Nowadays our society pays more and more attending to the public presentation measuring and the rating activities of the organisations, such as infirmaries, establishments, bureaus, companies and so on, because the public presentation measuring can efficiently back up the populace and private determinations, the public presentation measuring has a spectrum of customary analyses. There are many assortments of methods and techniques for the public presentation measuring, such as Multi- Criteria Decision Analyse ( MCDA ) , Balanced scorecard and so on. However, one time multiple inputs and end products need to be taken into history, jobs and restrictions from traditional methods in mensurating productiveness or efficiency may originate. Organizations pressing call for a more holistic rating solution to avoid blemished appraisal.

DEA ( Data Envelopment Analysis ) has been widely used in measuring public presentation of many different sorts of entities engaged in different states, in different contexts and different activities. It is a nonparametric method and mathematical scheduling technique used in operations research and economic sciences for the appraisal of production frontiers. It has besides been demonstrated practically in some organisational units – infirmaries, Bankss, concern companies, even in universities. Nevertheless, DEA is named to be the most effectual method in public presentation measuring, when the organisation uses different inputs to bring forth multiple end products.

The purpose of this seminar thesis is to research a full position and model of organisational public presentation rating. Together with the theoretical foundations and historical development of public presentation methods, the basic mathematical theoretical accounts every bit good as the thought and utile package from DEA will be at the first bloom introduced in Chapter 2 In Chapter 3, a deeper penetrations of practical applications in public sector will be given. After that strengths and restrictions from DEA method will be discussed in Chapter 4. The last chapter will so be the decision.

## Performance measuring

## Introduction of public presentation measuring

In recent old ages has the alleged public presentation measuring experienced a turning importance in research and pattern of the concern direction. However, it is non in the literature clearly clarified what it means truly to merely under public presentation measuring, the present chapter is a conceptual Praezisierung and content particular. However it is clear is that, the public presentation will be fundamentally as more or less affectivity and efficiency understood.

The public presentation measuring and ist appraisal is non harmonized between Anglo-Saxon and Germany. For this ground, the following tabular array collected some different construct elucidation and its development alternatively of a conceptual model that will incorporate the indispensable features of the construct. The public presentation and the company used for their assessment public presentation measuring is non the Anglo-Saxon or German talking harmonized. For this ground, writers make do without even wholly a conceptual elucidation and development alternatively a conceptual model ( Framework ) that will incorporate the indispensable features of the public presentation construct.

Table 1 provides some selected readings of the construct of public presentation measuring and conveys an feeling of the scope of different performance-understandings in the literature.

## Author ( s )

## Understanding of the termperformance measuring

## Berliner/Brimson ( 1988 )

“ a¦‹aˆ¦a¦?performance measurement a¦‹aˆ¦a¦?measures concern and works public presentation in relation to the ends and aims developed in the planning procedure ; provides timely information for identifying and extinguishing activities that add no value ; and provides timely information on causal factors that may take to fabricating betterments. ”

## Mentzner/Konrad ( 1991 )

“ a¦‹aˆ¦a¦?performance measuring is an analysis of both effectivity and efficiency in carry throughing a given undertaking. All rating is in relation to how good a end is met. ”

## Verma ( 1992 )

“ Performance measuring is an indispensable portion of direction control in that it validates whether the consequences anticipated from planned action are realized. ”

## Zairi ( 1994 )

“ Performance Measurement ( PM ) ” has been described as the systematic assignment of Numberss to entities.

## Bredrup ( 1995 )

“ Performance Measurement is defined as the procedure of quantifying actions. However, features of actions in a strategic degree differ dramatically from operational actions. Performance Measurement will so be rather different for the different for the different actions. ”

## Lynch/Cross ( 1995 )

“ a¦‹aˆ¦a¦?Performance Measurement a¦‹aˆ¦a¦?describes the feedback or information on activities with regard to run intoing client outlooks and strategic aims a¦‹aˆ¦a¦?we are concerned with two simple inquiries: are maps sections, and squads within a concern procedure making the right thing a¦‹anda¦?are they making them good? ”

## Neely et Al. ( 1995 )

“ Performance Measurement can be defined as the procedure of quantifying the efficiency and effectivity of action. ”

## Sinclair/Zairi ( 1995b )

“ Entire quality-based public presentation measuring can be defined as the measuring of non-financial public presentation at all degrees within the organisation ( including persons, squads, procedures, sections and the organisation as a whole ) , with a position to the uninterrupted betterment of public presentation against organisational aims. ”

## Gleich/Haindl ( 1996 )

“ Im Kern handelt es sich beim Performance Measurement um lair Aufbau und Einsatz meist mehrerer quantifizierbarer Ma?gro?en verschiedenster Dimensionen a¦‹aˆ¦a¦?die zur Beurteilung der Effektivitat und Effizienz der Leistung und Leistungspotentiale unterschiedlichster Objekte im Unternehmen ( Organisationseinheiten unterschiedlicher Gro?en, Mitarbeiter, Prozesse ) herangezogen werden. ”

## Atkinson et Al. ( 1997 )

“ Performance Measurement focal points and coordinates the decision-making activities of the cognition workers to whom a company has delegated determination doing duty by planing, monitoring, and measuring coherent, comprehensive public presentation measures. “

## Ziegenbein ( 1998 )

“ Das Instrumentarium zur Messung und Verbesserung einzelner Messgro?en sowohl monetarere ALSs auch nicht-monetarer Art bzw. ganzer Messgro?enbundel wird gemeinhin unter der Bezeichnung Performance Measurement zusammengefasst. ”

## Neuhauser-Metternich/Witt ( 2000 )

“ Das Performance-Measuring ist eng Massachusetts Institute of Technology dem Gedanken des Benchmarking und der DEA verknupft und versucht, qualitative Kennzahlen zur Leistungsbeurteilung zu generieren. Es handelt sich dabei besides nicht um ein konventionelles Kennzahlensystem a¦‹aˆ¦a¦?sondern vielmehr um ein Kennzahlenspektrum zur Analyse des Leistungspotential. “

## Lohmann et Al. ( 2004 )

“ A public presentation Indicator ( PI ) is a variable that expresses quantitatively the effectivity or efficiency or both, of a portion of or a whole procedure, or system, against a given norm or mark. PM is the activity of mensurating public presentation utilizing PIs. “

Table 1: Selected Interpretations of Performance Measurement

As Table 1 showed, the facets and sentiment of the public presentation are different. From the above different public presentation objects and the construct, the most attacks are the quantification of “ effectivity ” and / or “ efficiency ” , which contains pecuniary and non-monetary aim. As discussed earlier Leong, et Al. have suggested that the fabrication undertaking, and therefore the cardinal dimensions of fabrication public presentation, can be defined in footings of quality, clip, monetary value ( cost ) , and flexibleness. Other writers take a different stance. Following their survey of public presentation measuring in the service sector, Fitzgerald et Al. suggest that there are two basic types of public presentation step in any organisation – those that relate to consequences ( fight, fiscal public presentation ) , and those that focus on the determiners of the consequences ( quality, flexibleness, resource use and invention ) . This suggests that it should be possible to construct a public presentation measuring model around the constructs of consequences and determiners. In theory and pattern, there are a assortment of public presentation measuring systems. The best known are: Balanced Scorecard, EFQM-Modell, Tableau de Bord, Data Envelopment Analysis, Skandia Navigator, Performance Pyramid, Performance Prism, Quantum Performance Measurement System, value-based direction, Operative Index public presentation measuring, Performance Risikomanagement.

## Problem-related demands

This subdivision deals with the derivation of fundamental demands, which should run into a method for meaningful usage in the public presentation measuring. Some of the demand is already mentioned explicitly or implicitly in above ; in add-on, the demands groups, single demands and matter-of-fact demands are systematic cataloged in the Table 2. Principle, it can be categorized as the figure of possible demands based on the undermentioned issues: ( a ) Can this method in rule solves the job? ( B ) To what extent by utilizing the related method can the public presentation measuring work complete? ( degree Celsius ) The method is executable, i.e. there is an appropriate balance between their use- ” disbursals ” and the ensuing knowledge- ” income ” ?

Problem-related demands are derived from the features by the character from the undertaking of mensurating public presentation. They differ from the other demands, which they must needfully be met, at the same clip leting the public presentation measurement-related and matter-of-fact demand a greater design freedom. The first chief demand is the comparing a set of alternate classs of action.

Since by a figure of possible options is to be achieved ( eg, increased client satisfaction and a low energy ingestion ) , the methods have the ability to reexamine the instance of multiple marks. Sing the equity in measuring a priori weight of the aims are non asked for.

The tabular array 2 shows the demands class, groups and single demands of public presentation measuring Methods.

Requirements ‘ class

Requirements groups

individualrequirements

Problem-related demands

Abilityto comparea setofalternative classs of action

Capacity forperformance measurementinmulti-objective

Ability tomeasureperformancewithouta prioriobjectiveweighting

Performance Measurementrelated demands

Measurement of targetcharacteristics

Suitabilityfor treating ofdata of anyinformationdegree

Suitabilityfor processingofdata of anyseverityscale

Suitabilityfor treating ofdata of anyinformationalbasis

Suitabilityfor processing, every bit good as limited and unlimitedcontinuousanddiscrete informations

Measuring theperformance dimensions

Suitabilityfor measuringpartial and totaleffectiveness

Suitabilityfor measuringpartial and totalefficiency

High information content

Fitness for theidentification of individualstrengths and failings

Fitness for theformulation of recommended actions

Pragmaticrequirements

required clip

Simpletype of informations needed

Small quantityof required informations

Practicability

conceptual support

Technical Support

Result ‘s quality

Sensitivity of the consequences

Stability of the consequences

Resultacceptance

Interpretability of the consequences

High degree of awarenessofmethods

Table 2: Requirements for Performance Measurement Methods

The public presentation is as ( comparative ) effectivity and efficiency comparable units understand in this paper, so it leads to the inquiry: with which method can the effectivity and efficiency are evaluated. So, to find the grade of the effectivity and efficiency of the mark are really necessary. For this ground, one of the public presentation measuring method- Data enclosure Analysis ( DEA ) will be introduced in the following chapter, the strengths and failing of the method will be showed in chapter 4.

## Theoretical foundations of DEA

Data Envelopment Analysis ( DEA ) is a comparatively new “ informations oriented ” attack, which is used for mensurating the public presentation of a set of equal entities, which are called Decision Making Unit of measurements ( DMUs ) , which convert multiple inputs into multiple end products.

The basic theoretical foundations of the DEA will be foremost introduced in the undermentioned subdivision. The history and development of DEA every bit good as relevant context are discussed in 2.1. Then in the undermentioned parts the more elaborate account about DEA-Method will be introduced.

## History and development

The combinations of the Input and end product of a house are usually calculated with a production map ( Output/Input ) in microeconomic production theory. The Production engineering frontier can be constructed, because utilizing such a map dice soap. end product, which can be achieved with any possible combination of inputs, can be showed. ( Seiford & A ; Thrall 1990 ) . About 30 old ages ago DEA are used to get the better ofing the job of house, which can ne’er detect all the possible input-output combinations with the rule in empirical applications. Based on the thoughts of Farrell ( 1957 ) , since the seminal work “ Measuring the efficiency of determination doing units ” by Charnes, Cooper & A ; Rhodes ( 1978 ) applies for the first clip additive scheduling to gauge an empirical production engineering frontier. However, earlier the process was in Germany used to gauge the fringy productiveness of R & A ; D and other factors of production ( Brockhoff 1970 ) . A batch of books and diary articles since so have been written on DEA and the application of DEA. DEA has non merely been used in comparing efficiency across organisations, but besides used to compare the efficiency across houses. The DEA-Model was formalized by Banker, Charnes and Cooper ( BCC ) ( 1984 ) , and was extended by Fare, Grosskopf and Lovell ( 1985 ) with including the decomposition of overall efficiency into steps of proficient and scale efficiency. The DEA-Method is deterministic and nonparametric. Therefore, since the seminal work by Farrel ( 1957 ) on “ mensurating the efficiency of determination doing units ” ‘ , there are several types theoretical accounts of the DEA have emerged, which are largely based on the CCR-Modell, at the same clip a farther development on the DEA is the BCC theoretical account, which point at the changing returns to scale-either changeless returns to scale ( CRS ) or variable returns to scale ( VRS ) . A good description of DEA can be found in Seiford and Thrall ( 1990 ) and Seiford ( 1996 ) , the chief development of DEA are besides in this clip.

## The basic theoretical accounts

## CCR theoretical account

This portion deals with one of the most basic and of import DEA-Models, the CCR theoretical account ( Charnes, Cooper and Rhodes in 1978. ) . In DEA, the organisation under survey is called a DMU ( Decision Making Unit ) . DMU are used to measure in footings of the abilities to change over inputs into end products, and to let for applications to a broad assortment of activities. The definition of DMU is instead loose and flexible to utilize. Generically a DMU is the entity, which is responsible for change overing inputs into end products and whose public presentations are to be evaluated, which such as supermarkets, section shops and Bankss, and widen to auto shapers, infirmaries, schools, public libraries and so on. To do certain a comparative comparing a set of DMUs is used to measure each other with each DMU holding a certain grade of managerial freedom in determination devising. For each DMU, we formed the practical input and end product by ( yet unknown ) weights ( ) and ( ) :

Then utilizing additive scheduling to find the weight and so as to maximise the ratio:

Because he optimum weights of different DMUs may besides different from each other. Therefore, each DMU is assigned a best set of weights, which in progress are derived from the informations alternatively of being fixed.

Suppose there are n DMUs: , , aˆ¦ , . and Some common input and end product points for each of these j= 1, aˆ¦ , n DMUs are selected. Suppose m input points and s end product points are selected. Let the input and end product informations for be ( ) and ( ) , severally. The input informations matrix Ten and the end product informations matrix Y can be arranged as follows,

The input informations matrix Ten

The end product informations matrix Y

m end product

Ns DMUs

weights

weights

s input

## 1 2 3 aˆ¦ J aˆ¦ N

## v1 1 x11 x12 x13 aˆ¦ x1j aˆ¦ x1n

## v2 2 x21 x22 x23 aˆ¦ x2j aˆ¦ x2n

## . . . . . . aˆ¦ .

## six. . . . . Xij aˆ¦ .

## . . . . . . aˆ¦ .

## vm m xm1 xm2 xm3 aˆ¦ xmj aˆ¦ xmn

## y11 y12 y13 aˆ¦ y1j aˆ¦ y1n 1 u1

## y21 y22 y23 aˆ¦ y2j aˆ¦ y2n 2 u2

## . . . . . aˆ¦ . .

## . . . . yrj aˆ¦ . . ur

## . . . . . aˆ¦ . .

## ys1 ys2 ys3 aˆ¦ ysj aˆ¦ ysn s us

where Ten is an ( thousand A- N ) matrix and Y an ( s A- N ) matrix.

The efficiency of each DMUs will be measured with the given informations, one time and therefore necessitate n optimisations, one for each to be evaluated. Let the to be evaluated on any test to designated as ( o ranges over 1, 2, aˆ¦ n. ) We solve the undermentioned fractional scheduling job to obtain values for the input “ weights ” ( ) ( one = 1, aˆ¦ , m ) and the end product “ weights ” ( ) ( r = 1, aˆ¦ , s ) as variables.

The restraint means that for every DMU the ratio of “ practical end product ” vs. “ practical input ” should non transcend 1.

Now the above fractional plan will be replaced by the undermentioned additive plan:

Input-oriented

Envelopment theoretical account

Subject to

Output-oriented

Envelopment theoretical account

Subject to

Table 3: the CCR theoretical account in input- and output-oriented versions, each in the signifier of a brace of double additive plans.

With the 2 of import theorems:

“ Theorem 1 The fractional plan ( FP ) is tantamount to linear plan ( LP ) ”

“ Theorem 2 ( Unit of measurements Invariance Theorem ) The optimum values of soap in ( 2.3 ) and ( 2.7 ) are independent of the units in which the inputs and end products are measured provided these units are the same for every DMU. ”

shows that ( LP ) can be solved by the simplex method of additive scheduling, which will be more easy calculated. “ is CCR-efficient if and there exists at least one optimum ( ) , with and. Otherwise, is CCR-inefficient. ”

## Other DEA-models

The input-oriented CCR-Modell is merely one of the of import DEA-Modell, behind the definition of DEA there are a exemplary household. In the literature the many different DEA-Modells will be frequently called “ Basic DEA-Models ” . Because there is no unvarying definition of it, below the position of Allen, is the undermentioned DEA-based theoretical accounts chiefly with four features: foremost, they represent mileposts in the development of the DEA ; Second, they are applied in the empirical surveies ;

Third, they can be comparatively easy to cipher ; and last but non least, they are non some specific ways of DEA, but merely different in the technique adopted and used by the efficiency measuring. .

These characteristics limit the figure of possible discrepancies of DEA. Table 5 contains a categorization of popular DEA theoretical accounts based on the standards “ efficiency step ” and “ engineering ” . The base theoretical accounts of the DEA are summarized holla.

## Technology

## One-dimensionality

## ( changeless returns to graduated table )

## Radial

## Input-oriented

CCR-I

## Output-oriented

CCR-O

## linear

## Input-oriented

## Output-oriented

## unoriented

ASS- CRS

Tabelle 4: classifikation common DEA-based theoretical accounts

## DEA Software

## Software

## Webseite

## Kommerzielle Software

DEA-Solver-Pro Version 6.0

www.saitech-inc.com

Frontier Analyst Version 4

www.banxia.com

KonSi DEA Analysis

www.dea-analysis.com

xlDEA 2.0

www.prodtools.com/Products.html

PIM DEAsoft-V2

www.deasoftware.co.uk

GAMS/DEA

www.gams.com

DEAFrontier

www.deafrontier.com

## Nicht-kommerzielle Software

DEAP Version 2.1

www.uq.edu.au/economics/cepa/coelli.html

Win4DEAP Version 1.1.2

www.umoncton.ca/desliem/dea/install.html

MDeap Version 0.2.1

www.umoncton.ca/desliem/dea/mdeap.html

EMS – Efficiency Measurement System Version 1.3

www.holger-scheel.de/ems/

DEA-Solver-LV

www.prodtools.com/Products.html

myDEA

www.mydea.org

Qhull

www.qhull.org

ideas

www.isye.gatech.edu/ideas

Dea Solver Online Version 1.2

www.dea.uni-hohenheim.de

D.E.A.O.S. – Data Envelopment Analysis Online Software

www.deaos.com

Table 5: Interpretations of selected package from DEA

As table 3, there is much different package in the purpose to cipher the DEA, and they are really helpful to measure the DMU efficiency.

## Application stairss of DEA

The rating procedure of the applications of DEA-methods can be summarized as the undermentioned stairss.

Determine the intent of measuring

DEA- Evaluation and Analysis

Chose DMUs

Constitution of the input and end product system

Chose DEA -Model

Adjusting of the input and end product System

Satisfied?

A Evaluation Analysis Conclusiones

## Nitrogen

## Yttrium

Fig. 1 Application stairss for DEA

The above figure shows the application stairss for DEA-Method. For case, the measuring intent is to compare a set of Bankss, and foremost the Bankss have multiple-input and multiple-output features, so the DEA-method can be used in this rating. And so the rating procedure can be summarized as: take the right DMUs, and set up the input- and end product system, following measure make a DEA-Model and make the rating and analysis, when the consequence is all right, so comes the conclusions-the efficiency of the Bankss ; when non, travel back and make some adjusting in the input- and end product system so analyze once more.

## Diskussion

## Strengths of DEA

Compared to most signifiers of such as stochastic frontier analysis ( SFA ) , the DEA has many advantages, but its chief attractive force, is that it does non count if the manufacturers are different because no functional signifiers are imposed.

Drug enforcement administration can at the same clip handle multiple inputs and multiple end products. DEA does n’t necessitate associating inputs to end products, because as quantitative and qualitative standards can be processed. What ‘s more, the comparings are straight against equals and Inputs and end products can hold really different units. Credence of the DEA consequences in pattern is high. No DMU with another different weighting can be better calculated by DEA. Efficiency comparing is multidimensional.

## Restriction of DEA

Harmonizing to the features of DEA-Method, so we shed visible radiation on some of their comparative failings.

DEA uses info on input and end product measures, and as such it DEA does non mensurate “ absolute ” efficiency, can merely turn to the issue of proficient efficiency. DEA is nonparametric but deterministic. The compared DMUs are practical. At the same clip, with this method there is merely implicative map but no analysis of causes. Statistical trials are non applicable and big jobs can be computationally intensive. And what ‘s more, the mathematic is really complex in DEA, non easy to utilize ; Measurement mistake can do important jobs. The measuring consequence is strongly dependent of the choice of the DMUs and the input and end product sizes. Last but non least there is besides no quality designation.

## Decision

Data Envelopment Analysis ( DEA ) has been recognized as a valuable analytical research instrument and a practical determination support tool. DEA has been credited for non necessitating a complete specification for the functional signifier of the production frontier nor the distribution of inefficient divergences from the frontier. Rather, DEA requires general production and distribution premises merely. However, if those premises are excessively weak, inefficiency degrees may be consistently underestimated in little samples. In add-on, erroneous premises may do incompatibility with a prejudice over the frontier. Therefore, the ability to change, trial and choice production premises is indispensable in carry oning DEA-based research. However, the DEA theoretical accounts presently available offer a limited assortment of alternate production premises merely. And because none of the steps methods dominates all others on all dimensions, we conclude that the pick of appropriate measuring method should be suited to the inquiry addressed in each peculiar survey.