1
Chapter 1
Data Envelopment Analysis
Employees who em to work the least can often be the most
productive
1.1 P erformance Evaluation and Tradeoffs
心爱的娃娃计算机基础知识All business operations/process involve transformation—adding values and changes to materials and turning them into goods and rvices that customers want. Managers are often interested in evaluating how efficiently various process oper-ate with respect to multiple performance measures (or metrics). Organizations are interested in knowing their performance with respect to the u of resources such labor, materials, energy, machines, and other, and the outcomes such as the quality of finished products, rvices, customer satisfaction. Consider hospital operations, for example. The performance measures or metrics include doctors, nurs, medi-cal supplies, equipment, laboratories, beds, number of patients treated, number of interns and residents trained, and others. In a buyer-ller
supply chain, the buyer may be interested in comparing the performance of veral llers with respect to respon time, costs, flexibility, customer rvice, quality, and customization. Eliminating or improving inefficient operations decreas the cost and increas productivity. Performance evaluation and benchmarking help business operations/process to become more productive and efficient.
Performance evaluation is an important continuous improvement tool for busi-ness to stay competitive and plays an important role in the global market where competition is inten and grows more so each day. Performance evaluation and benchmarking positively force any business unit to constantly evolve and improve in order to survive and prosper in a business environment facing global competi-tion. Through performance evaluation, one can (i) reveal the strengths and weak-ness of business operations, activities, and process, (ii) better prepare the busi-ness to meet its customers’ needs and requirements, and (iii) identify opportunities to improve current operations and process, and create new products, rvices and process.
J. Zhu, Quantitative Models for Performance Evaluation and Benchmarking ,
DOI 10.1007/978-3-319-06647-9_1, © Springer International Publishing Switzerland 2014
早教益智玩具
Single-measure bad gap analysis is often ud as a fundamental method in per-formance evaluation and benchmarking. However, as pointed out by Camp (1995), one of the dilemmas that we face is how to show benchmarks where multiple mea-surements exist. It is rare that one single measure can suffice for the purpo of per-formance evaluation. The single output to input financial ratios, such as, return on investment (ROI) and return on sales (ROS), may be ud as indices to characterize the financial performance. However, they are unsatisfactory discriminants of “best-practice”, and are not sufficient to evaluate operating efficiency. Since a business unit’s performance is a complex phenomenon requiring more than a single criterion to characterize it. For example, as pointed out by Sherman (1984), a bank branch may be profitable when profit reflects the interest and the revenues earned on funds generated by the branch less the cost of the funds and less the costs of operating the branch. However, this profit measure does not indicate whether the resources ud to provide customer rvices are being managed efficiently.
Further, the u of single measures ignores any interactions, substitutions or trad-eoffs among various performance measures. Each business operation has specific performance measures or metrics with tradeoffs. For example, consider the tradeoff between total supply chain cost and supply chain respon time, measured by the amount of time between an order and its corresponding deliv
ery. Figure 1.1 illus-trates alternate supply chain operations S1, S2, S3, and S, and the best-practice (efficient) frontier or tradeoff curve determined by them. A supply chain who performance (or strategy) is on the efficient frontier is non-dominated (efficient) in the n that no alternate supply chain’s performance is strictly better in both cost and respon time. Through performance evaluation, the efficient frontier that reprents the best practice is identified, and an inefficient strategy (e.g., point S) can be improved (moved to the efficient frontier) with suggested directions for im-provement (to S1, S2, S3 or other points along the frontier).
Optimization techniques can be ud to estimate the efficient frontier if we know the functional forms for the relationships among various performance mea-sures. For example, stockout levels and inventory turns are two mutually depen-dent variables with performance tradeoffs. Technological and process innovations can shift the cost tradeoff curves by reducing the cost of achieving lower invento-ries at a particular stockout level or the cost of achieving lower stockouts at a par-ticular inventory level. Unfortunately, such information is usually not completely available.
Without a priori information on the tradeoffs, the functional forms cannot be specified. Conquently, we cannot fully characterize the business operations and process. Note that the objective of performance evaluation is to evaluate the cur-rent business operation internally and to benchmark a
gainst similar business op-erations externally to identify the best practice. Thus, such best-practices can be empirically identified. We can empirically identify or estimate the best-practice or efficient frontier bad upon obrvations on one business operation/process over time or similar business operations at a specific time period.
1.2 D ata Envelopment Analysis
This book is about data envelopment analysis (DEA) and its models using spread-sheet modeling. What is DEA? DEA is a data analysis tool for identifying best-practices as shown in Fig. 1.1 when such a best-practice frontier is characterized by multiple performance metrics. In DEA, performance metrics are classified as “inputs” and “outputs”. See Sect. 1.3 for detailed discussion on DEA inputs and outputs.
According to Cooper et al. (2011a ):
DEA is a relatively new “data oriented” approach for evaluating the performance of a t of peer entities called Decision Making Units (DMUs) which convert multiple inputs into multiple outputs. The definition of a DMU is generic and flexible. Recent years have en a great variety of applications of DEA for u in evaluating the performances of many dif-ferent kinds of entities engaged in many diff
erent activities in many different contexts in many different countries. The DEA applications have ud DMUs of various forms to evaluate the performance of entities, such as hospitals, US Air Force wings, universities, cities, courts, business firms, and others, including the performance of countries, regions, etc. Becau it requires very few assumptions, DEA has also opened up possibilities for u in cas which have been resistant to other approaches becau of the complex (often unknown) nature of the relations between the multiple inputs and multiple outputs involved in DMUs.
Throughout the book, we u decision making units (DMUs) to reprent business operations or process. Each DMU is evaluated bad upon a t of multiple per-formance measures that are classified as “inputs” and “outputs”.人像图片大全
For now, suppo we have a t of obrvations on n DMUs. Each obrvation consists of values of performance measures related to a DMU j ( j = 1, …, n ). The lected t of performance measures are classified as m inputs x ij ( i = 1, 2, …, m ) and s outputs y rj ( r = 1, 2, …, s ).
Fig. 1.1 Best practice (effi-cient) frontier of supply chain operations
DEA us linear programming techniques to identify the (empirical) efficient frontier or best-practice frontier for the n obrvations. The following two prop-erties ensure that we can develop a piecewi linear approximation to the efficient frontier and the area dominated by the frontier, as shown in Fig. 1.1.Property 1.1 Convexity . 1(1,2,,)n j ij
j x i m λ==…∑ and 1 n j rj j y λ=∑(,,,)r s =…12are possible input and output levels achievable by the DMU j , where
Ȝj ( j = 1, …, n ) are nonnegative scalars such that 11n j j λ==∑.
Property 1.2 Inefficiency . The same y rj can be obtained by using ˆij x
nba第一高人
, where ˆij ij x
x ≥ (i.e., the same output levels can be achieved by using more inputs); The same x ij can be ud to achieve ˆ,rj y
where ˆrj rj y y ≤ (i.e., the same input levels can be ud to achieve less outputs).
Consider Fig. 1.1 where total supply chain cost and supply chain respon time reprent two inputs. Applying Property 1.1 to S1, S2, and S3 yields the piecewi linear approximation to the curve shown in Fig. 1.1. Applying both properties ex-pands the line gments S1S2 and S2S3 into the area dominated by the curve.For specific x i ( i = 1, 2, …, m ) and y i ( r = 1, 2, …, s ), we have
(1.1)
The next step is to estimate the empirical (piecewi linear) efficient frontier char-acterized by (1.1). DEA us linear programming to implicitly estimate the trad-eoffs inherent in the empirical efficient frontier. DEA introduced by Charnes et al. (1978) has been proven an effective tool in identifying such empirical frontiers and in evaluating relative “efficiency”.
Here “efficiency” is a generic term that can reprent a variety of cas depend-ing on a particular t of DMUs and a t of associated performance measures. For example, if performance measures are inputs and outputs of a production process, then DEA “efficiency” is a “production efficiency”. If performance measures are quality indicators, then DEA “efficiency” yields a composite quality measure.
In fact, in addition to be ud as an estimate of “production efficiency”, DEA is a “balanced benchmar
king” (Sherman and Zhu 2013) that examines performance in multiple criteria and helps organizations to test their assumptions about perfor-mance, productivity, and efficiency. Under general benchmarking, the DEA score may no longer be referred to as “production efficiency”. In this ca, we may wish to refer to the DEA score as a form of “overall performance” of an organization. Such “overall performance” can appear in the form of composite measure that ag-gregates individual indicators (inputs and outputs) via a DEA model. For example, 1
1
1 1,2,..., 1,2, (1)
j ij i j n
j rj r j n j j x x i m y y r s λλλ===⎧≤=⎪⎪⎪⎪≥=⎨⎪⎪⎪=⎪⎩∑∑∑
手臂上长痣5 1.3 P erformance Metrics Classified as Inputs and Outputs
composite measures (DEA scores) of quality allow nior leaders to better bench-mark their organization’s performance against other high-performing organizations (Shwartz et al. 2009). The DEA inputs and outputs reprent more than the “inputs” and “outputs” under the notion of productio
n process, and DEA is more than an efficiency measure under the notion of production process. In the next ction, we will discuss what constitute DEA inputs and outputs.
DEA was designed to measure the relative efficiency where market prices are not available (e, e.g., Charnes et al. 1981; Johnson and Zhu 2002). However, by its ability to model multiple-input and multiple-output relationships without a priori underlying functional form assumption, DEA has also been widely applied to other areas. See Liu et al. (2013) for a comprehensive survey on DEA applications from 1978 to 2010. The authors identify the top five DEA applications areas as banking, health care, agriculture and farm transportation, and education, and the applications with the highest growth momentum recently as energy, environment, and finance.
Such previous DEA studies provide uful managerial information on improving the performance. In particular, DEA is an excellent tool for improving the produc-tivity of rvice business (Sherman and Zhu 2006).
In the current book, we prent various DEA approaches that can be ud in iden-tifying best-practice frontier and further in performance evaluation and benchmark-ing. Other recommended readings include veral DEA handbooks such as Cooper et al. (2011a), Cook and Zhu (2014), and Zhu (2015).
1.3 P erformance Metrics Classified as Inputs
and Outputswait现在分词
DEA requires that performance measures or metrics be classified into inputs and outputs. Whether it is the rearcher, the practitioner or the student, the u of the DEA methodology gives ri to an important question before proceeding to a DEA analysis:
What are the outputs and inputs to be ud to characterize the performance of tho DMUs?
学前班拼音拼读As discusd in Cook et al. (2014), in the literature, DEA is generally introduced as a mathematical programming approach for measuring relative efficiencies of DMUs, when multiple inputs and multiple outputs are prent. While the concept of inputs and outputs is well understood, it is often the ca that rearchers/urs take the notion for granted, and little attention tends to be paid to insuring that the lected measures properly reflect the “process” under study. As a ca in point, the original DEA model of Charnes et al. (1978, 1981), involving the study of school districts in Texas, was developed in a ratio form of Outputs/Inputs, but the authors provide little in the way of rationalization in regard to appropriate variables (inputs and outputs) for studying student performance. This is not to imply that the variables ud were not appropriate for the problem at han
d, but rather it rves to i llustrate
