Efficient DMUs Research Articles

A modified slacks-based measure of efficiency in data envelopment analysis

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.

A new methodology to measure efficiencies of inputs (outputs) of decision making units in Data Envelopment Analysis with application to agriculture

This paper aims at developing a new methodology to measure and decompose global DMU efficiency into efficiency of inputs (or outputs). The basic idea rests on the fact that global DMU's efficiency score might be misleading when managers proceed to reallocate their inputs or redefine their outputs. Literature provides a basic measure for global DMU's efficiency score. A revised model was developed for measuring efficiencies of global DMUs and their inputs (or outputs) efficiency components, based on a hypothesis of virtual DMUs. The present paper suggests a method for measuring global DMU efficiency simultaneously with its efficiencies of inputs components, that we call Input decomposition DEA model (ID-DEA), and its efficiencies of outputs components, that we call output decomposition DEA model (OD-DEA). These twin models differ from Supper efficiency model (SE-DEA) and Common Set Weights model (CSW-DEA). The twin models (ID-DEA, OD-DEA) were applied to agricultural farms, and the results gave different efficiency scores of inputs (or outputs), and at the same time, global DMU's efficiency score was given by the Charnes, Cooper and Rhodes (Charnes et al., 1978) [1], CCR78 model. The rationale of our new hypothesis and model is the fact that managers don't have the same information level about all inputs and outputs that constraint them to manage resources by the (global) efficiency scores. Then each input/output has a different reality depending on the manager's decision in relationship to information available at the time of decision. This paper decomposes global DMU's efficiency into input (or output) components' efficiencies. Each component will have its score instead of a global DMU score. These findings would improve management decision making about reallocating inputs and redefining outputs. Concerning policy implications of the DEA twin models, they help policy makers to assess, ameliorate and reorient their strategies and execute programs towards enhancing the best practices and minimising losses.

NATO ve EURO Bölgesindeki Savunma Sanayilerinin İktisadi Etkinliği ve Toplam Faktör Verimliliği

The main purpose of this study is to analyze the efficiency and total factor productivity (MTFP) of the 12 defense industries in NATO and the EUROZONE with the data of the 2013-2017 period. GDP, defense expenditures, import for the defense industry and logistics performance index were used as input variables; while total sales and export values of defense industry were used as output variables in accordance with the data acquired from World Bank (WB) and SIPRI. Static DEA and MTFP were applied to data. According to findings of the CCR models; the USA, UK, France, Germany, Spain, and Netherland were observed as efficient DMUs in all years; whereas the other six countries were inefficient ones. Additionally, according to BCC model, only Turkey and Canada were observed as inefficient ones for five years. MTFP analysis revealed that Turkey and Germany were the two countries experiencing TFP in all periods.

New approach for ranking efficient DMUs based on Euclidean norm in data envelopment analysis

New approach for ranking efficient DMUs based on Euclidean norm in data envelopment analysis

Efficiency Assessment of Public Education & Health Sector in Selected Middle-Income Countries with Special Reference to Millennium Development Goals (MDGs)

This study investigates relative efficiency of public education and health sector in selected middle income countries with special reference to Millennium Development Goals (MDGs). The study uses data for two reference years; 2000 (implementation year of MDGs for developing countries) and 2015 (the final year of MDGs). Data Envelopment Analysis (DEA) and Malmquist Productivity Index (MPI) are used to calculate relative efficiency, operating scale of the countries (DMUs) and productivity change in relative efficiency over time respectively. The paper conceptualizes relative efficiency of the countries in discretionary, multicriteria input-output variables context to investigate efficiency differences among the countries and deduce important takeaways. Educational expenditure, teachers at primary level, health expenditure, birth attended by skilled staff are used as input variables while enrollment at primary level, completion of primary level education, infant survival per annum and child survival per annum are used as output variables. The DEA results show that all countries could not operate at efficient level to target MDGs. The level of efficiency was not same under different DEA specifications in both the periods. Some countries were inefficient because of their size; either having too large size or too small size of operation. The sources of change in efficiency over the time were either because of real change in efficiency or change in technology frontier or both. The study identified a set of institutional and individuals factors which contribute to the efficiency and inefficiency of DMUs under investigation.

Efficiency Assessment of Public Education & Health Sector in Selected Middle-Income Countries with Special Reference to Millennium Development Goals (MDGs)

This study investigates relative efficiency of public education and health sector in selected middle income countries with special reference to Millennium Development Goals (MDGs). The study uses data for two reference years; 2000 (implementation year of MDGs for developing countries) and 2015 (the final year of MDGs). Data Envelopment Analysis (DEA) and Malmquist Productivity Index (MPI) are used to calculate relative efficiency, operating scale of the countries (DMUs) and productivity change in relative efficiency over time respectively. The paper conceptualizes relative efficiency of the countries in discretionary, multicriteria input-output variables context to investigate efficiency differences among the countries and deduce important takeaways. Educational expenditure, teachers at primary level, health expenditure, birth attended by skilled staff are used as input variables while enrollment at primary level, completion of primary level education, infant survival per annum and child survival per annum are used as output variables. The DEA results show that all countries could not operate at efficient level to target MDGs. The level of efficiency was not same under different DEA specifications in both the periods. Some countries were inefficient because of their size; either having too large size or too small size of operation. The sources of change in efficiency over the time were either because of real change in efficiency or change in technology frontier or both. The study identified a set of institutional and individuals factors which contribute to the efficiency and inefficiency of DMUs under investigation.

Measuring performance of a hybrid system based on imprecise data: Modeling and solution approaches

Data Envelopment Analysis (DEA) is one of the methods most widely used for measuring the relative efficiency of DMUs in the world today. The efficiency evaluation of the network structure opens the “black box” and considers the internal structure of systems. In this paper, a three-stage network model is considered with additional inputs and undesirable outputs and obtains the efficiency of the network, as interval efficiency in presence of the imprecise datum. The proposed model of this paper simulates a factory in the factual world with a production area, three warehouses and two delivery points. This factory is taken into consideration as a dynamic network and a multiplicative DEA approach is utilized to measure efficiency. Given the non-linearity of the models, a heuristic method is used to linearize the models. Ultimately, this paper concentrates on the interval efficiency to rank the units. The results of this ranking demonstrated that the time periods namely, (24) and (1) were the best and the poorest periods, respectively, in context to the interval efficiency within 24 phases of time.

An Application of Linear Programming in the Estimation of Technical Efficiency of DMU

The main objective of this research article is to propose linear programming problems for estimating the technical efficiency of DMU. This research article deals with the Shepard’s [1] input distance function and its properties are also evaluated. In addition to these extreme efficiency, efficiency but not extreme, weak efficiency and inefficient of a DMU are specifically examined here. In DEA the nature of returns to scale can be inferred. But we cannot quantify the returns to scale. The computations for the classification of RTS of a DMU are also derived in this discourse. In 2009, Barbara A. Mark et.al [2] in their paper, depicted an innovative method which is non-parametric to estimate technical efficiency. In 2011 S. Nuti et.al [3] inquired into the interrelations among technical efficiency scores, weighted per capita cost and overall performance. Gahe Zing Samuel Yannik et.al [4] used DEA to calculate technical assessment in banking sectors. In 2015 Smita Verma and others chosen a random sample of ten textile mills in India over the time period 2011-2013 and measures its technical efficiency using Data Envelopment Analysis

Incorporating decision makers’ preferences into DEA and common weight DEA models based on the best–worst method (BWM)

Incorporating decision makers’ (DMs’) judgments and preferences into DEA models is very important in some real-world problems. This paper presents an integrated data envelopment analysis (DEA)—best–worst method (BWM)—for considering DMs’ preferences in DEA and reducing flexibility in weights of inputs and outputs. First, the preferences vectors are designed using BWM, and then, a multi-objective DEA-BWM model is introduced. The proposed DEA-BWM model simultaneously maximizes the efficiency scores of DMUs and considers DMs’ preferences about weights of inputs and outputs. Finally, a goal programming model is suggested for extending the DEA-BWM model and finding common weights of inputs and outputs based on the DMs’ judgments. The proposed common weight DEA-BWM (CWDEA-BWM) model maximizes the efficiencies of DMUs, considers DMs’ preferences and uses a set of common weights. In order to illustrate the capability of proposed models, a numerical example is solved. Moreover, the proposed DEA-BWM and common weight DEA-BWM models are applied to evaluate 39 Iranian electricity distribution companies, and the results are analyzed and compared. The results indicate that the proposed DEA-BWM and CWDEA-BWM models are suitable for incorporating DMs’ preferences into DEA and fully ranking of DMUs.

Effectiveness Measurement Using DEA & BSC Methods in Public Health Services

Abstract It is well-known that health-care systems all over the world try to improve efficiency and effectiveness due to high pressure to pursue rational performance. Many of the health-care reforms in different countries are conducted with the objectives to rationalise costs, to make health services more available, and to increase, or at least not to reduce, the quality of health services. Adequate efficient metrics used in assessing health-care services are critical for the quality of decision-making. The subject of this research is efficiency measurement in the institutes of public health in Croatia oriented to preventive activities, i.e. monitoring, analysis, and evaluation of the health of the population. Diversity of the programmes and temporal variability are the characteristics of public health services, and it is therefore harder to measure the effects in the long run. This research aims to analyse and propose a new approach to the measurement system using two methods: the Data Envelopment Analysis (DEA) and the Balanced Score Card (BSC), combined into the DEABSC integrative model, which can be an efficient method for the decision-making process. The starting point of this research is the analysis of the measurement system in public-health services in Croatia. The results confirm a weak and inadequate efficiency measurement system and very low effectiveness measurement. To enhance the efficiency measurement, we have developed the conceptual integrative DEABSC model which has been tested at the Teaching Institute of Public Health – the Department of Health Ecology. Using DEA for 2017, we have identified relatively efficient units that helped establish future goals set in the BSC strategic map. The combination of DEA and BSC allows identifying options for improving the effectiveness of public-health service programmes. The study confirms that it is possible to determine the relative efficiency of different DMUs within the Department of Health Ecology and use best practice for each perspective in the BSC Cause & Effect conceptual model. This paper also provides recommendations for an easier establishment of performance measurement in order to achieve the mission of public health institutions, but also indicates some limitations in the application of the methods.

A New Robust Bootstrap Algorithm for the Assessment of Common Set of Weights in Performance Analysis

The performance of the units is defined as the ratio of the weighted sum of outputs to the weighted sum of inputs. These weights can be determined by data envelopment analysis (DEA) models. The inputs and outputs of the related (Decision Making Unit) DMU are assessed by a set of the weights obtained via DEA for each DMU. In addition, the weights are not generally common, but rather, they are very close to zero or they are even equal to zero. This means that some major criteria will not be considered. Another problem is the similarity of the efficiency scores of efficient DMUs. However, this is not the case in reality, and the performance of the DMUs should be completely ranked. Using common weights can solve these problems completely during measuring the performance of DMUs. There are some articles in the literature to determine common weight sets (CSWs), but none of them takes into account the bootstrap approach. This paper introduces a novel, empirical and robust algorithm based on bootstrapping technique to find CSWs.

A parameter-free approach for estimating the quality and quantity of the right and left returns to scale in Data Envelopment Analysis

One of the concepts that has gained important attention from economic and management-science research is that of the concept of returns to scale (RTS). There are several research papers on the behavior of the right and left RTS, as two specific directions of RTS, based on Data Envelopment Analysis (DEA) models. However, the main weakness of most of these methods is that they are based on the defined parameters, which itself leads to a high sensitivity of the models to variations in the magnitudes of the parameters and, thus, unreliable results. In this paper, we specially address this issue and propose a simple procedure for detecting the right and left RTS classification with an important feature that is independent of any predetermined parameters. In addition to the type of RTS, we also suggest a method to determine the value of the right and left RTS corresponding to each of the efficient DMUs. Finally, the superiority of the proposed parameter-free procedure over a parameter-based methods is elaborated by a real case in the banking system.

System efficiency evaluation of homogeneous parallel production systems: An aggregation approach

Existing models, for efficiency evaluation of DMUs with homogeneous parallel production-units, have limitations in the sense that production process of a DMU is compared with the production possibility set of all production-units. Moreover, same set of input-output weights is used to evaluate the efficiency, project inputs-outputs of a DMU and all its production-units. This means, all the production-units of a DMU operate in a similar way in the long run as if they are not separate production-units but one single entity. We propose an aggregation approach to evaluate the efficiency of DMUs with homogeneous parallel production-units. We also introduce Weighted Average Efficiency and System Efficiency. As opposed to the existing methodology, different set of weights are used to evaluate efficiency of different production-units of a DMU. Finally, the proposed methodology has been used to evaluate the efficiency of higher education sector of Bihar, one of the largest states in India.

A new DEA based Voting Method for Ranking and Evaluating the Influence of E-marketing on Bank Performance

Due to the importance of measuring banks' performance and because of the remarkable impact of recent growth of the internet on banking industry, this study evaluated the influence of e-marketing on bank performance by using a DEA-based voting methodology. In this way, usually more than one unit may be efficient in the DEA models and their scores are one. Therefore, how to rank DMUs and increase the power of discrimination among efficient DMUs become an important part of performance assessments. So, in order to provide a satisfactory ranking, this paper presents a voting methodology that uses the results of some ranking models. For this purpose, each DMU is considered as an alternative and each ranking method is considered as a decision maker. The proposed methodology is applied to evaluate the influence of e-marketing on Iranian's bank performance.

Modelling efficient and anti-efficient frontiers in DEA without explicit inputs

Data envelopment analysis (DEA) is one of the most widely used tools in efficiency analysis of many business and non-profit organisations. Recently, more and more researchers investigated DEA models without explicit input (DEA-WEI). DEA-WEI models can divide DMUs into two categories: efficient DMUs and inefficient DMUs. Usually there is a set of DMUs, which are 'efficient' so that conventional DEA models could not rank them. In this paper, we first develop a performance index based on efficient and anti-efficient frontiers in DEA-WEI models. Further, the corresponding performance index in DEA-WEI models with quadratic utility terms (quadratic DEA-WEI) is proposed also. Finally, we present two case studies on performance assessment of basketball players and the evaluation of research institutes in Chinese Academy of Sciences (CAS) to show the applicability and usefulness of the performance indices developed in this paper.

Modelling efficient and anti-efficient frontiers in DEA without explicit inputs

Data envelopment analysis (DEA) is one of the most widely used tools in efficiency analysis of many business and non-profit organisations. Recently, more and more researchers investigated DEA models without explicit input (DEA-WEI). DEA-WEI models can divide DMUs into two categories: efficient DMUs and inefficient DMUs. Usually there is a set of DMUs, which are ‘efficient’ so that conventional DEA models could not rank them. In this paper, we first develop a performance index based on efficient and anti-efficient frontiers in DEA-WEI models. Further, the corresponding performance index in DEA-WEI models with quadratic utility terms (quadratic DEA-WEI) is proposed also. Finally, we present two case studies on performance assessment of basketball players and the evaluation of research institutes in Chinese Academy of Sciences (CAS) to show the applicability and usefulness of the performance indices developed in this paper.

Full ranking of efficient and inefficient DMUs with the same measure of efficiency in DEA

Full ranking of efficient and inefficient DMUs with the same measure of efficiency in DEA

A TOPSIS, VIKOR and DEA integrated evaluation method with belief structure under uncertainty to rank alternatives

This study proposes a combined method, based on a new compromised solution method and DEA to evaluate the efficiency of DMUs. By using TOPSIS and VIKOR methods two concepts are considered simultaneously. First, the optimal alternative is closer to positive ideal solution and farther from negative ideal solution. Second, the proposed method provides a maximum 'group utility' for the 'majority' and a minimum of an individual regret for the 'opponent'. In this method, weight of efficiency obtained from new compromised solution method is multiplied by the weight of CCR model of DEA. The problem involves BELIEF parameters in the solution procedure. Thus, the new proposed method that applied the advantages of TOPSIS, VIKOR and DEA and BELIEF structure simultaneously was used as a group decision making problem to exploit many experts' judgments. Finally, to illustrate the proposed method, an illustrative example is provided.

A TOPSIS, VIKOR and DEA integrated evaluation method with belief structure under uncertainty to rank alternatives

This study proposes a combined method, based on a new compromised solution method and DEA to evaluate the efficiency of DMUs. By using TOPSIS and VIKOR methods two concepts are considered simultaneously. First, the optimal alternative is closer to positive ideal solution and farther from negative ideal solution. Second, the proposed method provides a maximum 'group utility' for the 'majority' and a minimum of an individual regret for the 'opponent'. In this method, weight of efficiency obtained from new compromised solution method is multiplied by the weight of CCR model of DEA. The problem involves BELIEF parameters in the solution procedure. Thus, the new proposed method that applied the advantages of TOPSIS, VIKOR and DEA and BELIEF structure simultaneously was used as a group decision making problem to exploit many experts' judgments. Finally, to illustrate the proposed method, an illustrative example is provided.

Educational Efficiency of State Boards of Secondary Education in India: SFA and D&ND DEA Analysis

The paper, using both stochastic Cobb-Douglas production frontier and the discretionary and non-discretionary DEA, empirically evaluated the performance of the BSEs of 28 states of India using the number of students passed Class X as the output. The mean efficiency score in SPF was more (0.792) compared to the DEA score (0.695). Around 43 per cent of the total DMUs were efficient in the range of 80 per cent and above. Gamma value of the SPF model inferred that 98 per cent of the variation in the efficiency score was due to technical inefficiency. The major factors determining the total students passed under a DMU are SCRR, PTR and RT. Out of GSE, SCSTE and PSRA, the SCSTE was positively and significantly affected the technical inefficiency. In the case of DEA introduction of nondiscretionary inputs reduced the mean score to 0.628 keeping the number of fully efficient states the same. The fully efficient states gave less weight to RT and PTR and all other inputs were assigned higher weights reflecting the relatively larger scarcity of these inputs. Due to non-discretionary inputs, the states affected most were Arunachal Pradesh, Assam, Goa, Manipur, Punjab and Sikkim. The fully efficient DMUs under DEA had also scored more than 90 per cent under SFA. On the basis of the result, the study concluded that appointment of regular teacher with appropriate benefits and perks, school infrastructure development, adoption of public-private partnership for bringing more investment in the infrastructure, at par treatment of the schools in the rural areas, uniform policy for all categories of students in the admission into the secondary schools and regular selfappraisal of the regular teachers will not only help in identifying the states with least performances but also the states who preferred to be peers for many inefficient performers but also about cost implication of the use of the inputs thereby warranting an effective management of the respective DMUs.