The measurement of profit, profitability, cost and revenue efficiency through data envelopment analysis: A comparison of models using BenchmarkingEconomicEfficiency.jl

We undertake a systematic comparison of existing models measuring and decomposing the economic efficiency of organizations. For this purpose we introduce the package BenchmarkingEconomicEfficiency.jl for the open-source Julia language including a set of functions to be used by scholars and professionals working in the fields of economics, management science, engineering, and operations research. Using mathematical programming methods known as Data Envelopment Analysis, the software develops code to decompose economic efficiency considering alternative definitions: profit, profitability, cost and revenue. Economic efficiency can be decomposed, multiplicative or additively, into a technical (productive) efficiency term and a residual term representing allocative (or price) efficiency. We include traditional decompositions like the radial efficiency measures associated with the input (cost) and output (revenue) approaches, as well as new ones corresponding to the Russell measures, the directional distance function, DDF (including novel extensions like the reverse DDF, modified DDF, or generalizations based on Hölder norms), the generalized distance function, and additive measures like the slack based measure, their weighted variants, etc. Moreover, regardless the underlying economic efficiency model, many of these technical inefficiency measures are available for calculation in a computer software for the first time. This article details the theoretical methods and the empirical implementation of the functions, comparing the obtained results using a common dataset on Taiwanese BanksJosé L. Zofío thanks the grant PID2019-105952 GB-I00 funded by Ministerìo de Ciencia e Innovación/ Agencia Estatal de Investigación /10.13039/50110001103

Far out or alone in the crowd: Classification of selfevaluators in DEA

The units found strongly efficient in DEA studies on efficiency can be divided into self-evaluators and active peers, depending on whether the peers are referencing any inefficient units or not. The contribution of the paper starts with subdividing the selfevaluators into interior and exterior ones. The exterior self-evaluators are efficient “by default”; there is no firm evidence from observations for the classification. These units should therefore not been regarded as efficient, and be removed from the observations on efficiency scores when performing a two-stage analysis of explaining the distribution of the scores. A method for classifying self-evaluators based on the additive DEA model is developed. The application to municipal nursing- and home care services of Norway shows significant effects of removing exterior self-evaluators from the data when doing a two-stage analysis.Self-evaluator; interior and exterior self-evaluator; DEA; efficiency; referencing zone; nursing homes

A novel multilevel network slacks-based measure with an application in electric utility companies

In this paper, we developed an alternative Network Slacks-Based Data Envelopment Analysis Measure (NSBM) wherein the overall efficiency is expressed as a weighted average of the efficiencies of the individual processes. The advantage of this new model is that both overall efficiency and multi-divisional efficiencies have been calculated with a unified framework. The major merits of the proposed model are its ability to provide appropriate measure of efficiency, obtaining weight of processes from model, simultaneous assessment of intermediate variables considering them as both input and output. Finally, an application in electric power companies shows the practicality of the proposed model

Increasing Sustainability of Logistic Networks by Reducing Product Losses: A Network DEA Approach

This paper considers a multiproduct supply network, in which losses (e.g., spoilage of perishable products) can occur at either the nodes or the arcs. Using observed data, a Network Data Envelopment Analysis (NDEA) approach is proposed to assess the efficiency of the product flows in varying periods. Losses occur in each process as the observed output flows are lower than the observed input flows. The proposed NDEA model computes, within the NDEA technology, input and output targets for each process. The target operating points correspond to the minimum losses attainable using the best observed practice. The efficiency scores are computed comparing the observed losses with the minimum feasible losses. In addition to computing relative efficiency scores, an overall loss factor for each product and each node and link can be determined, both for the observed data and for the computed targets. A detailed illustration and an experimental design are used to study and validate the proposed approach. The results indicate that the proposed approach can identify and remove the inefficiencies in the observed data and that the potential spoilage reduction increases with the variability in the losses observed in the different periods.Ministerio de Ciencia DPI2017-85343-PFondo Europeo de Desarrollo Regional DPI2017-85343-

A Data Envelopment Analysis Toolbox for MATLAB

The Data Envelopment Analysis Toolbox is a new package for MATLAB that includes functions to calculate the main data envelopment analysis models. The package includes code for the standard radial input, output and additive measures, allowing for constant and variable returns to scale, as well as recent developments related to the directional distance function, and including both desirable and undesirable outputs when measuring efficiency and productivity; i.e., Malmquist and Malmquist-Luenberger indices. Bootstrapping to perform statistical analysis is also included. This paper describes the methodology and implementation of the functions, and reports numerical results using a reliable productivity database on US agriculture to illustrate their use

Two-Phase Network Data Envelopment Analysis: An Example of Bank Performance Assessment

Data envelopment analysis (DEA) models assess decision-making units (DMUs), which directly convert multiple inputs into multiple outputs. Network DEA models have been studied extensively. However, the performance indices that link the two stages are assumed to be fixed or non-discretionary; their values are not adjustable. These models only assumed that the reductions on the inputs and additions on the outputs would improve the overall efficiency. But in the real world, the link is always adjustable. “Free links” means that the intermediate items are adjustable or discretionary, and each DMU can be increased or decreased from the observed one. The current chapter introduces a two-phase procedure with free links to assess system performance, Phase-I is a proposed slack-based measurement (SBM) model to partition the links into two sets: as-input and as-output. Phase-II is a modified SBM model to determine the slack of each input, as-input link, output and as-output link. This proposed model counts the slacks associated with the intermediate items in the efficiency scores and determines the entire system performance by the directional distance function. It is validated using network procedure and assesses the performance of supply chain management system

Disentangling the European airlines efficiency puzzle: a network data envelopment analysis approach

© 2015 Elsevier Ltd. In recent years the European airline industry has undergone critical restructuring. It has evolved from a highly regulated market predominantly operated by national airlines to a dynamic, liberalized industry where airline firms compete freely on prices, routes, and frequencies. Although several studies have analyzed performance issues for European airlines using a variety of efficiency measurement methods, virtually none of them has considered two-stage alternatives - not only in this particular European context but in the airline industry in general. We extend the aims of previous contributions by considering a network Data Envelopment Analysis (network DEA) approach which comprises two sub-technologies that can share part of the inputs. Results show that, in general, most of the inefficiencies are generated in the first stage of the analysis. However, when considering different types of carriers several differences emerge - most of the low-cost carriers' inefficiencies are confined to the first stage. Results also show a dynamic component, since performance differed across types of airlines during the decade 2000-2010

Advancing efficiency analysis using data envelopment analysis: the case of German health care and higher education sectors

The main goal of this dissertation is to investigate the advancement of efficiency analysis through DEA. This is practically followed by the case of German health care and higher education organizations. Towards achieving the goal, this dissertation is driven by the following research questions: 1.How the quality of the different DEA models can be evaluated? 2.How can hospitals’ efficiency be reliably measured in light of the pitfalls of DEA applications? 3.In measuring teaching hospital efficiency, what should be considered? 4.At the crossroads of internationalization, how can we analyze university efficiency? Both the higher education and the health care industries are characterized by similar missions, organizational structures, and resource requirements. There has been increasing pressure on universities and health care delivery systems around the world to improve their performance during the past decade. That is, to bring costs under control while ensuring high-quality services and better public accessibility. Achieving superior performance in higher education and health care is a challenging and intractable issue. Although many statistical methods have been used, DEA is increasingly used by researchers to find best practices and evaluate inefficiencies in productivity. By comparing DMU behavior to actual behavior, DEA produces best practices frontier rather than central tendencies, that is, the best attainable results in practice. The dissertation primarily focuses on the advancement of DEA models primarily for use in hospitals and universities. In Section 1 of this dissertation, the significance of hospital and university efficiency measurement, as well as the fundamentals of DEA models, are thoroughly described. The main research questions that drive this dissertation are then outlined after a brief review of the considerations that must be taken into account when employing DEA. Section 2 consists of a summary of the four contributions. Each contribution is presented in its entirety in the appendices. According to these contributions, Section 3 answers and critically discusses the research questions posed. Using the Translog production function, a sophisticated data generation process is developed in the first contribution based on a Monte Carlo simulation. Thus, we can generate a wide range of diverse scenarios that behave under VRS. Using the artificially generated DMUs, different DEA models are used to calculate the DEA efficiency scores. The quality of efficiency estimates derived from DEA models is measured based on five performance indicators, which are then aggregated into two benchmark-value and benchmark-rank indicators. Several hypothesis tests are also conducted to analyze the distributions of the efficiency scores of each scenario. In this way, it is possible to make a general statement regarding the parameters that negatively or positively affect the quality of DEA estimations. In comparison with the most commonly used BCC model, AR and SBM DEA models perform much better under VRS. All DEA applications will be affected by this finding. In fact, the relevance of these results for university and health care DEA applications is evident in the answers to research questions 2 and 4, where the importance of using sophisticated models is stressed. To be able to handle violations of the assumptions in DEA, we need some complementary approaches when units operate in different environments. By combining complementary modeling techniques, Contribution 2 aims to develop and evaluate a framework for analyzing hospital performance. Machin learning techniques are developed to perform cluster analysis, heterogeneity, and best practice analyses. A large dataset consisting of more than 1,100 hospitals in Germany illustrates the applicability of the integrated framework. In addition to predicting the best performance, the framework can be used to determine whether differences in relative efficiency scores are due to heterogeneity in inputs and outputs. In this contribution, an approach to enhancing the reliability of DEA performance analyses of hospital markets is presented as part of the answer to research question 2. In real-world situations, integer-valued amounts and flexible measures pose two principal challenges. The traditional DEA models do not address either challenge. Contribution 3 proposes an extended SBM DEA model that accommodates such data irregularities and complexity. Further, an alternative DEA model is presented that calculates efficiency by directly addressing slacks. The proposed models are further applied to 28 universities hospitals in Germany. The majority of inefficiencies can be attributed to “third-party funding income” received by university hospitals from research-granting agencies. In light of the fact that most research-granting organizations prefer to support university hospitals with the greatest impact, it seems reasonable to conclude that targeting research missions may enhance the efficiency of German university hospitals. This finding contributes to answering research question 3. University missions are heavily influenced by internationalization, but the efficacy of this strategy and its relationship to overall university efficiency are largely unknown. Contribution 4 fills this gap by implementing a three-stage mathematical method to explore university internationalization and university business models. The approach is based on SBM DEA methods and regression/correlation analyses and is designed to determine the relative internationalization and relative efficiency of German universities and analyze the influence of environmental factors on them. The key question 4 posed can now be answered. It has been found that German universities are relatively efficient at both levels of analysis, but there is no direct correlation between them. In addition, the results show that certain locational factors do not significantly affect the university’s efficiency. For policymakers, it is important to point out that efficiency modeling methodology is highly contested and in its infancy. DEA efficiency results are affected by many technical judgments for which there is little guidance on best practices. In many cases, these judgments have more to do with political than technical aspects (such as output choices). This suggests a need for a discussion between analysts and policymakers. In a nutshell, there is no doubt that DEA models can contribute to any health care or university mission. Despite the limitations we have discussed previously to ensure that they are used appropriately, these methods still offer powerful insights into organizational performance. Even though these techniques are widely popular, they are seldom used in real clinical (rather than academic) settings. The only purpose of analytical tools such as DEA is to inform rather than determine regulatory judgments. They, therefore, have to be an essential part of any competent regulator’s analytical arsenal

Multiregional sustainability at a sectoral level: Towards more effective environmental regulations

Aquesta tesi està dedicada al desenvolupament d'eines per ajudar als responsables polítics en la creació de normatives eficaces de manera eficient i metòdica. La tesi està organitzada en quatre seccions principals. A la secció 1, presentem la introducció, on establim les bases dels mètodes i dades utilitzades en aquest treball, així com els buits bibliogràfics que cobrim amb els nostres estudis. La secció 2 es basa en el primer treball, on estudiem l'eco-eficiència dels sectors manufacturers de la UE combinant taules MREEIO amb el mètode DEA i seguint aproximacions basades en la producció i el consum. Això permet identificar els sectors que requereixen regulacions en impactes específics. A continuació, a la secció 3, utilitzem DEA per determinar l'eficiència de sostenibilitat dels mixos elèctrics de la UE analitzant els trets socials, econòmics i ambientals de cadascun d’ells. En una segona etapa, utilitzem un model matemàtic a mida anomenat EffMixF per obtenir la nova composició elèctrica per als països que han resultat ineficients en la primera etapa. Aquests nous mixos es poden utilitzar com a full de ruta en l’elaboració de normatives específiques per al sector, indicant quines tecnologies s'han de fomentar, o bé obstaculitzar a cada país ineficient. Finalment, a la secció 4, determinem els factors clau de l'impacte ambiental a escala global. Per aconseguir-ho, primer comparem dues tècniques de descomposició, els mètodes SDA i Shapley-Sun, per tal d’establir les seves similituds i introduir una equació general simplificada que es pot utilitzar en substitució d’ambdós mètodes. Per acabar, apliquem aquests mètodes en un cas d’estudi, on considerem una selecció d’impactes ambientals en un període de 15 anys, per determinar la utilitat dels mètodes de descomposició. Les eines desenvolupades en aquesta tesis proporcionen informació valuosa respecte a les debilitats i oportunitats de millora dels sectors econòmics a nivell macroeconòmic.Esta tesis está dedicada al desarrollo de herramientas para ayudar a los responsables políticos en la creación de regulaciones efectivas de manera eficiente y metódica. La tesis contiene cuatro secciones principales. En la sección 1, presentamos la introducción, donde se establecen los métodos y datos utilizados en esta tesis, así como las lagunas bibliográficas que cubrimos con nuestros estudios. La sección 2 se basa en el primer trabajo, donde estudiamos la ecoeficiencia de los sectores manufactureros de la UE mediante la combinación de las tablas MREEIO con el método DEA y siguiendo enfoques basados en la producción y el consumo. Esto nos permite identificar los sectores que requieren regulaciones en impactos específicos. A continuación, en la sección 3 usamos DEA para determinar la eficiencia de sostenibilidad de los mixes eléctricos de la UE analizando las características sociales, económicas y medioambientales de cada uno de ellos. En una segunda etapa, utilizamos un modelo matemático a medida llamado EffMixF para obtener nuevos mixes eléctricos para los países ineficientes. Estos nuevos mixes pueden ser utilizados como plan estrategico en la elaboración de reglamentos específicos para el sector, indicando qué tecnologías deben ser fomentadas, o bien obstaculizadas, en cada país ineficiente. Finalmente, en la sección 4, determinamos los factores clave del impacto ambiental a escala global. Para conseguirlo, primero comparamos dos técnicas de descomposición, SDA y Shapley-Sun, para establecer sus similitudes e introducir una ecuación general simplificada como sustitución de ambos métodos. Posteriormente, aplicamos estos métodos en un caso de estudio donde consideramos una selección de impactos ambientales en un período de 15 años para determinar la utilidad de los métodos de descomposición. Las herramientas desarrolladas en esta tesis proporcionan información valiosa respecto a las debilidades y oportunidades de los sectores económicos a nivel macroeconómico.This thesis is dedicated to the development of tools to assist policy makers in the creation of effective regulations in an efficient and methodical way. The thesis is organized into four main sections. In section 1, we present the introduction, where we establish the background of the methods and data used in this work, as well as the literature gaps that we cover with our studies. Section 2 is based on the first work, where we study the eco-efficiency of the EU manufacturing sectors by combining MREEIO tables with the DEA method, following the production and consumption-based approaches. This allows us to identify the sectors requiring regulations in specific burdens. Then, in section 3, we use DEA to determine the sustainability efficiency of the EU electricity mixes by analyzing the social, economic and environmental features of each portfolio. In a second stage, we use a tailored mathematical model named EffMixF to obtain new electricity mixes for the countries found inefficient in the previous step. These new mixes can be used as roadmap to devise specific regulations for the sector, indicating which technologies should be boosted and which hindered in each inefficient country. Finally, in section 4, we determine the key driving factors of the environmental impact on a global scale. For this, we first compare two decomposition techniques, the SDA and the Shapley-Sun methods, establishing their similarities and introducing a simplified general equation that can be used in substitution of both methods. Then, we apply these methods in a case study, where we consider a selection of environmental impacts in a 15-year period, to determine the usefulness of the decomposition methods. The tools developed in this thesis provide valuable insight regarding the weaknesses and improvement opportunities of the economic sectors in a macroeconomic scale