Data Envelopment Analysis With R

This book introduces readers to the use of R codes for optimization problems. First, it provides the necessary background to understand data envelopment analysis (DEA), with a special emphasis on fuzzy DEA. It then describes DEA models, including fuzzy DEA models, and shows how to use them to solve optimization problems with R. Further, it discusses the main advantages of R in optimization problems, and provides R codes based on real-world data sets throughout. Offering a comprehensive review of DEA and fuzzy DEA models and the corresponding R codes, this practice-oriented reference guide is intended for masters and Ph.D. students in various disciplines, as well as practitioners and researchers.

This book covers recent advances in efficiency evaluations, most notably Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA) methods. It introduces the underlying theories, shows how to make the relevant calculations and discusses applications. The aim is to make the reader aware of the pros and cons of the different methods and to show how to use these methods in both standard and non-standard cases. Several software packages have been developed to solve some of the most common DEA and SFA models. This book relies on R, a free, open source software environment for statistical computing and graphics. This enables the reader to solve not only standard problems, but also many other problem variants. Using R, one can focus on understanding the context and developing a good model. One is not restricted to predefined model variants and to a one-size-fits-all approach. To facilitate the use of R, the authors have developed an R package called Benchmarking, which implements the main methods within both DEA and SFA. The book uses mathematical formulations of models and assumptions, but it de-emphasizes the formal proofs - in part by placing them in appendices -- or by referring to the original sources. Moreover, the book emphasizes the usage of the theories and the interpretations of the mathematical formulations. It includes a series of small examples, graphical illustrations, simple extensions and questions to think about. Also, it combines the formal models with less formal economic and organizational thinking. Last but not least it discusses some larger applications with significant practical impacts, including the design of benchmarking-based regulations of energy companies in different European countries, and the development of merger control programs for competition authorities.

From the Foreword: 'This book is an excellent tool for practitioners who are interested in the merits and pitfalls of the technique.... (The author's) research is an example of inventiveness, diligence and accuracy' - Freerk A. Lootsma, Delft Institute of Technology Data envelopment Analysis is a Mathematical Programme for measuring performance efficiency of organizational units. The organizational units, termed as decision-making units (DMU) can be of any kind: manufacturing units, a set of schools, banks, hospitals, power plants, police stations, prisons, a set of firms etc. DEA has been unsuccessfully applied to measure the performance efficiency of these different kinds of DMUs which share a common characteristic - that they are non-profit organization where measurement of performance efficiency is difficult. DEA has been employed for assessing the relative performance of a set of firms that use a variety of identical inputs-say in the case of a school: quality of students, teachers, grants etc.,-to produce a variety of identical outputs-number of students who pass the final year, average grades obtained by the students in the final year etc. DEA assumes the performance of the DMUs by using the concepts of efficiency or productivity which is measured as the ratio of total outputs to total inputs. Also, the efficiencies estimated are relative to the best performing DMU or DMUs. The best performing DMU is given a score of 100% and the performance of other DMUs vary between 0 -100%.

This handbook covers DEA topics that are extensively used and solidly based. The purpose of the handbook is to (1) describe and elucidate the state of the field and (2), where appropriate, extend the frontier of DEA research. It defines the state-of-the-art of DEA methodology and its uses. This handbook is intended to represent a milestone in the progression of DEA. Written by experts, who are generally major contributors to the topics to be covered, it includes a comprehensive review and discussion of basic DEA models, which, in the present issue extensions to the basic DEA methods, and a collection of DEA applications in the areas of banking, engineering, health care, and services. The handbook's chapters are organized into two categories: (i) basic DEA models, concepts, and their extensions, and (ii) DEA applications. First edition contributors have returned to update their work. The second edition includes updated versions of selected first edition chapters. New chapters have been added on: different approaches with no need for a priori choices of weights (called “multipliers) that reflect meaningful trade-offs, construction of static and dynamic DEA technologies, slacks-based model and its extensions, DEA models for DMUs that have internal structures network DEA that can be used for measuring supply chain operations, Selection of DEA applications in the service sector with a focus on building a conceptual framework, research design and interpreting results.

This handbook serves as a complement to the Handbook on Data Envelopment Analysis (eds, W.W. Cooper, L.M. Seiford and J, Zhu, 2011, Springer) in an effort to extend the frontier of DEA research. It provides a comprehensive source for the state-of-the art DEA modeling on internal structures and network DEA. Chapter 1 provides a survey on two-stage network performance decomposition and modeling techniques. Chapter 2 discusses the pitfalls in network DEA modeling. Chapter 3 discusses efficiency decompositions in network DEA under three types of structures, namely series, parallel and dynamic. Chapter 4 studies the determination of the network DEA frontier. In chapter 5 additive efficiency decomposition in network DEA is discussed. An approach in scale efficiency measurement in two-stage networks is presented in chapter 6. Chapter 7 further discusses the scale efficiency decomposition in two stage networks. Chapter 8 offers a bargaining game approach to modeling two-stage networks. Chapter 9 studies shared resources and efficiency decomposition in two-stage networks. Chapter 10 introduces an approach to computing the technical efficiency scores for a dynamic production network and its sub-processes. Chapter 11 presents a slacks-based network DEA. Chapter 12 discusses a DEA modeling technique for a two-stage network process where the inputs of the second stage include both the outputs from the first stage and additional inputs to the second stage. Chapter 13 presents an efficiency measurement methodology for multi-stage production systems. Chapter 14 discusses network DEA models, both static and dynamic. The discussion also explores various useful objective functions that can be applied to the models to find the optimal allocation of resources for processes within the black box, that are normally invisible to DEA. Chapter 15 provides a comprehensive review of various type network DEA modeling techniques. Chapter 16 presents shared resources models for deriving aggregate measures of bank-branch performance, with accompanying component measures that make up that aggregate value. Chapter 17 examines a set of manufacturing plants operating under a single umbrella, with the objective being to use the component or function measures to decide what might be considered as each plant’s core business. Chapter 18 considers problem settings where there may be clusters or groups of DMUs that form a hierarchy. The specific case of a set off electric power plants is examined in this context. Chapter 19 models bad outputs in two-stage network DEA. Chapter 20 presents an application of network DEA to performance measurement of Major League Baseball (MLB) teams. Chapter 21 presents an application of a two-stage network DEA model for examining the performance of 30 U.S. airline companies. Chapter 22 then presents two distinct network efficiency models that are applied to engineering systems.

This volume systematically details both the basic principles and new developments in Data Envelopment Analysis (DEA), offering a solid understanding of the methodology, its uses, and its potential. New material in this edition includes coverage of recent developments that have greatly extended the power and scope of DEA and have lead to new directions for research and DEA uses. Each chapter accompanies its developments with simple numerical examples and discussions of actual applications. The first nine chapters cover the basic principles of DEA, while the final seven chapters provide a more advanced treatment.

The combination of DEA and ratio analysis is introduced as a suitable field for evaluating the performance of DMUs. In this regard, DEA-R is also proposed as a hybrid technique for calculating efficiency, ranking DMUs, and finding efficient faces. Therefore, the relationship between DEA and DEA-R provides a suitable field for researchers in the field of evaluating the performance of DMUs. The audience of this book is not limited to researchers in mathematics fields, but experts and students in industrial engineering and management fields also benefit from the topics of this book.

Data Envelopment Analysis (DEA) is often overlooked in empirical work such as diagnostic tests to determine whether the data conform with technology which, in turn, is important in identifying technical change, or finding which types of DEA models allow data transformations, including dealing with ordinal data. Advances in Data Envelopment Analysis focuses on both theoretical developments and their applications into the measurement of productive efficiency and productivity growth, such as its application to the modelling of time substitution, i.e. the problem of how to allocate resources over time, and estimating the "value" of a Decision Making Unit (DMU). Contents:AcknowledgementsPrefaceIntroduction:The DEA Technology and Its Representation(Axiomatic) Properties of the DEA ModelAppendixLooking at the Data in DEA:Data DiagnosticsTechnical ChangeData TranslationAppendix: Distance FunctionsDEA and Intensity Variables:On Shephard's Duality TheoryAdjoint Transformations in DEAThe Diet ProblemPricing Decision Making UnitsDEA and Directional Distance Functions:Directional VectorsAggregation and Directional VectorsEndogenizing the Directional VectorAppendixDEA and Time Substitution:Theoretical UnderpinningReassessing the EU Stability and Growth PactMethodSome Limitations of Two DEA Models:The Non-Archimedean and DEASuper-Efficiency and ZerosReferences Readership: Advanced postgraduate students and researchers in operations research and economics with a particular interest in production theory and operations management. Keywords:Optimization Techniques;Multifactor Productivity;Intertemporal Firm Choice;Technological Change: Choices and Consequences;Diffusion Processes;Data Envelopment Analysis;Operations Research