Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top

2014 | Book

Data Envelopment Analysis Read chapter Read first chapter

Quantitative Models for Performance Evaluation and Benchmarking

Data Envelopment Analysis with Spreadsheets

Author: Joe Zhu

Publisher: Springer International Publishing

Book Series : International Series in Operations Research & Management Science

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

Login to get access
insite
SEARCH

About this book

The author is one of the prominent researchers in the field of Data Envelopment Analysis (DEA), a powerful data analysis tool that can be used in performance evaluation and benchmarking. This book is based upon the author’s years of research and teaching experiences.

It is difficult to evaluate an organization’s performance when multiple performance metrics are present. The difficulties are further enhanced when the relationships among the performance metrics are complex and involve unknown tradeoffs. This book introduces Data Envelopment Analysis (DEA) as a multiple-measure performance evaluation and benchmarking tool. The focus of performance evaluation and benchmarking is shifted from characterizing performance in terms of single measures to evaluating performance as a multidimensional systems perspective.

Conventional and new DEA approaches are presented and discussed using Excel spreadsheets — one of the most effective ways to analyze and evaluate decision alternatives. The user can easily develop and customize new DEA models based upon these spreadsheets.

DEA models and approaches are presented to deal with performance evaluation problems in a variety of contexts. For example, a context-dependent DEA measures the relative attractiveness of similar operations/processes/products. Sensitivity analysis techniques can be easily applied, and used to identify critical performance measures. Two-stage network efficiency models can be utilized to study performance of supply chain. DEA benchmarking models extend DEA’s ability in performance evaluation. Various cross efficiency approaches are presented to provide peer evaluation scores.

This book also provides an easy-to-use DEA software — DEAFrontier. This DEAFrontier is an Add-In for Microsoft® Excel and provides a custom menu of DEA approaches. This version of DEAFrontier is for use with Excel 97-2013 under Windows and can solve up to 50 DMUs, subject to the capacity of Excel Solver. It is an extremely powerful tool that can assist decision-makers in benchmarking and analyzing complex operational performance issues in manufacturing organizations as well as evaluating processes in banking, retail, franchising, health care, public services and many other industries.

Table of Contents

Frontmatter
1. Data Envelopment Analysis
Abstract
All business operations/processes involve transformation—adding values and changes to materials and turning them into goods and services that customers want . Managers are often interested in evaluating how efficiently various processes operate with respect to multiple performance measures (or metrics). Organizations are interested in knowing their performance with respect to the use of resources such labor, materials, energy, machines, and other, and the outcomes such as the quality of finished products, services, customer satisfaction. Consider hospital operations, for example. The performance measures or metrics include doctors, nurses, medical supplies, equipment, laboratories, beds, number of patients treated, number of interns and residents trained, and others. In a buyer-seller supply chain, the buyer may be interested in comparing the performance of several sellers with respect to response time, costs, flexibility, customer service, quality, and customization. Eliminating or improving inefficient operations decreases the cost and increases productivity. Performance evaluation and benchmarking help business operations/processes to become more productive and efficient.
Joe Zhu
2. Envelopment DEA Models
Abstract
This chapter presents some basic DEA models that are used to determine the best-practice frontier characterized by (Sect. 1.1) in Chap. 1. These models are called envelopment models, because the identified best-practice frontier envelops all the observations (DMUs). The shapes of best-practice (or efficient) frontiers obtained from these models can be associated with the concept of Returns-to-Scale (RTS) which will be discussed in details in Chap. 13. This is because the best-practice (or efficient) frontiers can be viewed as exhibiting of various types of RTS. However, if the inputs and outputs are not related to a “production function”, RTS concept cannot be applied. Under such cases, RTS is merely used to refer to different shapes of frontiers.
Joe Zhu
3. Multiplier DEA Model
Abstract
The dual linear programming problems to the envelopment models are called multiplier models as shown in Table 3.1.
Joe Zhu
4. DEA Cross Efficiency
Abstract
While DEA has been proven an effective approach in identifying the best practice frontiers, its flexibility in weighting multiple inputs and outputs and its nature of self-evaluation have been criticized. The cross efficiency method is developed as a DEA extension to rank DMUs with the main idea being to use DEA to do peer evaluation, rather than in pure self-evaluation mode. Cross efficiency has been further investigated by Doyle and Green. There are mainly two advantages for cross-evaluation method. It provides an ordering among DMUs and it eliminates unrealistic weight schemes without requiring the elicitation of weight restrictions from application area experts.
Joe Zhu
5. Slack-Based DEA Models
Abstract
The input-oriented DEA models consider the possible (proportional) input reductions while maintaining the current levels of outputs. The output-oriented DEA models consider the possible (proportional) output augmentations while keeping the current levels of inputs. Charnes et al. develop an additive DEA model which considers possible input decreases as well as output increases simultaneously. The additive model is based upon input and output slacks.
Joe Zhu
6. Measure-Specific DEA Models
Abstract
Although DEA does not need a priori information on the underlying functional forms and weights among various input and output measures, it assumes proportional improvements of inputs or outputs. This assumption becomes invalid when a preference structure over the improvement of different inputs (outputs) is present in evaluating (inefficient) DMUs (see also Chap. 7). We need models where a particular set of performance measures is given pre-emptive priority to improve.
Joe Zhu
7. Non-radial DEA Models and DEA with Preference
Abstract
We can call the envelopment DEA models as radial efficiency measures, because these models optimize all inputs or outputs of a DMU at a certain proportion. Färe and Lovell (J Econ Theory 19:150–162, 1978) introduce a non-radial measure which allows non-proportional reductions in positive inputs or augmentations in positive outputs. Table 7.1 summarizes the non-radial DEA models with respect to the model orientation and frontier type.
Joe Zhu
8. Modeling Undesirable Measures
Abstract
Both desirable (good) and undesirable (bad) outputs and inputs may be present. For example, the number of defective products is an undesirable output. One wants to reduce the number of defects to improve the performance. If inefficiency exists in production processes where final products are manufactured with a production of wastes and pollutants, the outputs of wastes and pollutants are undesirable and should be reduced to improve the performance.
Joe Zhu
9. Context-dependent Data Envelopment Analysis
Abstract
Adding or deleting an inefficient DMU or a set of inefficient DMUs does not alter the efficiencies of the existing DMUs and the best-practice frontier. The inefficiency scores change only if the best-practice frontier is altered. i.e., the performance of DMUs depends only on the identified best-practice frontier. In contrast, researchers of the consumer choice theory point out that consumer choice is often influenced by the context. e.g., a circle appears large when surrounded by small circles and small when surrounded by larger ones. Similarly a product may appear attractive against a background of less attractive alternatives and unattractive when compared to more attractive alternatives.
Joe Zhu
10. Super Efficiency
Abstract
When a DMU under evaluation is not included in the reference set of the envelopment models, the resulting DEA models are called super-efficiency DEA models. Charnes et al. (Int J Systems Sci 23:789–798, 1992) use a super-efficiency model to study the sensitivity of the efficiency classifications. Zhu (Eur J Operational Res 90:451–460, 1996) and Seiford and Zhu (Eur J Operational Res 108:127–139, 1998) develop a number of new super-efficiency models to determine the efficiency stability regions (see Chap. 11, Sensitivity Analysis). Andersen and Petersen (Manage Sci 39:1261–1264, 1993) propose using the CRS super-efficiency model in ranking the efficient DMUs. Also, the super-efficiency DEA models can be used in detecting influential observations (Wilson J Prod Anal 6:27–45, 1995) and in identifying the extreme efficient DMUs (Thrall Ann Oper Res 66:109–138, 1996). Seiford and Zhu (INFOR 37:174–187, 1999) study the infeasibility of various super-efficiency models developed from the envelopment models in Table 11.2, Chap. 11 (Sensitivity Analysis) presents other super-efficiency models that are used in sensitivity analysis.
Joe Zhu
11. Sensitivity Analysis
Abstract
One important issue in DEA which has been studied by many DEA researchers is the efficiency sensitivity to perturbations in the data. Some DEA sensitivity studies focus on the sensitivity of DEA results to the variable and model selection. Most of the DEA sensitivity analysis studies focus on the misspecification of efficiency classification of a test DMU. However, note that DEA is an extremal method in the sense that all extreme points are characterized as efficient. If data entry errors occur for various DMUs, the resulting isoquant may vary substantially. We say that the calculated frontiers of DEA models are stable if the frontier DMUs that determine the DEA frontier remain on the frontier after particular data perturbations are made.
Joe Zhu
12. Benchmarking Models
Abstract
Benchmarking is a process of defining valid measures of performance comparison among peer DMUs, using them to determine the relative positions of the peer DMUs and, ultimately, establishing a standard of excellence. In that sense, DEA can be regarded as a benchmarking tool, because the frontier identified can be regarded as an empirical standard of excellence.
Joe Zhu
13. Returns-to-Scale
Abstract
As demonstrated in Fig. 2.3 (Chap. 2, Envelopment DEA Models), the VRS envelopment model identifies the VRS frontier with DMUs exhibiting IRS (increasing returns to scale), CRS (constant returns to scale), and DRS (decreasing returns to scale). In fact, the economic concept of RTS (returns to scale) has been widely studied within the framework of DEA. RTS have typically been defined only for single output situations. DEA generalizes the notion of RTS to the multiple-output case. This, in turn, further extended the applicability of DEA.
Joe Zhu
14. DEA Models for Two-Stage Network Processes
Abstract
While the definition of a DMU is generic and DMUs can be in various forms such as hospitals, products, universities, cities, courts, business firms, and others, DMUs can have a two-stage structure in many cases. For example, banks use labor and assets to generate deposits which are in turn used to generate load incomes. Seiford and Zhu (Management Science, 45(9), 1270–1288, 1999) use a two-stage process to measure the profitability and marketability of US commercial banks. In their study, profitability is measured using labor and assets as inputs, and the outputs are profits and revenue. In the second stage for marketability, the profits and revenue are then used as inputs, while market value, returns and earnings per share are used as outputs. Chilingerian and Sherman (Handbook on Data Envelopment Analysis, Chapter 17, 2004) describe another two-stage process in measuring physician care. Their first stage is a manager-controlled process with inputs including registered nurses, medical supplies, and capital and fixed costs. These inputs generate the outputs or intermediate measures (inputs to the second stage), including patient days, quality of treatment, drug dispensed, among others. The outputs of the second (physician controlled) stage include research grants, quality of patients, and quantity of individuals trained, by specialty.
Joe Zhu
15. Models for Evaluating Supply Chains and Network Structures
Abstract
So far, the value-added processes or systems have been treated as a “black-box”. We examine the resources available to the processes or systems and monitor the “conversions” of these resources (inputs) into the desired outputs. However, each process or system can include many subprocesses. For example, if the process is to make a car, then important subprocesses include assembling and painting. If we evaluate the efficiency of a supply chain system, then we need to measure the performance of each individual supply chain components, including suppliers, manufacturers, retailers, and customers.
Joe Zhu
16. Congestion
Abstract
Congestion, as used in economics, refers to situations where reductions in one or more inputs generate an increase in one or more outputs. Examples can be found in underground mining and agriculture. For example, too much fertilizer applied to a given plot could reduce the overall output. We here adopt the following definition of congestion from Cooper et al. (Annals of Operations Research, 66, 3–45, 1996).
Joe Zhu
17. Identifying Critical Measures in DEA
Abstract
Since each DMU has its own inherent tradeoffs among the multiple measures that significantly influence the performance, it is extremely important for the management to know the critical measures. The current chapter introduces the approach of Chen and Zhu (Annals of Operations Research, 124 (1–4), 225–244, 2003) for identifying the critical measures to DMUs’ performance. Note that once the DEA evaluation is done, the management needs to either (i) maintain the best practice for the efficient DMUs or (ii) achieve the best practice for the inefficient DMUs. Thus, when a set of multiple performance measures is determined, measures that are influential to maintaining and achieving the best practice should be regarded as critical to the performance of DMUs. Also, it is believed that a critical measure is signaled by whether changes in its value affect the performance, not by whether inclusion or exclusion of the measure affects the performance.
Joe Zhu
18. Interval and Ordinal Data in DEA
Abstract
So far, all previous chapters have assumed that data in DEA are known exactly. In the DEA literature, there are models for dealing with rank data and interval data. For example, some outputs and inputs may be only known as in forms of bounded or interval data, ordinal data, and ratio bounded data. Cook et al. (Journal of Operational Research Society, 44, 133–140, 1993; Journal of Operational Research Society, 47, 945–953, 1996) were the first who developed a modified DEA structure where the inputs and outputs are represented as rank positions in an ordinal, rather than numerical sense.
Joe Zhu
19. DEAFrontier Software
Abstract
Previous chapters include how to use DEAFrontier software to solve DEA models discussed. This version of DEAFrontier software requires Excel 2007–2013 9 (under Windows) and can solve up to 50 DMUs with unlimited number of inputs and outputs (subject to the capacity of the standard Excel Solver). To install the software, copy the file “DEAFrontier.xlam” to your hard drive. Please visit www.​deafrontier.​net for software support.
Joe Zhu
Backmatter
Metadata
Title
Quantitative Models for Performance Evaluation and Benchmarking
Author
Joe Zhu
Copyright Year
2014
Publisher
Springer International Publishing
Electronic ISBN
978-3-319-06647-9
Print ISBN
978-3-319-06646-2
DOI
https://doi.org/10.1007/978-3-319-06647-9