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Über dieses Buch

This book offers new transparent views and step-by-step methods for performance evaluation of a set of units using Data Envelopment Analysis (DEA). The book has twelve practical chapters. Elementary concepts and definitions are gradually built in Chapters 1-6 based upon four examples of one input and one output factors, two input factors, two output factors, and four input and three output factors. Simultaneously, the mathematical foundations using linear programming are also introduced without any prerequisites. A reader with basic knowledge of mathematics and computers is able to understand the contents of the book. In addition, to prevent pre-judgment about the available concepts and definitions in the DEA literature, some new phrases are introduced and, after elucidating each phrase in detail in Chapters 1-6, they are reintroduced for industry-wide accuracy in Chapter 7. After that, some of the more advanced DEA topics are illustrated in Chapters 8-12, such as: production-planning problems, output-input ratio analysis, efficiency over different time periods, Malmquist efficiency indexes, and a delta neighborhood model.
A clear overview of many of the elementary and advanced concepts of DEA is provided, including Technical Efficiency, Relative Efficiency, Cost/Revenue/Profit Efficiency, Price/Overall Efficiency, the DEA axioms, the mathematical background to measure technical efficiency and overall efficiency, the multiplier/envelopment form of basic DEA models in input/output-orientation, the multiplier/envelopment of Additive DEA model, the multiplier/envelopment of slacks-based models, and others. The book also covers a variety of DEA techniques, input-output ratio analysis, the natural relationships between DEA frontier and the ratio of output to input factors, production-planning problems, planning ideas with a centralized decision-making unit, context-dependent DEA, Malmquist efficiency index, efficiency over different time periods, and others. End-of-chapter exercises are provided for each chapter.

Inhaltsverzeichnis

Frontmatter

Chapter 1. The Gemstone Example

Abstract
In this chapter, a simple example is provided to explain several concepts which are important to measure the performance of a set of homogenous factories, organizations, firms and so on. No computer knowledge is needed in this chapter, but a very elementary knowledge of mathematics will be required, such as sketching a line in a plane. The section is started with a question about a jewelry company which would like to evaluate 17 candidates according to the results of a task. The concepts are logically discussed to pave the way to introduce different aspects of the company and to establish the corresponding mathematical foundation for further complex questions on measuring the performance of firms. Several figures are provided to elucidate the concepts. Of course, the provided concepts are not new and have been mentioned in the literature of Economics, Management, Engineering and Operations Research; however, in order to avoid any confusion, these concepts are re-introduced and the pros and cons of each concept are generally illustrated. At the end of this chapter, readers will have learned the elementary requirements and concepts of measuring the performance evaluation of firms.
Dariush Khezrimotlagh, Yao Chen

Chapter 2. Possibility and Practicability

Abstract
In this chapter, we continue the discussions in Chap. 1. Step by step, we built the mathematical background of the requirement axioms to measure the performance of homogenous firms. We similarly start with a question from the gemstone company and gradually illustrate the new concepts. The provided concepts are not new, and have been mentioned in the literature of operations research; however, in order to avoid any confusion and pretend judgment based on the literature, only the concepts are re-introduced and the pros and cons of each concept are demonstrated. We also provide a philosophical argument to clarify some of the concepts. At the end of this chapter, readers will have an understanding of the overall concepts used to measure the performance of firms and will be ready to develop the mathematical background for complex situations.
Dariush Khezrimotlagh, Yao Chen

Chapter 3. The Petroleum Example

Abstract
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Dariush Khezrimotlagh, Yao Chen

Chapter 4. The Optimization Approach

Abstract
In this chapter, we continue the discussion in Chap. 3, and gradually build optimization approaches and linear programming models, without pre-required knowledge in operations research. In order to solve a linear programming, Microsoft Excel Solver software and Microsoft Visual Basic software are used and the required instructions are comprehensively illustrated, so that no previous knowledge about the software are needed. We also discuss a different view for the Petroleum example with two output factors. Two important theorems are provided to explain when a score should be called a ‘relative score’. In addition, two necessary types are added to Types 1–4 in Chap. 1, when the number of input factors and the number of output factors are more than 1. These two types provide a transparent view to rank and benchmark firms through the feasible area, as well as a direction for future arguments on these topics. At the end of this section, readers are prepared to calculate the performance evaluation of a set of homogenous firms and explain the related concepts visibly.
Dariush Khezrimotlagh, Yao Chen

Chapter 5. The Airport Example

Abstract
In this chapter, an example of eight Persian international airports is proposed to illustrate how to adjust the introduced concepts in the previous chapters when the number of input factors and the number of output factors are more than two. The mathematical methods, the linear programming models, and the computer programming are developed with detailed illustrations. Several different approaches are discussed and the strengths and shortcomings of each approach is gradually represented. At the end of this chapter, readers are prepared to generalize the concepts of doing the job right/well for a set of homogenous firms with multiple input factors and multiple output factors.
Dariush Khezrimotlagh, Yao Chen

Chapter 6. The Delta Neighborhood

Abstract
In this chapter, the relative scores, under certain conditions, are measured for the example of eight homogenous airports from the previous chapter. As discussed in the previous chapters, each supposed condition can result different relative scores and ranks for airports. In other words, the relative scores of firms are completely dependent upon the supposed relationship between factors or the supposed weight/worth/price for each factor. The optimization approach is applied while the weights/prices of factors are the same for the airports and one of the conditions such as decreasing the overall input values, increasing overall output values or both decreasing the input values and increasing the output values are assumed. After that, a delta neighborhood of a firm is introduced to find a bridge between the concepts ‘doing the job rights’ and ‘doing the job well’. Mathematical arguments are provided as well as computer programming with detailed illustrations. At the end of this chapter, readers are completely prepared to utilize the performance evaluation of a set of homogenous firms with multiple input factors and multiple output factors.
Dariush Khezrimotlagh, Yao Chen

Chapter 7. Data Envelopment Analysis

Abstract
The outcomes from the previous chapters provide useful information from the literature of operations research and economics on measuring the performance of a set of homogenous firms with multiple input factors and multiple output factors as well as ranking and benchmarking firms. If firms are not homogenous, the situation is the same as when each factor has a different unit of measurement from one firm to another, and therefore, no meaningful discrimination can be expressed, unless the simple conditions of discrimination, which are represented in Sect. 2.​3, are satisfied. In this chapter, the concepts introduced in the previous chapters are adapted with the literature and the philosophical background is discussed.
Dariush Khezrimotlagh, Yao Chen

Chapter 8. The Ratio of Output to Input Factors

Abstract
In the previous chapters, we provided transparent steps to learn the foundation of DEA to estimate the performance of a set of homogenous firms. In this chapter, we demonstrate mathematical properties to describe the natural relationships between the DEA frontier and the ratio of output to input factors.
Dariush Khezrimotlagh, Yao Chen

Chapter 9. Production Planning Problem

Abstract
Production in large firms with a centralized decision-making unit usually involves the contribution of several individual units. Supermarket chains or organizations with several workshops include more than one unit in which each unit contributes to a part of the entire production. For example, a sales plan is decided by a bank’s cooperate management for its divisions regarding the number of credit cards to be issued and the number of loans to be processed. The central division defines a plan to optimize the average or overall production performance in the entire organization after planning. In this chapter, a production-planning problem which is regularly faced by the central decision-making units is illustrated. Two planning ideas, proposed by Du et al. (2010), are discussed to arrange new input and output plans for all specific units when demand deviations can be predicted.
Dariush Khezrimotlagh, Yao Chen

Chapter 10. Context-Dependent DEA

Abstract
In this chapter, the context-dependent DEA is discussed. Since a product can appear attractive in comparison with a contextual of less attractive or unattractive alternatives, the performance of firms can be influenced by the context. For an example, twenty-three Tokyo public libraries are considered and a context-dependent DEA proposed by Chen et al. (2005) is discussed. The attractiveness of each library on a particular performance level in comparison with other libraries are measured. Libraries are classified on several empirical efficient frontiers, where each frontier is used to evaluate the attractiveness. The performance of the technically efficient libraries changes as the technically inefficient libraries change their performance. The context-dependent DEA also represents another view to differentiate the performance of efficient DMUs. When DMUs in a particular level are observed as having the same performance, the attractiveness measure lets us discriminate the “equal performance” based upon the third option or the same particular evaluation context. We also develop the VBA procedure to measure the attractiveness with just one click.
Dariush Khezrimotlagh, Yao Chen

Chapter 11. Efficiency Change Over Different Times

Abstract
In the literature of macroeconomics and the business economic press, there is a strong interest in the variation of efficiency over different times (Ray 2004). There are two methods to address this issue, such as, the Tornqvist and the Fisher productivity indexes. These two indexes use the price information of input and output factors without requiring the production technology of firms. Caves et al. (1982) introduced an index called the Malmquist efficiency index to construct a production frontier to represent the production technology of firms. Färe et al. (1992) combined ideas on the Farrell measurement and Caves et al. (1982) efficiency measurement to construct a Malmquist efficiency index directly from the input and output factors using DEA. The Malmquist efficiency index can be decomposed into two components. One component is to measure the technical change and the other component is to measure the frontier shift. In this chapter, we first illustrate the basic Malmquist index. After that, we illustrate the works of Chen and Ali (2004) to provide an extension to the Malmquist index by analyzing the above two components with an example of computer industry. Finally, a non-linear Malmquist index, proposed by Chen (2003), is discussed.
Dariush Khezrimotlagh, Yao Chen

Chapter 12. Delta Neighborhood Extension

Abstract
In this chapter, the introduced mathematical model in Chap. 6 is improved to fairly rank firms in various conditions, and the chapter is finished with several outcomes of the model.
Dariush Khezrimotlagh, Yao Chen

Backmatter

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