A new decision support system for performance measurement using combined fuzzy TOPSIS/DEA approach

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A new decision support system forperformance measurement usingcombined fuzzy TOPSIS/DEA approachMithat Zeydan a & Cüneyt Çolpan ba Department of Industrial Engineering, Engineering Faculty ,Erciyes University , Kayseri, Turkeyb Production Planning, Turkish 2nd Air Supply and MaintenanceCenter Command , Kayseri, TurkeyPublished online: 15 May 2009.

To cite this article: Mithat Zeydan & Cüneyt Çolpan (2009) A new decision support system forperformance measurement using combined fuzzy TOPSIS/DEA approach, International Journal ofProduction Research, 47:15, 4327-4349, DOI: 10.1080/00207540802662870

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International Journal of Production ResearchVol. 47, No. 15, 1 August 2009, 4327–4349

A new decision support system for performance measurement using

combined fuzzy TOPSIS/DEA approach

Mithat Zeydana* and Cuneyt Colpanb

aDepartment of Industrial Engineering, Engineering Faculty, Erciyes University,Kayseri, Turkey; bProduction Planning, Turkish 2nd Air Supply and

Maintenance Center Command, Kayseri, Turkey

(Received 12 April 2008; final version received 1 December 2008)

It is apparent that there is a need for integrated criteria in the performancemeasurement of modern organisations when dealing with the performancemeasurement of manufacturing businesses. This paper addresses this issue in thecontext of measuring the performance of the 2nd Air Supply and MaintenanceCenter Command manufacturing/maintenance jobshops of Turkey by usinga new framework which combines fuzzy TOPSIS (technique for order preferenceby similarity to ideal solution) for measuring qualitative performance withDEA (data envelopment analysis) for measuring quantitative performance.This proposed approach provides a comprehensive measure of performanceincorporating both quantitative and qualitative attributes, which in general reflectefficiency and effectiveness of the manufacturing jobshops respectively.

Keywords: fuzzy TOPSIS; DEA; MCDM; performance measurement

1. Introduction

The choice of performance indicators has a major impact on the operation of anyorganisation and the direction it takes for the future. Thus, knowledge of the factors whichdrive the behaviour of the organisation and influence its performance becomes crucial(Audit Commission for Local Authorities 2000). The performance indicators could be, ingeneral, considered as measures of efficiency and effectiveness. It is worth expanding hereon these two words which sound similar but are often used interchangeably albeitmistakenly. Effectiveness is a measure of obtaining desired results such as the right productwith expected quality. Efficiency is defined as the ratio of output to input as in dataenvelopment analysis (DEA) (Meredith 1992, Vonderembse and White 1995). In otherwords, effectiveness is doing the right things, and efficiency is doing things right(Chase and Aquilano 1992). Hence, the measure of effectiveness is a strategic parameterwhich must be taken into consideration in long-term decision-making, whereas themeasure of efficiency is an operational parameter for short-term decision-making.An organisation or a decision making unit is effective as well as efficient to the degreeto which it achieves its goals in terms of the right output produced in the right way.According to Neely et al. (1995), the performance measurement is defined as the process ofquantifying the efficiency and effectiveness of an action and the performance measure is

*Corresponding author. Email: [email protected]

ISSN 0020–7543 print/ISSN 1366–588X online

� 2009 Taylor & Francis

DOI: 10.1080/00207540802662870

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defined as a metric used to quantify the efficiency and/or the effectiveness of an action.Even though the above concept of combining effectiveness and efficiency as a measure ofthe performance of an organisation is appealing, some researchers (Ammons 1996,Berman 1998) are of the opinion that only quantitative measurements provide reliablemeasures of the performance of a business. The latter view is more suitable toenvironments in which the inputs and outputs are quantitative measures. However,qualitative measures are becoming more important indicators of how an organisation’sperformance is perceived by its customers. Hence, performance criteria which includequalitative measures provide a richer and multi dimensional picture of performancereflecting the effectiveness for any organisation and in particular for manufacturing sectororganisations. In recent years, this is reflected by the fact that performance evaluationin many organisations has changed to be based on customer satisfaction as an outcome.At the other end of the spectrum, some researchers suggest that effectiveness based onqualitative measures of the firm is a better performance indicator (Hershey and Blanchard1969). This view could be considered to be biased towards qualitative measures excessivelyand does not give sufficient credit to equally important quantitative measures inperformance evaluation. Any organisation which aims to be a world class organisationshould consider both effectiveness and efficiency in its performance measure and, hence,should be based on both quantitative and qualitative measures (Sahay 2005). Real-worlddecision-making problems, both in manufacturing and service systems, cannot beevaluated based on only a single performance measurement criterion as they are toocomplex and difficult to be defined completely in terms of the optimum decision.A unidimensional approach in recognition of real systems cannot provide and supplya solution to measure and evaluate, even it can result in unrealistic decisions. Thus,MCDM (multiple criteria decision making) methods have been used for efficientmeasurement and evaluation in systems (Triantaphyllou 2000). Generally, the basicsteps of MCDM methods are as follows: establishing the system evaluation criteria forachieving the goals; generating alternatives; assessing alternatives in terms of criteria;applying a multi criteria decision making method; determining and ordering thealternatives from the best (optimal) to the worst; and finally, if this solution isunacceptable, collecting the new data and repeating all steps. MCDM which isa qualitative performance measurement and evaluation approach needs the criteriaconsistency with the goals of systems and decision makers that will be able to give the trueinformation. Many MCDM methods have been defined in the literature (Hwang andYoon 1981). The ratings and importance weights of the criteria in classical MCDMtechniques are assumed to be known precisely.

In the work presented in this paper, two performance measurement methodologies,namely fuzzy TOPSIS and DEA both based on quantitative as well as qualitative measuresare used in combination for the performance measurement and evaluation of the 2nd AirSupply and Maintenance Center Command manufacturing jobshops in Turkey. This studyalso has significance in that it provides a new framework for determining the performanceof manufacturing systems in general. Such a framework is essential to reach some strategicdecisions concerning manufacturing provisions. Generally, there are two approaches forthe measurement of performance. One approach involves using parametric methods inwhich the production function is assumed to be known or estimated statistically – e.g.,statistical comparison methods such as stochastic frontier analysis, ordinary least squares,etc. The other approach is to use non-parametric methods in which the model isempirically built from observed inputs and outputs – e.g., output/input ratios, work

4328 M. Zeydan and C. Colpan

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measurement methods, DEA, AHP (analytic hierarchy process), quality plus techniques,

practice variations studies, performance measurement matrix, activity based costing,

balanced-scored card, performance prism, performance pyramid, results and determinants

structure, strategic measurement analysis and reporting technique, performance measure-

ment questionnaire, theory of constraints, Malcolm Baldridge criteria for performance

excellence: these are the most frequently used performance measurement methods

(McLaughlin and Coffey 1990, Ghalayani and Noble 1996). Gomes et al. (2004) gives

more detailed information on parametric and non-parametric approaches. Recently, Simar

and Wilson (2008) analysed the statistical properties of DEA and FDH (free disposal hull)by using bootstrap methods but there exists some open issues and problems, this method

is suitable for theoreticians but not for practitioners. In this work, a hybrid tool which

combines two non-parametric methods namely the fuzzy TOPSIS and DEA is used to

identify which decision making units (jobshops) are the best.

2. Methodology and literature survey

Hwang and Yoon (1981) proposed the TOPSIS method which is a multiple criteria method

to identify a solution from a finite set of points. The basic principle is that the chosen

points should have the ‘shortest’ distance from the positive ideal and the ‘farthest’ distance

from the negative ideal solution. There have been a wide variety of studies related with

many different areas on the TOPSIS method in the literature (Parkan and Wu 1999, Deng

et al. 2000, Jee and Kang 2000). Hence, the TOPSIS method is not considered here.

Instead of taking into consideration the TOPSIS method, we prefer to focus on the fuzzy

TOPSIS method which is one of the topics of this paper.Fuzzy logic which is also known as multivalued logic is a method used for modelling

the imprecise reasoning of human and dynamic systems for defining and converting into

a specified value. It has been applied in various different fields such as home appliances,

robotics, automation, image processing, space, defence applications since Zadeh (1965)

introduced this technique with his paper. Defining the real life service and manufacturing

systems using crisp values (bi-valued logic) is not reasonable and appropriate as humanjudgement and behaviour have very complicated structures and cannot be estimated in

advance with an exact numerical value. The fuzzy TOPSIS method is very suitable for

solving the group decision making problem under a fuzzy environment.In this new methodology, the qualitative and quantitative (in other words intangible

and tangible) data relating to the characteristics of processes are collected and the

qualitative data which cannot be directly input into the DEA process is separated to be

input into fuzzy the TOPSIS analysis.The fuzzy TOPSIS analysis transforms this qualitative data into some equivalent

quantitative measure. This quantitative measure is used in the DEA as one of the

outputs along with other quantitative data (inputs and outputs) for final evaluation

and measurement. The manufacturing jobshops which achieve an efficiency value of 1 in

the DEA result are considered as ‘efficient’ jobshops. All DEA were evaluated using

the Efficiency Measurement System (EMS) version 1.3 software package and itssuper efficiency choice for ordering among themselves the most efficient jobshops

(Scheel 2000). EMS software has been used in the Andersen and Petersen (AP) super

efficiency model. Even though several discussions regarding the application of the

AP model have been made in the literature (Banker and Chang 2006, Li et al. 2007),

International Journal of Production Research 4329

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some authors continue to use the AP super efficiency model for analysing the case studies

in their papers (Jablonsky 2007, Adler and Raveh 2008, Li et al. 2008). We also use the AP

super efficiency model for ranking the efficient units.There have been limited combined MCDM models in the literature. Some of them

are Yang and Kuo (2003), Bhattacharya et al. (2005), Yurdakul and _Ic (2005), and

Rao (2008). The new methodology is shown in Figure 1. Since Chen (2000) proposed the

fuzzy TOPSIS multiple attribute decision making method, many authors have provided

very elegant and understandable discourses of fuzzy TOPSIS (Chu 2002, Chu and Lin

2003, Chen et al. 2006). Hence, repetitions of the details of these techniques are not

thought to be necessary. In this work, these techniques have been combined in a different

way leading to a new methodology. Even though these techniques work in their usual

normal mode in this new methodology, the structure of their interactions achieves the aim

of producing a performance measure which combines both efficiency and effectiveness of

decision making units. In Section 4, this new methodology will be applied to a real case

study together with the theory of fuzzy TOPSIS and DEA for solving a business

performance measurement and evaluation problem.In the literature, there have been various applications evaluating the performance of

some armies in the world using DEA. Some of them are Charnes et al. (1985), Bowlin

(1987), Roll et al. (1989), Clarke (1992), and Sun (2004). There has not been any study in

the literature about a combined fuzzy TOPSIS/DEA approach before. When the literature

is widely looked through, the qualitative MCDM techniques generally used are focused on

D ec is io n

T ra n s fo rm ed Q u a li ta tiv e D a ta (u sed a s a n o u tp u t d a ta in D E A )

In p u t an d O u tp u t D a ta

D a ta C o llec tio n

F u z z y T O P S IS a n a lys is fo r q u a lita tiv e d a ta ev a lu a tion

Q u an ti ta tiv e D a ta

D E A a n a lys is fo r f in a l ev a lu a tio n

Figure 1. New methodology.


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both TOPSIS and AHP. There have been some advantages and disadvantages when

compared with each other. But, mostly, we think that there have been advantages of

TOPSIS more than those of AHP. Some of these main reasons summarised theoretically

and practically related with this study are defined as follows:

. AHP regarding rank reversals is uniformly worse than TOPSIS.

. According to the AHP methodology, there is not any interaction among the

criteria whereas it is not important for TOPSIS whether there is any interaction

among criteria or not.. TOPSIS method is intuitive, easy to understand and to implement.. TOPSIS is simple as well as it yields a highly reliable preference order.. As the number of employees working in some jobshops run into approximately

50 people, it causes difficulty in calculating the AHP consistency index.

Compared with other classical MCDM methods, the effectiveness of the system

using fuzzy TOPSIS is about 23% higher than AHP, 17% higher than FO (fuzzy

optimum), 11% higher than TOPSIS and 10% higher than the GRA (gray relation

analysis) (Wang et al. 2007). Therefore, by approximately 12%, TOPSIS is more effective

than AHP. In our study, the evaluation of personnel employment record form with fuzzy

TOPSIS having linguistic variables is easier than fuzzy AHP since the evaluation process

takes more time. These considerations are the motivation of why this algorithm is

appropriate. Because of the above results, we prefer using fuzzy TOPSIS in our

application.

3. The structure and identification of the Turkish Air Forces manufacturing system

The 2nd Air Supply and Maintenance Center Command jobshops is the one of three air

supply and maintenance centres in Turkey that realise logistics support activities of all

troops of the Turkish Air Force Command. Air supply and maintenance centres realise

service and material productions which are needed through manufacturing units

established from within itself. Capacity planning is performed depending on basic

weapon systems by assessing current capacity with the schedule prepared by the air supply

and maintenance centres annually. The manufacturing and maintenance requirements of

the Air Forces Command are delivered to defined units after realising the quarterly

production schedule. There are 28 jobshops performing the production schedule in the 2nd

Air Supply and Maintenance Center Command. In this application, the performance of

employees working in the Turkish 2nd Air Supply and Maintenance Center Command

jobshops is evaluated by a jobshop supervisor and a manager in terms of decision criteria

for the years 2005 and 2006. In performance evaluation, each qualification of employees in

the performance evaluation form used in the jobshops is considered as a decision criterion

and the performance of jobshops is evaluated based on these decision criteria. There are

many qualitative factors (indicators) that affect the jobshop performance. Some of them

are design conformity, purchasing policy effectiveness, tool and model development, new

material and machine selections, technological effectiveness, etc. In our study, we use

indicators related with personnel management functionality since we think these indicators

are more important than the other factors for qualitative evaluation of jobshops. In this

context, qualitative factors related with personnel management consist of 10 performance

evaluation criteria defined from C1 to C10 in jobshops as follows: C1� occupational


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knowledge and capability; C2� expeditious working, and the usage of working time;C3� the usage and appraisal of material and the protection and the maintenance ofmachines, tools, equipment; C4� the capability of self-education and teaching, self-development, perception; C5� enthusiasm and performing the job very well; C6� obeyingorders and instructions, abide by occupational health and safety principles; C7� attitudeand behaviour toward supervisor and superordinate; C8� attitude and collaborationfor his/her environement and business friends; C9� adopting responsibility; andC10� outward appearance.

The supervisor of each jobshop and five managers who are responsible for the 28jobshops are the decision makers. The supervisor of each jobshop is responsible forevaluating the performance of employees in the jobshop. A team of five people consistingof jobshop managers are responsible for evaluating the performances of employees anddetermining the weights of the decision criteria in jobshops. The supervisor of eachjobshop and managers found the performance of each jobshop by performingperformance evaluation of employees working in jobshops, separately. Firstly, thesupervisor of each jobshop reached the performance value of the jobshop by taking theaverage of performance values of employees working in the jobshop based on decisioncriteria. In the same way, managers reached the performance value of the jobshop with theaverage of performance values of employees working in the jobshop based on decisioncriteria. Real jobshop performance was obtained by taking the average of performanceevaluation values of the jobshop supervisor and managers. Until now, there has been nosystematic study assessing the performance of these jobshops as multidimensional in thisregion as is the case for every other region in Turkey. The method proposed here isexpected to serve at least as an initial framework for the performance measurementand evaluation. This work aims to establish a robust framework for measuring theperformance of manufacturing sector institutions by measuring accurately and reliably theperformance of these jobshops through a different hybrid methodology combining fuzzyTOPSIS and DEA. The fuzzy TOPSIS analysis attempts to incorporate vital qualitativeattributes in performance analysis. As mentioned in the methodology section, this newmethodology uses fuzzy TOPSIS at the front end to convert qualitative attributes intoa quantitative measure as another output which is fed into a DEA model along with otherquantitative inputs and outputs. The data relevant to these jobshops for the DEA and thefuzzy TOPSIS was collected from the 2nd Air Supply and Maintenance Center Commandrecords in the region.

In Table 1, the real input and output definitions are given as related with the inputs andoutputs used in the DEA and the combined fuzzy TOPSIS/DEA models. The first input(I1) variable means the number of personel working in the jobshop. The second input (I2)is the operational cost per man-hour. The first output (O1) shows the efficiency use ofworker resource. The second output (O2) can be obtained with the unworked man-hoursdivided by worked man-hours and this statement is extracted by 1. The third output (O3)is evaluated with some criteria such as plant, machine/equipment, documentation,education. The combined fuzzy TOPSIS/DEA performance analysis is performed andapplied by adding as a fourth output called satisfaction criteria (O4) which determines theperformance of jobshops to three output variables of DEA as a result of fuzzy TOPSISanalysis based on 10 decision criteria (C1 to C10).

The DEA has been used as a prime method of measuring the performance of jobshopsin the existing literature and hence could be a benchmark for assessing the efficiency of thework presented here. It is used to determine the relative efficiency of these jobshops over


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two years, namely 2005 and 2006. The traditional interpretation of these DEA resultswould help to understand the proposed method better. It is well known that the DEA findsa performance envelope which gives the relative efficiency of different organisations itis analysing. We use equal weighting of input-output variables in our model whileperforming DEA. Traditionally, any unit (organisation) which has a score of 1 isconsidered to be efficient in comparison to its compatriots. Consequently, any unit whichhas a score of less than 1 is considered inefficient. When a unit is inefficient, for examplewith an efficiency score of 0.95 it could be interpreted that an efficient unit could obtain atleast this level of output (0.95) with only 95% of input resources which the inefficient unitis using. In this study, firstly, after performing the fuzzy TOPSIS analysis for the years of2005 and 2006, this variable value obtained as a result of fuzzy TOPSIS analysis has beenused in DEA-BCC (Banker-Charnes-Cooper) output oriented model as an output calledsatisfaction ratio.

4. Fuzzy TOPSIS method and its application

In the present study, we use triangular fuzzy numbers for evaluating alternative ratingsand criteria weights. The importance weights of various criteria and the ratings ofqualitative criteria are considered as linguistic variables. These linguistic variables,importance weights and ratings, can be expressed in positive triangular fuzzy numbers asshown in Tables 2 and 3, respectively. The weights of employees’ performances evaluationcriteria given in Table 2 and evaluation ratings of employees’ performances evaluationgiven in Table 3 are quantified by using linguistic values. Ten decision criteria based on thelinguistic variables in Table 2 are weighted by five managers. Also, performance evaluationof personnel is performed by jobshop supervisors and managers based on the linguisticvariables in Table 3. The assessments carried out by using linguistic variables are given asa membership function by transforming fuzzy triangular numbers. For instance, if somemanager evaluates any decision criterion as ‘very high’, the membership function is definedas (0.9, 1, 1) and it is transformed into a fuzzy triangular number. The decision makers use

Table 1. Input and output variables for DEA and combined fuzzy TOPSIS/DEA model.

DEA model Fuzzy TOPSIS/DEA model

Input variables Output variables Input variables Output variables

I1 – The number of personel O1 – Completionratio ofoperations atthe right time

I1 – The numberof personnel

O1 – Completionratio ofoperations atthe right time

I2 – Operation unit cost O2 – Labourcapacity ratioused

I2 – Operationunit cost

O2 – Labourcapacity ratioused

O3 – Qualityadequacy scoreof jobshop

O3 – Qualityadequacy scoreof jobshop

O4 – Satisfactionratio


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the linguistic weighting variables as shown in Table 4 to assess the importance of thecriteria and then 10 decision criteria were evaluated by five managers and are presentedin Table 5. The performance of employees are evaluated by jobshop supervisors andmanagers based on the qualitative attributes (criteria) and reached the jobshopperformance, as an example, for jobshop A9 given in Table 6. This condition is thesame as the performance of jobshops.

Table 2. Linguistic variables forweight of each criterion (used bymanagers of jobshops).

Very high (VH) (0.9, 1, 1)High (H) (0.7, 0.9, 1)Medium high (MH) (0.5, 0.7, 0.9)Medium (M) (0.3, 0.5, 0.7)Medium low (ML) (0.1, 0.3, 0.5)Low (L) (0, 0.1, 0.3)Very low (VL) (0, 0, 0.1)

Table 3. Linguistic variables for theratings (used by managers and super-visors of jobshops).

Very good (VG) (9, 10, 10)Good (G) (7, 9, 10)Medium good (MG) (5, 7, 9)Fair (F) (3, 5, 7)Medium poor (MP) (1, 3, 5)Poor (P) (0, 1, 3)Very poor(VP) (0, 0, 1)

Table 4. Decision matrix using fuzzy linguistic variables.

Decision criteria DM1 DM2 DM3 DM4 DM5

C1 Occupational knowledge and capability VH H H MH HC2 Expeditious working, and the usage of working time H VH VH MH HC3 The usage and appraisal of material and the protection and

the maintenance of machines, tools, equipmentH MH H ML M

C4 The capability of self-education and teaching,self-development, perception

VH VH VH VH VH

C5 Enthusiasm and performing the job very well H H VH H VHC6 Obeying orders and instructions, abide by occupational

health and safety principlesH MH VH MH ML

C7 Attitude and behaviour toward supervisor and superordinate MH M H ML HC8 Attitude and collaboration for his/her environment

and business friendsMH MH H M H

C9 Adopting responsibility H VH H H VHC10 Outward appearance L ML MH L M


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Generally, the fuzzy TOPSIS procedure can be used in the following steps as suggestedby Chen (2000). The steps of the new methodology fuzzy TOPSIS are as follows:

Step 1: The importance weight of the decision criteria and the ratings for jobshopperformance are calculated using Equations (1) and (2), respectively:

~wj ¼1

K~w1j ðþÞ ~w

2j ðþÞ � � � ðþÞ ~w

Kj

h ið1Þ

~xij ¼1

K~x1ijðþÞ ~x

2ijðþÞ � � � ðþÞ ~x

Kij

h i: ð2Þ

~wKj and ~xKij are the importance weight and the rating of the Kth decision maker,

respectively. ~wj is the weight of criterion Cj and is a fuzzy number. ~xij is the rating ofjobshop Ai related with criterion Cj and is a fuzzy number. C1, . . . , C10 are decision criteriaevaluated by five managers with which jobshop performance is measured. A1, . . . , A28 arejobshops among which decision makers (supervisors and managers) have to choose. Fuzzyattribute weights are calculated for each decision criteria in Table 5. For instance, fuzzyattribute weight for the first decision criteria evaluated by five managers is calculatedas follows:

~w1 ¼ð0:9, 1, 1Þ þ ð0:7, 0:9, 1Þ þ ð0:7, 0:9, 1Þ þ ð0:5, 0:7, 0:9Þ þ ð0:7, 0:9, 1Þ

5

¼ ð0:70, 0:88, 0:98Þ:

The jobshop supervisor and managers separately use the linguistic rating variables givenin Table 3 for the evaluation of the jobshop employees’ performance. The supervisor ofJobshop A9 evaluated the performance of jobshop employees as linguistic and the averageof linguistic performance values of jobshop employees was taken by transformingtriangular fuzzy numbers based on decision criteria. Jobshop performance values ofmanagers based on decision criteria are given as the triangular fuzzy number in Table 6for jobshop A9 by taking the average. The real jobshop performance was obtained bytaking the average of these two values (performance values of managers and supervisor).In other words, employees working in the jobshops are rated for assessing the jobshops.The linguistic performance evaluation results are converted into symmetric triangular

Table 5. Fuzzy attribute weights.

Decision criterion Weights

C1 (0.70, 0.88, 0.98)C2 (0.74, 0.90, 0.98)C3 (0.46, 0.66, 0.82)C4 (0.90, 1.00, 1.00)C5 (0.78, 0.94, 1.00)C6 (0.54, 0.72, 0.86)C7 (0.46, 0.66, 0.82)C8 (0.54, 0.74, 0.90)C9 (0.78, 0.94, 1.00)C10 (0.18, 0.34, 0.54)


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Table

6.Thefinalaggregatedresultsobtained

from

ratingsgiven

byjobshopsupervisors

andmanagers.

Perform

ance

evaluationresultsperform

edby

jobshopsupervisorofjobshopA

9em

ployees

Perform

ance

evaluation

averages

perform

edbyjobshopmanager

ofjobshopA

9em

ployees

Perform

ance

evaluation

averages

ofjobshop

A9(jobshopA

9

supervisorþjobshop

A9manager/2)

Decision

criterion

P1

P2

P3

P4

P5

P6

Averageof

jobshop

supervisor

C1

GG

GG

GVG

(7.33,9.17,10.00)

(7.72,9.20,9.79)

(7.53,9.18,9.89)

C2

MG

GVG

GG

VG

(7.33,9.00,9.83)

(7.64,9.18,9.83)

(7.49,9.09,9.83)

C3

GG

GG

GVG

(7.33,9.17,10.00)

(8.22,9.52,9.87)

(7.78,9.34,9.93)

C4

FMG

GG

VG

VG

(6.67,8.33,9.33)

(7.88,9.29,9.80)

(7.27,8.81,9.57)

C5

GG

GG

GVG

(7.33,9.17,10.00)

(7.97,9.47,9.98)

(7.65,9.32,9.99)

C6

GG

GG

GG

(7.00,9.00,10.00)

(7.78,9.33,9.92)

(7.39,9.17,9.96)

C7

VG

GG

GG

VG

(7.67,9.33,10.00)

(8.16,9.54,9.94)

(7.91,9.44,9.97)

C8

GG

FF

GVG

(6.67,8.50,9.67)

(6.97,8.60,9.25)

(6.82,8.55,9.46)

C9

FF

GF

FVG

(6.00,7.83,9.33)

(6.28,7.81,8.45)

(6.14,7.82,8.89)

C10

GG

GG

GVG

(7.12,8.89,9.98)

(8.10,9.70,9.99)

(7.65,9.32,9.99)


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fuzzy numbers to construct the fuzzy decision matrix as shown in Table 6. For instance,

jobshop A9 rating value based on the decision criteria C1 is calculated as follows:

~x91 ¼ð7:33, 9:17, 10:00Þ þ ð7:72, 9:20, 9:79Þ

2

¼ ð7:53, 9:18, 9:89Þ:

Final aggregated results for the jobshop A9 are calculated and presented in Table 6.

Fuzzy decision matrix for the year 2005 is calculated and shown in Table 7 based on

linguistic variables for ratings in Table 3.

Step 2: It is possible to obtain the normalised fuzzy decision matrix denoted by R:

~R ¼ ~rij� �

m�n, ð3Þ

Let B and C be the set of benefit criteria and set of cost criteria, respectively, then:

~rij ¼aijc�

j

,bijc�

j

,cijc�

j

!, j 2 B; ð4Þ

c�

j ¼ maxi

cij, if j 2 B; ð5Þ

~rij ¼a�jcij

,a�jbij

,a�jaij

� �, j 2 C; ð6Þ

a�j ¼ mini

aij, if j 2 C: ð7Þ

The normalised fuzzy decision matrix is constructed using Equation (3) as shown

in Table 8. For instance, it is calculated as follows for ~r11 and ~r31:

~r11 ¼ ð0:90, 1:00, 1:00Þ

~r31 ¼ ð0:65, 0:80, 0:90Þ:

Step 3: The weighted normalised fuzzy decision matrix is constructed using Equation (8)

as shown in Table 9:

~V ¼ ~vij� �

m�n, i ¼ 1, 2, . . . ,m,

j ¼ 1, 2, . . . , n,ð8Þ

where ~Vij ¼ ~rijð�Þ ~wj. For instance, it is calculated for ~V11 and ~V14 as follows:

~V11 ¼ ~r11ð�Þ ~w1 ¼ ð0:90, 1:00, 1:00Þð�Þð0:70, 0:88, 0:98Þ

¼ ð0:63, 0:88, 0:98Þ

~V14 ¼ ~r14ð�Þ ~w4 ¼ ð0:80, 0:95, 1:00Þð�Þð0:90, 1:00, 1:00Þ

¼ ð0:72, 0:95, 1:00Þ:


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Table

7.Fuzzydecisionmatrix

fortheyear2005.


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Table

8.Norm

alisedfuzzydecisionmatrix

fortheyear2005.


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Table

9.Fuzzy-w

eighteddecisionmatrix

fortheyear2005.


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Step 4: Fuzzy positive-ideal solution (FPIS, A*) and fuzzy negative-ideal solution

(FNIS, A�) are defined as:

A� ¼ ð1, 1, 1Þ; ð1, 1, 1Þ; ð1, 1, 1Þ; ð1, 1, 1Þ; ð1, 1, 1Þ½ �

A� ¼ ð0, 0, 0Þ; ð0, 0, 0Þ; ð0, 0, 0Þ; ð0, 0, 0Þ; ð0, 0, 0Þ½ �:

The distances of each candidate from FPIS and FNIS are calculated, respectively, using

Equation (9). As defined in the literature (Chen 2000), the vertex method is an easy-

effective way to apply and calculate the distance between two triangular fuzzy numbers

if the membership function is linear. The distance of each alternative Ai (i¼ 1, 2, . . . ,m)

from A* and A� can be calculated as:

d�i ¼Xnj¼1

d ~vij, ~v�j

� �, i ¼ 1, 2, . . . ,m

d�i ¼Xnj¼1

d ~vij, ~v�j

� �, i ¼ 1, 2, . . . ,m:

ð9Þ

For instance, d�1 and d�1 are calculated for jobshop A1 in the year 2005 as follows:

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið1� 0:63Þ2 þ ð1� 0:88Þ2 þ ð1� 0:98Þ2

3

s¼ 0:2249ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ð1� 0:14Þ2 þ ð1� 0:32Þ2 þ ð1� 0:54Þ2

3

s¼ 0:6864

9>>>>>=>>>>>;d�1 ¼ 3:2296

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið0� 0:63Þ2 þ ð0� 0:88Þ2 þ ð0� 0:98Þ2

3

s¼ 0:8480ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ð0� 0:14Þ2 þ ð0� 0:32Þ2 þ ð0� 0:54Þ2

3

s¼ 0:3712

9>>>>>=>>>>>;d�1 ¼ 7:4208:

Step 5: According to Equation (10), the closeness coefficient is calculated for each

candidate as:

CCi ¼d�i

d�i þ d�i, i ¼ 1, 2, . . . ,m: ð10Þ

Some results related with similarity coefficient for jobshop 1 and jobshop 2 respectively are

given using Equation (10) as follows:

CC1 ¼7:4208

3:2296þ 7:4208¼ 0:6968

CC2 ¼7:2205

3:4898þ 7:2205¼ 0:6742:


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The ranking order of the 28 jobshops based on closeness coefficients is shown inTable 10. At the end of this process, performance values for the years 2005 and 2006 asa fourth output variable are obtained from Table 10. After the evaluation of fuzzyTOPSIS, the performance of jobshops obtained as quantitative is evaluated with DEA astwo input and four output variables.

5. Data envelopment analysis of the 2nd Air Supply and Maintenance Center Command

jobshops

In this stage, jobshop performance values obtained as a result of fuzzy TOPSIS analysisare considered as the fourth output variable O4 (satisfaction criteria). Input-output valuescollected from the manufacturing and quality records are given in Table 11.

Table 10. The distances from fuzzy negative (d �i ) and positive ideal solution (d �i ) for 2005 and 2006.

2005 2006 2005 2006

d �i d �i d �i d �i

Jobshopscoefficiency

Similaritycoefficient Rank

Similaritycoefficient Rank

A1 3.2296 7.4208 3.5915 7.1011 CC1 0.6968 2 0.6641 11A2 3.4898 7.2205 3.8349 6.9368 CC2 0.6742 9 0.6440 16A3 3.9076 6.7891 3.2299 7.4192 CC3 0.6347 23 0.6967 2A4 3.3723 7.2933 3.2194 7.4248 CC4 0.6838 5 0.6975 1A5 3.4893 7.1848 3.6580 6.9413 CC5 0.6731 10 0.6549 14A6 3.7694 6.9868 3.9729 6.7669 CC6 0.6496 17 0.6301 21A7 3.6706 7.0866 3.7987 7.0287 CC7 0.6588 13 0.6492 15A8 3.6916 6.9499 3.9966 6.7116 CC8 0.6531 16 0.6268 22A9 3.7853 6.9264 4.0374 6.7092 CC9 0.6466 18 0.6243 23A10 3.4570 7.2608 3.5824 7.1807 CC10 0.6775 8 0.6672 10A11 3.4331 7.2519 3.3425 7.3451 CC11 0.6787 7 0.6873 6A12 3.3073 7.3656 3.2520 7.3961 CC12 0.6901 3 0.6946 3A13 3.4007 7.2715 3.2604 7.3970 CC13 0.6814 6 0.6941 4A14 4.0710 6.6624 4.1848 6.5478 CC14 0.6207 25 0.6101 24A15 3.8931 6.7282 3.8132 6.8259 CC15 0.6335 24 0.6416 17A16 3.2078 7.4333 3.7267 7.0895 CC16 0.6985 1 0.6555 13A17 3.6622 7.0460 3.8332 6.8370 CC17 0.6580 14 0.6408 18A18 3.3072 7.3292 3.2775 7.3882 CC18 0.6891 4 0.6927 5.A19 3.8139 6.8369 4.1996 6.5422 CC19 0.6419 20 0.6090 25A20 4.0929 6.6116 4.3967 6.3735 CC20 0.6176 26 0.5918 28A21 3.7091 7.0094 3.5040 7.2046 CC21 0.6540 15 0.6728 8A22 3.8649 6.8548 3.9236 6.8500 CC22 0.6395 22 0.6358 20A23 4.2350 6.3890 3.4541 7.2525 CC23 0.6014 28 0.6774 7A24 3.5017 7.1995 4.3591 6.4050 CC24 0.6728 11 0.5950 26A25 4.2886 6.4762 4.3394 6.3592 CC25 0.6016 27 0.5944 27A26 3.8621 6.8538 3.8926 6.8323 CC26 0.6396 21 0.6370 19A27 3.6097 7.1623 3.5345 7.1895 CC27 0.6649 12 0.6704 9A28 3.8072 6.9195 3.6130 7.0231 CC28 0.6451 19 0.6603 12

Notes: d �i : the sum of separation from fuzzy negative ideal solution;d �i : the sum of distance from fuzzy positive ideal solution;CCn: similarity coefficiency of nth jobshop.


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Jobshop efficiency is calculated using all variable values of Table 11 within the DEA

mathematical model below. The DEA output-oriented BCC model for decision-making

units is summarised as follows (Banker et al. 1984):

Objective function:

Ek ¼ max �þ "Xmi¼1

s�i þ "Xpr¼1

sþr :

Subject to: Pnj¼1

xij�j þ s�i � xik ¼ 0, i ¼ 1, . . . ,m

Pnj¼1

yrj�j � sþr � �yrk ¼ 0, r ¼ 1, . . . , p

Pnj¼1

�j ¼ 1

�j � 0, j ¼ 1, . . . , n

sþr � 0, s�i � 0, i ¼ 1, . . . ,m,

r ¼ 1, . . . , p:

Table 11. Input and output data for jobshops.

DMU*

I1 I2 O1 O2 O3 O4

2005 2006 2005 2006 2005 2006 2005 2006 2005 2006 2005 2006

A1 31 24 36.6 33.2 99 98 89.3 90.7 93 90 69.68 66.41A2 32 32 32.6 31.7 88 80 91.2 89.4 88 75 67.42 64.40A3 12 13 38.2 37.4 84 93 90.4 91 87 81 63.47 69.67A4 13 11 36.3 34.9 49 84 91.2 90.6 97 85 68.38 69.75A5 26 25 37.8 35.1 99 92 90.6 90.9 88 80 67.31 65.49A6 13 12 36.8 35.3 80 84 89.5 90.7 97 98 64.96 63.01A7 6 6 37.8 37.2 97 98 91.1 90.9 97 97 65.88 64.92A8 26 24 36.4 34.7 93 86 89.3 90 83 89 65.31 62.68A9 6 8 36.7 37 86 83 91.9 90.1 91 79 64.66 62.43A10 22 22 35.8 35.2 95 75 89.2 87.2 94 70 67.75 66.72A11 9 7 36.3 32.9 78 68 85.3 89 92 85 67.87 68.73A12 14 12 35.9 33.6 94 98 90.9 90.8 99 88 69.01 69.46A13 10 10 39.7 38 88 91 90.4 90.6 90 72 68.14 69.41A14 49 47 39 34.7 94 86 88.9 89.4 92 98 62.07 61.01A15 40 40 35.7 34 98 92 89.3 89.6 88 91 63.35 64.16A16 22 16 36.3 40.3 99 86 90.8 90.7 92 93 69.85 65.55A17 37 31 37.8 34.5 97 86 90.6 89.1 92 86 65.80 64.08A18 17 13 39.3 42.2 97 99 90 90.2 87 85 68.91 69.27A19 25 27 38.3 36.1 98 99 89.8 90.3 91 98 64.19 60.90A20 2 6 37.9 40.1 85 94 87.4 87.6 93 90 61.76 59.18A21 22 12 37 35.8 84 78 89.1 88.9 93 85 65.40 67.28A22 8 6 39.4 37.4 88 94 86.8 90.8 95 81 63.95 63.58A23 48 39 36 32.5 96 98 89.2 87.9 85 85 60.14 67.74A24 33 28 36.4 34.6 92 93 90.3 90.3 88 81 67.28 59.50A25 7 7 37.9 34.7 78 61 90.6 91.1 77 97 60.16 59.44A26 12 11 38.7 35.6 84 90 87.7 91.5 83 99 63.96 63.70A27 37 35 36.4 33.6 95 100 88.8 89.4 98 86 66.49 67.04A28 15 12 37.7 35 92 85 88.2 91.5 93 76 64.51 66.03

Note: *DMU, Decision Making Unit (Jobshops).


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Table

12.Output-orientedBCC

reference

setandefficiency

ofjobshops.

DMU*

2005

2006

Efficiency

Reference

frequency

Reference

set

Efficiency

Reference

frequency

Reference

set

A1

100.00

3100.00

5A

2100.00

4100.00

A3

98.42

A9(1.00)

100.00

4A

4100.00

4100.00

A5

100.00

199.63

A3(0.00),A

12(0.33),A

26(0.62),A

28(0.05)

A6

98.39

A4(0.09),A

7(0.11),A

12(0.80)

99.84

A1(0.06),A

14(0.03),A

25(0.16),A

26(0.76)

A7

100.00

7100.00

4A

897.92

A2(0.01),A

9(0.31),A

16(0.69)

98.64

A1(0.31),A

26(0.43),A

28(0.28)

A9

100.00

998.84

A7(0.41),A

25(0.24),A

26(0.35)

A10

99.16

A2(0.09),A

12(0.45),A

16(0.46)

95.82

A3(0.42),A

12(0.58),A

28(0.00)

A11

100.00

100.00

A12

100.00

7100.00

6A

13

100.00

100.00

A14

97.54

A7(0.94),A

9(0.06)

100.00

1A

15

100.00

98.50

A1(0.66),A

26(0.31),A

28(0.03)

A16

100.00

10

99.39

A3(0.17),A

12(0.21),A

26(0.62)

A17

99.49

A7(0.75),A

16(0.25)

97.63

A1(0.34),A

12(0.05),A

26(0.29),A

28(0.32)

A18

99.90

A7(0.15),A

12(0.32),A

16(0.53)

100.00

A19

98.99

A1(0.00),A

5(0.01),A

16(0.99)

100.00

A20

100.00

96.37

A7(1.00)

A21

97.53

A4(0.10),A

9(0.43),A

12(0.47)

97.74

A3(0.34),A

7(0.04),A

12(0.53),A

26(0.09)

A22

97.44

A7(0.75),A

12(0.25)

99.89

A7(1.00)

A23

98.13

A2(0.08),A

9(0.02),A

16(0.90)

100.00

A24

98.99

A2(0.01),A

4(0.03),A

9(0.35),A

16(0.61)

99.02

A1(0.05),A

12(0.44),A

26(0.51)

A25

98.58

A9(1.00)

100.00

2A

26

95.90

A4(0.08),A

9(0.59),A

16(0.16)

100.00

9A

27

99.92

A1(0.07),A

7(0.24),A

12(0.69)

100.00

A28

96.64

A7(0.58),A

9(0.14),A

12(0.20),A

16(0.09)

100.00

5

Note:*DMU,DecisionMakingUnit(Jobshops).


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Where:

Ek: total efficiency score for the particular jobshop (k);�: efficiency score;yrj: output r for jobshop j;xij: input i for jobshop j;

Si, Sr: slack and surplus corresponding to input i, and output r, respectively;�j: weights attached to inputs and outputs of jobshop j;

xik, yrk: inputs (i) and outputs (r) of the particular jobshop (k) whose efficiency

is being evaluated;": is a non-Archimedean small and positive number.

In our study, results were obtained based on the model of VRS (variable returns to

scale)–BCC. A VRS model allows for the level of outputs to grow proportionally higher

or lower than a corresponding increase in inputs.Reference set and the efficiency of all jobshops obtained are shown in Table 12 after

DEA of this system is performed in the EMS version 1.3 software package. Since the

DEA-CCR (Charnes-Cooper-Rhodes) and DEA-BCC models are weak in discriminating

between efficient jobshops (Andersen and Petersen 1993), we use the super efficiency

model for comparing the efficient jobshops with each other as shown in Table 14 which

compares the efficiency results of the fuzzy TOPSIS model (for only qualitative values), the

DEA model (for only quantitative values) and the combined fuzzy TOPSIS-DEA model

(for qualitative and quantitative values). As an example, Table 13 provides detailed

calculations of jobshop A6’s composite jobshop from the reference set of jobshops for the

year 2005. The composite of jobshop A6 in 2005 is formed from the weighted average of

best-practice jobshops in the efficiency frontier of jobsop A6 i.e., jobshop A4 (0.09 A4),

jobshop A7 (0.11 A7) and jobshop A12 (0.80 A12). Jobshop A6’s comparative efficiency

rating of 98.39 per cent indicates the extent to which the efficiency of jobshop A6 is lacking

in comparison to the efficiency of its reference set of jobshops. Jobshop A6 is 98.39 per

cent as efficient as its reference set of jobshops (A4,A7,A12). This efficiency reference set of

jobshops represent the basis vector in the linear program solution for jobshop A6. That is,

a convex combination of the actual outputs and inputs of the reference subset of jobshops

results in a composite jobshop that produces as much or more outputs as jobshop A6, but

uses as much or less inputs than jobshop A6. In order to be able to increase the efficiency

of A6, target values and potential improvements are calculated and shown in Table 13

Table 13. Computation of the composite reference set for jobshop A6 in year 2005.

Real value Reference setTargetvalue

Potentialimprovement

A6 �4 A4 �7 A7 �12 A12 A�6 ¼ ��4A4 þ �

�7A7 þ �

�12A12 (A�6 �A6)/A6

I1 13 12 6 14 12.94 � 0.46%I2 36.8 36.3 37.8 35.9 36.15 � 1.78%O1 80 0.09 49 0.11 97 0.80 94 90.28 12.85%O2 89.48 91.18 91.08 90.9 90.95 1.64%O3 97 97 97 99 98.60 1.65%


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which documents the values of deficient inputs and excess outputs that existed within

jobshop A6 in the year 2005.As a result of the solution of this model (combined fuzzy TOPSIS super efficiency

DEA model), Table 14 is obtained. As known, according to the output oriented-BCC

model, a score greater than 1 is not efficient, but a score less than 1 is efficient. In order to

better understand Table 14, we made some adjustments. As a result of EMS, the efficiency

of jobshop A6 in the year 2005 is 101.63. This result is transformed from 101.63 to 98.39

((100/101.63) * 100) by making some corrections. This transformation is applied to all

scores in Table 14.

6. Concluding remarks

While efficiency is about producing maximum output with minimum input (in the DEA it

is manifested as an efficiency score of 1), effectiveness is about assessing whether the

Table 14. Comparison of the jobshop efficiency with fuzzy TOPSIS, DEA and combined fuzzyTOPSIS-DEA (CFTDEA).

2005 2006

Jobshop

Fuzzy

TOPSIS Rank DEA Rank CFTDEA Rank

Fuzzy

TOPSIS Rank DEA Rank CFTDEA Rank

A1 69.68 2 100.3 8 100.34 10 66.41 11 103 7 102.95 7

A2 67.42 9 Big 1 Big 1 64.40 16 Big 1 Big 1

A3 63.47 23 98.43 20 98.43 20 69.67 2 99.67 16 100.23 16

A4 68.38 5 100 9 100.12 11 69.75 1 99.16 18 100.57 14

A5 67.31 10 100 10 100 12 65.49 14 99.6 17 99.63 19

A6 64.96 17 98.39 21 98.39 21 63.01 21 99.75 15 99.84 18

A7 65.88 13 110.1 4 110.1 4 64.92 15 Big 1 Big 1

A8 65.31 16 97.92 23 97.92 23 62.68 22 98.64 23 98.64 23

A9 64.66 18 Big 1 Big 1 62.43 23 98.83 22 98.83 22

A10 67.75 8 99.16 14 99.16 16 66.72 10 95.22 28 95.93 28

A11 67.87 7 99.93 11 103.56 6 68.73 6 Big 1 Big 1

A12 69.01 3 106.6 5 106.55 5 69.46 3 120.5 4 120.51 4

A13 68.14 6 98.66 18 100.76 9 69.41 4 99.16 19 100.96 12

A14 62.07 25 97.53 24 97.53 24 61.01 24 102.1 9 102.08 9

A15 63.35 24 100.8 7 100.81 8 64.16 17 98.5 24 98.5 24

A16 69.85 1 102.6 6 102.56 7 65.55 13 99.12 20 99.39 20

A17 65.80 14 99.49 13 99.49 15 64.08 18 97.63 25 97.63 26

A18 68.91 4 98.98 16 99.9 14 69.27 5 100.5 12 100.86 13

A19 64.19 20 98.99 15 98.99 17 60.90 25 102.3 8 102.29 8

A20 61.76 26 Big 1 Big 1 59.18 28 96.37 27 96.37 27

A21 65.40 15 97.52 25 97.52 25 67.28 8 97.09 26 97.74 25

A22 63.95 22 97.44 26 97.44 26 63.58 20 99.89 14 99.89 17

A23 60.14 28 98.14 22 98.14 22 67.74 7 109.4 5 109.37 5

A24 67.28 11 98.89 17 98.99 18 59.50 26 99.02 21 99.02 21

A25 60.16 27 98.58 19 98.58 19 59.44 27 107.1 6 107.05 6

A26 63.96 21 95.62 28 95.9 28 63.70 19 102 10 101.97 10

A27 66.49 12 99.92 12 99.92 13 67.04 9 101.7 11 101.74 11

A28 64.51 19 96.67 27 96.74 27 66.03 12 100.3 13 100.31 15


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service is actually achieving what it set out to do (the set objective must be reached forexample, customer-satisfaction must be more than 95%). The main purpose of this studyhas been to form a framework to find not only efficient but also effective jobshops – i.e.,high performance jobshops by using and combining the fuzzy TOPSIS and the DEAmethods as performance measurement and evaluation tools. Also, this study has provideda prototype model (framework) in the general area of organisations in the manufacturingsector. The performance measure of 28 jobshops in the 2nd Air Supply and MaintenanceCenter Command manufacturing jobshops in Turkey was evaluated using newmethodology, which was proposed in this paper. When the results of DEA and fuzzyTOPSIS models in Table 14 are looked into, there seem to be some differences. In the year2005, the sequences of A1, A4, A5, A10, A11, A13, A15, A16, A17, A18, A19, A24 and A27

jobshops changed by combining the DEA model into the results of the fuzzy TOPSIS.Thus, the efficiency score of A11, A13, A18 and A26 increased. In the year 2006, thesequences of A4, A5, A6, A13, A17, A18, A21, A22 and A28 jobshops changed by combiningthe DEA model into the results of the fuzzy TOPSIS. Hence, the efficiency score of A6, A10

and A21 increased. Although these two methodologies have been found in the existingliterature separately as fuzzy TOPSIS and DEA, this is the first time this methodology hasbeen used to evaluate the performance of organisations in the manufacturing sector, i.e.,jobshops by combining these two multiple criteria decision making methods. The proposalof combining fuzzy TOPSIS and DEA could be in finding a set of jobshops which reallyperform well in fuzzy TOPSIS as well as DEA. This stringent identification of ‘bestperforming’ jobshops will provide an opportunity for many jobshops to introspect on theirperformance and to improve further. The new methodology presented in this paper hasincorporated qualitative attributes in the performance evaluation in more than one novelway by combining fuzzy TOPSIS and DEA differently. There has not been any studyin the literature about the application and theory of combined fuzzy TOPSIS/DEAmethodology before. While making the performance measurement and evaluation in themanufacturing and service systems as qualitative and quantitative, we can use thiscombination easily. In further studies, the criteria which is given importance by the topmanager can be defined by weighting input and output variables with AHP.

Acknowledgements

The authors want to express their thanks to the Turkish 2nd Air Supply and Maintenance CenterCommand staff because of all the support given in collecting all data which was required and toDr. Meeran from the Department of Decision Analysis, School of Management at Bath Universityin the UK for his help. In addition, we would like to thank the reviewers because of their valuablecomments and suggestions for preparation of the revised manuscript.

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Documents

A new decision support system for performance measurement using combined fuzzy TOPSIS/DEA approach