulations for the core function and for the scaling law provide global representations of all piecewise linear functional forms. A simulation study evaluates the performance of the proposed estimation procedure of an S-shaped production function.

The current paper estimates the overall inefficiency indicator of a bank under a network Data Envelopment Analysis (DEA) in the presence of undesirable inputs and outputs. We primarily contribute to the DEA literature in four ways. First, we decompose banks’ overall inefficiency performance indicator into five component indicators, namely, the sub-indicators of innovation, two kinds of stability, profitability and corporate social responsibility. Second, since the proposed model, which is an absolute value optimization problem, does not give the overall inefficiency score directly, we introduce a two-step procedure to obtain all sub-indicator scores and the overall inefficiency score. Third, we extend the by-production framework by proposing not only a concept and interpretation of “strategic disposability” for an intermediate undesirable output in estimating the stability sub-indicators, but also another concept of “strategic disposability” for an intermediate undesirable input in gauging the sub-indicator related to corporate social responsibility. Our results show that 1) the Chinese banking industry has a high level of innovation inefficiency and profitability inefficiency is higher than primary business stability inefficiency, strategic management stability inefficiency and corporate social responsibility inefficiency for all the bank ownership types except the state-owned commercial banks; 2) state-owned commercial banks have a higher level of corporate social responsibility inefficiency compared to the other inefficiencies; 3) state-owned commercial banks, rural commercial banks and joint-stock commercial banks are the best three performers with different ownership types performing well in different perspectives; 4) all different ownership types experience a level of performance volatility over the examined period.

Radiotherapy treatment (RT) irradiates a patient's tumour volume while minimising damage to healthy tissue and surrounding critical organs at risk (OAR). In the conventional RT planning process, the RT planner has to iteratively adjust either the planning objectives (tumour or OAR dose levels) or the weights of the planning objectives until an acceptable plan is obtained that satisfies the minimum requirements. At the end of this iterative process, it remains unknown whether this plan is the best that can be obtained for the patient. The oncologist reviews each plan and decides to either treat using this plan or request further plan development, which may or may not lead to an actual improvement of the reviewed plan. We describe how Data Envelopment Analysis (DEA) is used as a real-time decision support tool to assess quality of RT plans for head and neck cancer patients by applying a knowledge-based comparison of each new plan to a library of previous clinically approved plans. This library allows benchmarking, which gives planners and oncologists a better idea of the relative quality of their plan and its improvement potential, resulting in improved use of resources and better quality treatments for patients. Our DEA-based approach provides a novel way of capturing multiple measures of plan quality as well as anatomical differences between patients in the benchmarking process. We present the developed DEA model and results for a set of benchmark instances. Initial results of integrating DEA-based quality feedback into the RT planning process are presented showing that operations research can contribute significantly to planning quality in this setting.

Data envelopment analysis (DEA) is a technique used to measure the relative efficiency of a set of production units that applies multiple inputs to produce multiple outputs. In its original settings, the data is required to be nonnegative. To allow for negative data, several methods have been proposed. While these methods have merits, they also have weaknesses and limitations. This paper generalizes the construction of the production possibility set from production units with nonnegative observations to those with real values. Given the signs of the aggregate target and aggregate observed outputs of the production units to be evaluated, different models are developed to calculate the efficiencies under both variable and constant returns to scale technologies, and an additive model is used to identify the signs of the aggregate target and aggregate observed outputs. Since the efficiencies are calculated from the original observations without transformation or manipulation, the proposed method does not have the drawbacks of the existing methods. A case of the Detroit National Bank shows that the results obtained from the proposed method are more representative and reliable as compared to those obtained from a data transformation method.

Banks have two primary strategies for adapting to a regulation change in the era of big data which can be characterized as natural disposability and managerial disposability. Natural disposability implies a negative strategy by which a bank attempts to decreases its vector of inputs to decrease undesirable outputs. In contrast, managerial disposability indicates a positive strategy by which a bank considers a regulation change as an opportunity and adapt the regulation change by utilizing big data technology. The operational process of a bank can be decomposed into a productivity stage and a profitability stage. Furthermore, the operation costs, a shared resource, can be used to characterize natural disposability and managerial disposability. Based on natural disposability and managerial disposability, this paper proposes two network models to estimate the efficiencies of banks. To test their practical implications, the proposed models were applied to examine the efficiencies of Chinese commercial banks in the period 2014−2018. Our key findings are as follows. (1) There exist great disparities in the inefficiencies between two adaptive strategies. The inefficiencies are primarily driven by the profitability stage under natural disposability, whereas the inefficiencies are equally attributed to both stages under managerial disposability. (2) The efficiency differences among different types of banks are insignificant under natural disposability but are significant under managerial disposability. (3) Joint-stock commercial banks are more oveall efficient than state-owned commercial banks, city commercial banks and rural commercial banks, while state-owned commercial banks show worst practice for overall efficiency and profitability stage efficiency.

Data envelopment analysis (DEA) is a useful tool for measuring the relative efficiencies of participating nations in the Olympic Games. DEA models with restricted multipliers have been used to refine efficiency evaluations by imposing additional information. Existing DEA models for evaluating Olympic medals do not focus on multiplier restrictions regarding input. To fill this research gap, this study incorporates a data fitting technique of medal prediction using ordinary least squares regression in input multiplier restrictions of the conventional DEA model. We show that the efficiency of the proposed model can be decomposed into the achievement ratio of substantial medal total and the unit value index of medals. Such decompositions can be used to analyze the effectiveness of host nations and athlete development initiatives. For an illustrative empirical application, we examine the target that the Brazilian Olympic Committee (BOC) set for the 2016 Summer Olympic Games (Rio 2016). Our results explain the extremely high feasibility of Brazil’s target of being in the top 10 medals table in Rio 2016.

Ghasemi, Ignatius, and Rezaee (2019) (Improving discriminating power in data envelopment models based on deviation variables framework. European Journal of Operational Research 278, 442– 447) propose a procedure for ranking efficient units in data envelopment analysis (DEA) based on the deviation variables framework. They claim that their procedure improves the discriminating power of DEA and can be an alternative to the super-efficiency model that is well-known to have the infeasibility problem and the cross-efficiency approach which suffers from the presence of multiple optimal solutions. However, we demonstrate, in this short note, that their procedure is developed based upon inappropriate use of deviation variables which leads to the development of a ranking approach that does not meet their expectations and as a result, an unreasonable ranking of decision making units (DMUs). We also show that the use of deviation variables, if interpreted and used correctly, can lead to developing a cross-inefficiency matrix and approach.

We develop a new network data envelopment analysis (DEA) approach for two-stage network systems considering a match between the production scale of the substages and the intermediate measure levels. Several explicit production axioms are introduced to build a production possibility set. New models are developed based on the production possibility set and a frontier projection procedure with the production scale matching process. Unlike the existing approach which assumes the intermediate measures are free-setting decision variables, the new envelopment network DEA models project the intermediate measures of a unit using the radial projection technique. Correspondingly, the resulting multiplier network DEA models allow for weight flexibility on the intermediate measures while holding a total value flow equivalence between a unit's two stages. We show that our approach does not suffer the known network DEA pitfalls. It identifies the overall efficiency, divisional efficiencies, and frontier projection using either an envelopment or a multiplier network DEA model, i.e., the primal-dual correspondence holds in our approach. Our approach also avoids uncertainties in determining divisional efficiencies by generating a unique pair of divisional efficiencies for each unit. Additionally, the adoption of the production scale matching process explains clearly the frontier projection procedure from the practical point of view. The proposed approach is illustrated with a numerical example and compared with the existing approaches with a case study of commercial bank branches.

Grasping the intricacy and diversity of complex systems dealing with ever-growing amounts of data is essential to public and private institutions’ continuous improvement. Composite indicators (CIs) emerge as aggregators of key performance indicators, providing a single measure that reflects those multidimensional performance aspects. One way to build such measures is based on the use of data envelopment analysis (DEA). Several DEA models can be used to generate CIs. Still, not many of them can deal concurrently with desirable and undesirable outputs, and incorporate the decision-making actors’ preference information. Based on the directional ‘Benefit-of-the-Doubt’ model, we propose a novel approach consisting of the simultaneous use of weight restrictions and an artificial target reached via a range directional vector. The resulting CI assesses the Portuguese public hospitals’ performance under two perspectives of hospital activity: users and providers. In the end, managerial and policy implications are withdrawn from the results of this study conducted in cooperation with the Portuguese Ministry of Health.

The literature on data envelopment analysis (DEA) and, more broadly, production theory employs different notions of efficiency for the characterization of boundary points of production technologies. These include the strong and weak (Pareto) efficiency, and the Farrell input and output efficiency. For the conventional constant and variable returns-to-scale technologies, the relationship between the different notions of efficiency has been explored in the literature and is well understood now. In this paper we show that, in the general case, which includes many recently developed technologies, the conventional relationship between the different notions of efficiency is no longer valid. We show that such relationship depends on the properties of a particular technology such as convexity, disposability and returns-to-scale characteristics. Our results are applicable to many new technologies for which the different notions of efficiency and methods of their testing have not been fully explored.

Most of the previous cross efficiency evaluation methods consider the evaluated system as a “black box” system. This probably leads to misleading results. For example, the system is efficient but all of its divisions are inefficient. This paper firstly investigates the cross efficiency for a general two-stage system. In such system, some outputs of one stage are taken as inputs of the other stage, and some other outputs directly become the final products. Since the optimal weight vector for the self-evaluation of a decision making unit (DMU) may be non-unique, we apply the leader-follower method for the decomposition of the system's efficiency and then adopt the optimal weights to obtain the peer-evaluation. Then, multiplicative hesitant fuzzy elements (MHFEs) are applied to denote the ratio of all possible cross efficiencies of any two DMUs. Based on MHFEs, multiplicative hesitant fuzzy preference relations (MHFPRs) are used to express these relationships comprehensively. Furthermore, the optimization models for deriving acceptably consistent MHFPRs with the minimum total adjustment and the minimum number of adjusted elements are built when the consistency of MHFPRs is unacceptable. An algorithm for decomposing the overall efficiency according to the cross efficiency and acceptably consistent MHFPRs in the setting of the general two-stage system is provided. Finally, our method is applied to the analysis of nine top universities in China.

This paper applies the additive relational network DEA model to examine the multi-period efficiency and productivity of Regional Banks I and II in Japan between 2002 and 2017. The examined timeframe covers two turbulent periods; the Global Financial Crisis and the economic recession in the aftermath of the Great East Japan Earthquake. We extend the additive relational network DEA model into a multi-period structure in order to evaluate the overall efficiency for the time period in question, as well as the annual period efficiencies. We show that the overall efficiency can be expressed as a weighted average of the period efficiencies. In addition, we examine the implications of different returns to scale assumptions. The newly proposed model is able to calculate common-weight Malmquist Productivity Indices. The results reveal a dispersion of inefficiency levels for Japanese Regional Banks in general, and a difference between Regional Banks I and II in particular. Furthermore, the Global Financial Crisis caused a significant negative effect on the productivity growth and the technical progress of Japanese Regional Banks, while the Great East Japan Earthquake had a negative effect on the technical efficiency change.

Charnes, Cooper, Seiford, and Stutz (1982, 1983) and Banker and Maindiratta (1986) suggested multiplicative radial measures for efficiency gauging. More recently, Peyrache and Coelli (2009) presented a multiplicative directional distance function that was elaborated by Mehdiloozad, Sahoo, and Roshdi (2014). In this paper, we extend these studies and propose an exponential approach based upon a new exponential distance function endowed with a multiplicative production structure. The main purposes of this paper are twofold: one is to provide a general production theoretic basis for the approach and the other is to extend it to a nonparametric framework. The first purpose is accomplished as follows: (1) the exponential distance function is formally defined and its properties are established; (2) it is shown how the exponential distance function is characterized under a Napierian technology; (3) a duality relationship between Napierian profit and the exponential distance functions is established; (4) shadow prices of inputs and outputs are derived based on the Napierian technology. The second purpose is accomplished by providing nonparametric programming extensions, which include data envelopment analysis (DEA) models, productivity indexes and returns to scale models. Here, the efficacy of our nonparametric theoretical results is demonstrated by applying DEA to the data on accommodation establishments in OECD.

This paper extends the multiplier dynamic data envelopment analysis (DEA) by using directional distance function (DDF). Based on the duality theory, a multiplier network DDF model is proposed for the dynamic system which consists of a sequence of periods linked by carryovers. The proposed multiplier dynamic model is non-oriented and is able to handle negative data that possibly exist in inputs, carryovers and outputs. The overall efficiency score calculated by the proposed multiplier dynamic model can be decomposed into a weighted average of period efficiency scores. The approach that determines a unique efficiency score for each period is also proposed. To demonstrate the validity and practicality of the proposed dynamic model, we apply it to evaluate the performance of mutual funds in the American market. The empirical results show that the proposed multiplier dynamic model has strong ability to discriminate performance and good practice value for the actual portfolio selection.

The measurement of technical efficiency attracts considerable interest in the literature. In fact, following on from the seminal works by Koopmans (1951) , Debreu (1951) , Shephard (1953) and Farrell (1957), a substantial amount of literature has been dedicated to methods for estimating production frontiers and measuring the technical efficiency of production units. Data Envelopment Analysis (DEA) has an important role among current techniques for determining technical efficiency due to its flexibility when it comes to confronting multiple inputs and outputs as well as its non-parametric nature. Many different DEA-based technical efficiency measures have evolved over the last forty years, including radial, hyperbolic, directional, (weighted) additive, slacks-based measures, etc. Nevertheless, there is still room for harnessing new measures that are capable of satisfying interesting properties. For instance, slacks-based measures generally yield solutions with zero values in some slacks, which may mean overloading some of the other dimensions to reach the efficient frontier, thereby involving unbalanced efforts that are unrealistic. Moreover, the projection point determined by standard measures is not unique which is a further weakness from a benchmarking perspective. The purpose of this paper is to propose a novel technical efficiency performance measure in DEA on the premise of maximizing the hypervolume, while dealing with these problems and satisfying additional properties at the same time. In particular, we prove that the new approach yields unique projection points, which is not a usual property of DEA technical efficiency measures. From a computational perspective, second-order cone programming is capable of solving the new measure. Finally, an empirical example extracted from the literature serves to illustrate the new methodology.

Measures of capacity utilization and capacity output are important metrics for evaluating firm performance. This is true whether capacity is considered from a cost accounting framework, an engineering standpoint, or an economics orientation. Ultimately, the crux of the capacity question is about resources not being used to their fullest extent. In an economics context, understanding where firms are producing on their average cost curve provides information about whether capacity utilization is greater than, less than or equal to unity. In real life, most firms are multi-output, multi-input in nature which makes estimation of capacity utilization and capacity output challenging if a cost based measure is desired. This is further complicated in a short run analysis incorporating multiple outputs and multiple fixed inputs where the relevant concept is the minimum of ray average cost. This paper develops appropriate mathematical programming models for measuring capacity utilization in the short-run for multiple-outputs and multiple fixed inputs. We offer a simple transformation that linearizes the non-linear DEA problem to estimate average, or ray average cost, and to determine capacity utilization and optimal output. The models are empirically tested on data from a number of U.S. electricity producers for the single output case, and a sample of dental practices for the multi-output case. Results show that for both industries, most firms were operating at less than full capacity, and needed to expand output to minimize their average costs.

Some input-output classifier data envelopment analysis (DEA) models in multiplier and envelopment forms were developed to designate the status of flexible measures, playing either input or output roles. These models ignore the role of non-Archimedean epsilon in the input-output classification process. We show that these epsilon-free models may ignore some flexible measures in the performance evaluation process and hence the status of such flexible measure(s) can be randomly and inappropriately identified. To fill this gap, we develop a pair of epsilon-based multiplier and envelopment classifier models. We also develop an approach to find a suitable epsilon value for our developed classifier models. A case study of the supplier selection problem in the Iranian Space Research Center (ISRC) is provided to illustrate the potential application of our new epsilon-based approach.

In practice, the concept of incentives is extensively applied in the allocation process for guiding the behaviours of an organization's units to satisfy the goals of the organization. However, this concept is rarely considered in data envelopment analysis (DEA)-based allocation research. This paper proposes a two-step incentive approach for allocating common revenues or fixed costs. The first step is performance evaluation. Considering the noncooperative game relationship of decision-making units (DMUs), a DEA game cross-efficiency method is selected to measure the efficiency scores of DMUs in this paper. The second step is incentive allocation. Based on the performance evaluation, we propose our incentive method for allocating revenues or fixed costs. We further provide simple equations to calculate the global optimal solution for our nonlinear programme allocation models. Several properties are explored, and we i) obtain the allocation interval rule of DMUs with the incentives, ii) investigate the quantitative relationship between the allocation gap and the optimal allocation plan, and iii) prove that the optimal allocation plan obtained by our allocation model is unique. The results of an empirical application highlight the applicability of our allocation method and solution approach. In this study, we obtain several important practical insights, including that (i) our method has positive effects on performance improvement and (ii) our method can work well even in an information asymmetric decision-making environment.

This study examines innovation performance of high-tech companies in China, using a dynamic network data envelopment analysis (DEA) approach. The innovation process is decomposed into a research and development (R&D) stage and a commercialization stage. In addition, innovation is conceptualized as a consecutive event that goes through multiple time intervals, requiring a dynamic structure of the methodological framework. Using a newly developed dynamic network DEA, the current study calculates a R&D performance index and a commercialization index for the R&D stage and commercialization stage, respectively. The multi-process innovation system is integrated with dynamic carryover items. This results in a highly non-linear dynamic network DEA model. Second order cone programming and nested partitions strategies are employed to solve the nonlinear dynamic network DEA model. Our empirical study indicates disparities in innovation performance among different Chinese high-tech companies. The innovation heterogeneity and inefficient performance sources are also investigated.

How to evaluate the performance of decision-making units (DMUs) with fixed-sum outputs is a timely and challenging question in data envelopment analysis (DEA). Two major challenges are (1) how to determine a common equilibrium efficient frontier and (2) how to deal with multiple feasible equilibrium efficient frontiers. This paper first uses a simple dataset to illustrate the possibility of multiple equilibrium efficient frontiers and the corresponding major differences in the DMUs’ efficiencies and rankings resulting from these frontiers. We address these challenges by considering all feasible equilibrium efficient frontiers and develop several models to obtain the corresponding efficiency intervals, ranking intervals and dominance relations for the DMUs with fixed-sum outputs. We illustrate the proposed approach with two numerical examples and show that it gives more informative results than previous DEA approaches. For example, there are interesting dominance relations between DMUs under the fixed-sum outputs; yet these relations do not exist when there are no fixed-sum outputs. In addition, the efficiency ranges and ranking intervals can be narrowed by accounting for policy suggestions such as adjustment constraints of fixed-sum outputs for DMUs.

The measurement of technical efficiency is a topic of great interest. Since the beginning, many researchers have developed new approaches to gauge technical efficiency, mainly in the non-parametric area of Data Envelopment Analysis (DEA). However, the first measures in DEA, the well-known radial models, only accounted for radial inefficiency, which motivated the introduction in the literature of the so-called Global Efficiency Measures (GEMs); non-oriented and non-radial in nature. Two famous GEMs are the Russell Graph Measure and the Enhanced Russell Graph Measure, also known as the Slacks-Based Measure. These approaches aggregate input and output specific efficiencies through the arithmetic mean, which may not be the most appropriate aggregator function when input and output efficiency ratios are considered, as will be shown. In this paper, in contrast, we propose aggregating input and output specific inefficiencies by applying the geometric average, which will allow us to define new multiplicative versions of the Russell Graph Measures. We also prove some theoretical results and introduce an iterative algorithm, based upon Second Order Cone Programming, to solve the new models. Finally, the implementation of the introduced approaches is empirically illustrated through a data set taken from the literature.

There is an increasing awareness about the importance of the role that small food and beverage producers play in the socio-economic development in many countries. However, since they face many specific problems which create obstacles for their existence, small producers should be identified and supported. To properly analyze their position, one should consider multiple criteria within their operational, financial, marketing and strategic activities. This paper analyzes small food and drink producers from selected countries in the European Union and estimates their financial efficiency using raw financial variables instead of financial ratios. The research is based on the data obtained from the Amadeus database for the period from 2011 to 2015. The relative efficiency is determined by using the data envelopment analysis (DEA). The results show that the number of efficient small companies in the sample had varied throughout the analyzed period. The same holds for the number of efficient companies within countries and within the food and drink industry. Approximately 23% of food producers were relatively efficient, while the share of efficient drink producers increased over time from approximately 20% to 23%. Moreover, we detect countries having the greatest percentage of efficient small producers in the sample. The DEA approach identified efficient producers which have better liquidity, efficiency, leverage and profitability and pointed out cash liquidity as the area of inefficiency for the inefficient companies. This analysis provides policy makers with information for developing policies which could improve the strength of small food and drink producers on a country level.

Highlights • We develop nested dynamic network DEA models to measure a portfolio's efficiency. • We measure the multi-period efficiency of a portfolio and its comprised assets. • Target portfolio is benchmarked against all other possible portfolios. • A CVaR optimization problem is included. • A two-stage method is proposed to help investors construct their desired portfolios., Portfolio performance evaluation is a major data envelopment analysis (DEA) application in the finance field. Most proposed DEA approaches focus on single-period portfolio performance assessment based on aggregated historical data. However, such an evaluation setting may result in the loss of valuable information in past individual time periods, and violate real-world portfolio managers’ and investors’ decision making, which generally involves multiple time periods. Furthermore, to our knowledge, all proposed DEA approaches treat the financial assets comprising a portfolio as a “black box”: thus there is no information about their individual performance. Moreover, ideal portfolio evaluation models should enable the target portfolio to compare with all possible portfolios, i.e., enabling full diversification of portfolios across all financial assets. Hence, this research aims at developing nested dynamic network DEA models, an additive model being nested within a slacks-based measure (SBM) DEA model, that explicitly utilizes the information in each individual time period to fully and simultaneously measure the multi-period efficiency of a portfolio and its comprised financial assets. The proposed nested dynamic network DEA models, referred to as NDN DEA models, are linear programs with conditional value-at-risk (CVaR) constraints, and infinitely many decision making units (DMUs). In conducting the empirical study, this research applies the NDN DEA models to a real-world case study, in which Markov chain Monte Carlo Bayesian algorithms are used to obtain future performance forecasts in today's highly volatile investment environments.

Cross-efficiency evaluation methods have long been suggested as an alternative for the ranking of decision making units (DMUs) in data envelopment analysis (DEA). So far, little research on cross-efficiency evaluation takes the bounded rationality of DMUs into account. In this paper, we propose a neutral cross-efficiency evaluation method based on interval reference points (IRPs) to consider bounded rational behavior. As such, we take the prospect value, which reflects the bounded rationality of DMUs when facing gain and loss, as secondary goals. This approach allows us to determine the input and output weights for each DMU from its own point of view. Each reference point (RP) of the prospect value is defined as an elastic interval reference point (IRP), which can degenerate into a precise reference point (PRP) or an IRP by adjusting the parameters. As a result, the proposed cross-efficiency evaluation method not only takes the bounded rational behavior of DMUs into account, but is also more neutral and flexible. Numerical examples are provided to illustrate the applications of the cross-efficiency evaluation method based on IRPs in DEA ranking.

This paper proposes an innovative approach to evaluate the causal impact of a policy change in a multi-input multi-output setting. It combines insights from econometric impact evaluation techniques and efficiency analysis. In particular, the current paper accounts for endogeneity issues by introducing a quasi-experimental setting within a conditional multi-input multi-output efficiency framework and by decomposing the overall efficiency between ‘group-specific’ efficiency (i.e., reflecting internal managerial inefficiency) and ‘program’ efficiency (i.e., explaining the impact of the policy intervention on performance). This framework allows the researcher to interpret the efficiency scores in terms of causality. The practical usefulness of the methodology is demonstrated through an application to secondary schools in Flanders, Belgium. By exploiting an exogenous threshold, the paper examines whether additional resources for disadvantaged students impact the efficiency of schools. The empirical results indicate that additional resources do not causally influence efficiency around the threshold. ispartof: European Journal Of Operational Research vol:290 issue:3 pages:1111-1124 status: published

The World Bank's Ease of Doing Business (EDB) index is well-known and widely used to quantify and monitor the ‘ease of doing business’ within a country. The index attracted notable criticism for being too reliant on a ‘one size fits all’ approach (equal weighting) to the weighting step of its construction. The present paper recomputes the EDB index by employing a more flexible ‘Benefit-of-Doubt’ weighting method. Using different versions of this method, changes in EDB are examined for the period 2010–2019, whilst grouping countries according to regional classifications as defined by the World Bank. In addition, year-by-year trends in the EDB index are explored. The results show considerable differences in changes in the EDB index both between and within different regions. Within some regions there were also signs of clustering in terms of similar rates of improvement or deterioration over time.

The selection of input and output variables is a key step in evaluating the relative efficiency of decision-making units (DMUs) in data envelopment analysis (DEA). In this paper, we present a methodology based on Monte Carlo simulations and bootstrapping for calculating the critical values of relevance measures in variable selection methods in DEA. Additionally, we define a set of metrics to study the methods’ performance when using such critical values. We conducted an extensive simulation study, applying the proposed methodology to two variable selection methods in 28 single-output model specifications (i.e., different number of inputs and DMUs in the DEA model) under multiple scenarios, varying factors related to the functional form of the production function, the probability of an input being relevant in the model, the probability distribution of the inputs, and the theoretical efficiencies of the DMUs. The simulation study shows that (i) our proposed methodology yields consistent results for the two methods studied, in terms of the generated critical values and the performance metrics, and (ii) for most model specifications, the critical values can be estimated with a linear model with a high adjusted R2, using factors related to the input probability distribution and the probability of an input being relevant as independent variables. Furthermore, we describe and compare the performance of the two methods studied, provide guidelines for using our methodology and the results presented in this paper, and propose suggestions for future research.

Hospitals have different departments for treating specific diseases. Some hospitals are specialized into one department while others are diversified into many departments. Since many inputs for different departments can be shared, running a diversified hospital is probably less costly than running several specialized hospitals separately due to economies of scope. In this paper, we examine whether expanding the scope of hospitals with a limited number of departments is worthwhile using hospitals in China as the context. The degree of economies of scope is measured in terms of efficiencies gained via a data envelopment analysis. The results show that economies of scope exist for expanding general hospitals lacking one department into general hospitals with all departments. In cases of very specialized hospitals with departments such as dentistry and ophthalmology, it is more efficient to operate them separately. Adding these departments to hospitals with a narrow scope exhibits diseconomies of scope. An expansion network is constructed, with eight optimal paths identified, to guide hospitals of different types to expand their scopes into general comprehensive hospitals stage by stage in a scope-economic way. Since the department to be added is different at each stage of the expansion, the returns to scope do not exhibit a consistent trend for different methods of expansion.

Marginal abatement cost (MAC) is a critically important concept for efficient environmental policy and management. In this paper we argue that most empirical studies using frontier estimation methods such as data envelopment analysis (DEA) over-estimate MACs. The first methodological contribution of this paper is to clarify the conceptual distinction between the shadow price and MAC in order to analyze three sources of upward bias due to the limited set of abatement options, inefficiency, and noisy data. Our second methodological contribution is to develop a novel MAC estimation approach based on convex quantile regression. Compared to the traditional methods, convex quantile regression is more robust to the choice of the direction vector, random noise, and heteroscedasticity. Empirical application to the U.S. electric power plants demonstrates that the upward bias of DEA may be a serious problem in real-world applications.

In data envelopment analysis (DEA), non-radial graph models represent an important class characterized by the independent treatment of each input and output factor in the efficiency measurement. The extensive literature on this topic often analyses individual models in isolation, so much so that the same model may be known under different names due to alternative formulations of different authors. In this paper, a unified analysis of non-radial graph models is offered, viewing each of them via two equivalent schemes: the slack-variables scheme and the Russell-type scheme. Under these schemes, the properties common to the whole class are specified and justified. Along with the two envelopment form schemes, a general dual (multiplier) form is presented. Primal-dual relationships between the envelopment and multiplier non-radial models are analyzed in order to reveal new useful properties and insights.

Genetic improvement of animals has been an important source of productivity growth in dairy farming. Studying the effect of genetic progress on productivity growth of farms requires a long-term dynamic perspective due to the long generation interval of dairy animals, and the slow, persistent and cumulative effects of genetics. It is also essential from a farm decision-making perspective to disentangle overall productivity growth in relation to each variable input and investment in quasi-fixed input while accounting for adjustment costs associated with the slow changes in quasi-fixed inputs. This paper contributes to the literature by combining input- and investment-specific dynamic productivity growth analysis with impulse response analysis. The application focuses on panel data of Dutch specialized dairy farms over 2007–2013. The results show that farms that adopt improved genetic materials, as proxied by farm expenses on artificial insemination and breeding stock investment spike, achieved higher input- and investment-specific productivity growth in the first two years after the year of the expenses/spike. That is, farms that produce more efficiently after adopting quality genetics are also those farms that utilise their resources efficiently. The positive relationships suggest a potential positive spill-over effect from using high quality genetics on managerial efficiencies.

Uniqueness and Pareto-optimality of cross-efficiency scores are two main issues in the cross-efficiency evaluation. We address the Pareto-optimality issue in the cross-efficiency evaluation by presenting a natural notion of Pareto-optimality in the cross-efficiency evaluation which is based on a new self-prioritizing principle and aligned with the concept of dominance. This Pareto-optimality notion is devised using less stringent postulates, compared to those used to devise the existing Pareto-optimality notions in the current literature. We then propose a multi-objective model whose Pareto-optimal solutions generate all the Pareto-optimal cross-efficiency scores sets that fulfill the self-prioritizing principle. It is shown that there is a Pareto-optimal solution to the proposed multi-objective programming model which assigns a common set of weights to all decision making units. We then propose a linear model to obtain such an optimal solution using the weighted sum technique, thereby we can determine an optimal weights profile to generate a set of Pareto-optimal cross-efficiency scores by solving only one linear model. Having started with less stringent postulates, we have more flexibility in enhancing cross-efficiency scores of decision making units and can hence provide a non-dominated set of cross-efficiency scores as illustrated by a real data example. We also demonstrate the possibility of better, compared to other cross-efficiency evaluation methods, resource allocation using another real data example.

This paper aims to investigate the capacity utilization (CU) of selected large Chinese iron and steel enterprises by using the data envelopment analysis (DEA) approach. In this paper, we first propose a DEA model with an unrestricted capacity directional output distance function by incorporating two joint cost disposability relations and differentiating between non-emission-causing inputs and emission-causing inputs. Second, we define the status of decision-making units (DMUs) with excess capacity and design a method to identify insufficient variable inputs. We use a group of 48 largest Chinese iron and steel enterprises as our sample to investigate their performance in terms of CU indicator. The main findings are summarised and can be used to support the corresponding policymaking for the managers of both government and enterprises.

In many applications of data envelopment analysis, there are situations in which a central body manages a large set of similar units delivering some services. In such multi-unit organizations, the central management desires a mechanism by which the local management of each unit is incentivized to perform towards the improvement of the performance of the organization as a whole. In a recent paper, Afsharian et al. (2017) have proposed a system of incentives under these circumstances. In their approach, – which relies on the original concept of super-efficiency – units with outstanding performance are identified and incentivized by some reward compatible with the level of their impact on the overall performance of the organization. We discuss why the conventional super-efficiency approach may not be optimal in such situations. We revisit the definition of the collective impact and propose a new method, which can identify – in a controlled manner – a subset of k outstanding DMUs among n existing units in the system. The proposed approach is illustrated using data from a German retail bank.

The slacks-based measure (SBM) model can divide the set of observations into two mutually exclusive and collectively exhaustive sets: efficient and inefficient. However, it fails to provide more details about efficient DMUs, which reveals the lack of discrimination power in the SBM model. With the aim of addressing this issue, the super SBM (SupSBM) model has been suggested which can rank the SBM-efficient DMUs without providing any useful information about SBM-inefficient DMUs. As a result, in order to fully rank both efficient and inefficient DMUs, one needs to run both SBM and SupSBM models which leads to a significant increase in the number of required computations. This paper tackles this problem and modifies the SBM model which measures SBM-efficiency score for inefficient DMUs and SupSBM-efficiency score for strong efficient DMUs, simultaneously. Finally, a simulation study is presented to illustrate the superiority of our proposed model over the existing models with various problem sizes.

Balancing fairness and efficiency has become an emerging issue in today's society. In this paper we propose a balanced benchmarking methodology to address the fairness issue in performance evaluation. The methodology used to create performance measures is data envelopment analysis (DEA), a tool designed to evaluate the relative efficiencies of comparable decision-making units (DMUs); i.e. all DMUs use the same inputs and outputs and experience the same general operating conditions. In many applications, however, the DMUs may experience non-homogenous operating conditions or environments. An example might be a set of manufacturing plants where some have been upgraded and others not. Such settings can necessitate modifying the DEA structure such as to make allowance for different environmental conditions. Such a model is developed herein to create a level playing field for performance evaluation in two different settings: a setting involving hybrid and conventional (non-hybrid) vehicles; and another setting involving bank branches located in poverty and non-poverty regions. Our model and empirical tests contribute not only to the advance of balanced benchmarking methodologies, but also to the practice of incorporating fairness in performance evaluation across multiple products and organizations.