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Int J Adv Manuf Technol (2014) 73:749–771 DOI 10.1007/s00170-014-5826-3

ORIGINAL ARTICLE

A fuzzy DEMATEL-based solution approach for facility layout problem: a case study Serkan Altuntas & Hasan Selim & Turkay Dereli

Received: 20 August 2013 / Accepted: 31 March 2014 / Published online: 8 May 2014 # Springer-Verlag London 2014

Abstract Facility layout in production systems is a difficult activity since both qualitative and quantitative factors affect the location decision, and also influence and causal relationship between these factors should be determined for a better location. In this respect, it is demonstrated in this study that fuzzy decision-making trial and evaluation laboratory (fuzzy DEMATEL) method can effectively be used in handling facility layout problems in practice. The qualitative factors that described by linguistic terms can be taken into account through fuzzy structure of the method. Considering this, a fuzzy DEMATEL-based solution approach for facility layout problem is proposed in this study. The proposed approach takes into account both qualitative and quantitative location factors. To address the need in practice, six important location factors are considered in this study. These are material flow, information flow, personnel flow, equipment flow, environmental condition, and supervision of personnel. This study differs from the previous works in that it applies fuzzy DEMATEL method to facility layout problem. To explore the viability of the proposed approach, a real world problem in a machinery industry firm is handled.

S. Altuntas (*) Faculty of Engineering, Department of Industrial Engineering, Bayburt University, 69000 Bayburt, Turkey e-mail: [email protected] S. Altuntas e-mail: [email protected] H. Selim Faculty of Engineering, Department of Industrial Engineering, Dokuz Eylul University, 35397 Izmir, Turkey e-mail: [email protected] T. Dereli Faculty of Engineering, Department of Industrial Engineering, University of Gaziantep, 27310 Gaziantep, Turkey e-mail: [email protected]

Keywords Facility layout . Fuzzy DEMATEL . Machine allocation

1 Introduction Facility layout is one of the most important issues for modern manufacturing systems [1]. Engineers, workers, and decision makers at enterprises have researched the best or appropriate location to establish their departments/machines or locate their facilities in a layout in view of the fact that their located spaces affect material flow distance, total product produced, cycle time, waiting time, facility utilization, etc. Researchers classified facility layout problem into three types, namely, static facility layout problem [2, 3], dynamic facility layout problem [4, 5], and stochastic facility layout problem [6, 7]. In this study, we handle the static facility layout problem that deals with the question of where m numbers of facilities (each with area ai) are arranged within a given location when there is no variability in product demand. Herein, the facilities having the high level of relation have to be located adjacently. Several approximate or heuristic approaches were proposed for facility layout problem such as genetic algorithms [8] and particle swarm optimization [9]. The reader can refer to review studies [7, 10-15] for the details on facility layout problem. In handling facility layout problem in practice, qualitative factors should be taken into account effectively. As in our current study, some researchers used fuzzy logic-based solution approaches for facility layout problem. Among these studies, Grobelny [16] proposed a fuzzy constructive-type algorithm based on HC-66 method. The algorithm takes into account the relationship degrees for facility, costs of installation of each facility in each possible place, and the distance between location places in the form of fuzzy sets. In another study, Grobelny [17] presented a linguistic pattern approach based on possibility theory and Lukasiewiez multivalued implication formula. Evans et al. [18] presented a constructive-

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type heuristic-based on fuzzy sets for layout design. Raoot and Rakshit [19] formulated a multiple criteria facility layout problem based on a linguistic pattern approach. They illustrated their solution methodology with a numerical example by considering material flow, service link, organization link, environment link, and different facility size. Cheng et al. [20] introduced the concept of fuzzy interflow into facility layout problem. They presented material flows among facilities as fuzzy numbers. The solution was performed by genetic algorithm. Dweiri and Meier [21] introduced a new fuzzy decision-making-based solution approach for facility layout problem and presented a numerical example by considering three factors; material flow, information flow, and equipment flow. Szwarc et al. [22] considered fuzzy demand and machine capacity for cell formation. Aiello and Enea [23] proposed a fuzzy approach for facility layout in uncertain production environments. The approach considers production capacity of each facility and fuzzy demand for each product. Turkbey [24, 25] proposed a fuzzy method for the multiobjective machine sequencing problem. Deb and Bhattacharyya [26, 27] proposed a fuzzy decision support system for manufacturing facilities layout planning. The decision support system considers four factors: material flow, supervision link, information link, and environment link. They also considered pickup and drop-off points between the facilities. Enea et al. [28] treated uncertain production demand through fuzzy numbers. They implemented genetic algorithm to model the facility layout problem. Karray et al. [48] proposed an approach based on fuzzy logic and genetic algorithms for the facility layout. They took three factors, material flow, information flow, and equipment flow into account for layout arrangement. Grobelny [49] presented a fuzzy approach for facility layout problem and the proposed approach was verified using a simple example. Sangwan [29] presented a multicriteria heuristic model in a fuzzy environment to solve facility layout problem taking into account quantitative and qualitative factors, namely, material flow, safety rating, and noise rating. Altuntas et al. [30] proposed fuzzy weighted association rulebased data mining approaches for facility layout problem. Aksaraylı and Altuntas [50] compared the basic layout types using simulation technique. Raoot and Rakshit [51] presented a fuzzy approach based on experts’ opinions for constructiontype facility layout problem. They considered flow, control, process, organization personnel, and environmental relationships between facilities. Mohamadghasemi and HadiVencheh [52] proposed an integrated synthetic value of fuzzy judgments and a nonlinear programming methodology for ranking the facility layout patterns. They incorporated qualitative criteria besides the quantitative criteria into facility layout design problem. In addition, multicriteria decisionmaking (MCDM) based solution approaches were proposed for facility layout problem. For instance, Ertugrul and Karakasoglu [31] used fuzzy analytic hierarchy process (fuzzy

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AHP) and fuzzy technique for order preference by similarity to ideal solution (fuzzy TOPSIS) for the selection of the location of a textile company in Turkey. Bashiri and Hosseininezhad [32] can be referred for the details on the applications of MCDM techniques to facility layout problem. Facility location in production systems is a difficult activity since there exist both qualitative and quantitative factors that affect the location decision. In addition, influence and causal relationship between these factors should be determined for a better location. In this regard, we assert that fuzzy decisionmaking trial and evaluation laboratory (fuzzy DEMATEL) method can effectively be used in handling facility layout problems in practice. Additionally, qualitative factors that described by linguistic terms can be taken into account easily through fuzzy structure of the method. Fuzzy DEMATEL method is applied to various problems in practice such as evaluation of R&D projects [33], development of a cause and effect model of municipal solid waste management [34], analysis of supplier selection criteria [35], and evaluation of critical success factors in agile new product development [36]. On the other hand, to our knowledge, DEMATEL and fuzzy DEMATEL methods have not been employed to solve the facility layout problem. Considering this gap, a fuzzy DEMATEL-based solution approach for facility layout problem is proposed in this study. We utilize this approach to find the closeness ratings between the facilities to be located. This paper is further organized as follows. Section 2 describes fuzzy DEMATEL method. In Section 3, the proposed approach is introduced. A real world case study is presented in Section 4. Finally, conclusions and future research directions are given in Section 5.

2 Fuzzy DEMATEL method In this section, DEMATEL method is described briefly before presenting fuzzy DEMATEL method. 2.1 DEMATEL Method DEMATEL is a comprehensive method for analyzing and building a structural model involving causal relationships between complex factors. Basic steps of DEMATEL method is presented in the following [37, 38]. Step 1: Compute the average initial direct-relation matrix (A). Herein, generally a survey is conducted by asking related experts. The survey includes the comparison scale to find influence and direction among criteria with respect to expert opinions. Comparison scale includes four levels: (0) no influence, (1) low influence, (2) medium influence, and (3) high

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influence. The notations to compute A=[aij] are presented in the following. n H xkij

number of factors number of respondents (experts) degree to which respondent k believes factor i affects factor j Herein, aij can be computed as follows.

aij ¼ ð1=H Þ

H X

Table 1 Linguistic variables and corresponding triangular fuzzy numbers Linguistic variables

Corresponding triangular fuzzy numbers

No influence (NI) Very low influence (VLI) Low influence (LI) High influence (HI)

(0, 0.1, 0.3) (0.1, 0.3, 0.5) (0.3, 0.5, 0.7) (0.5, 0.7, 0.9)

Very high influence (VHI)

(0.7, 0.9, 1)

ð1Þ

xkij

k¼1

Step 2: Compute normalized initial direct-relation matrix (D). S ¼ 1=ð max

1< i< n

n X

aij Þ

&

ð2Þ

k ak Δmax min ¼ max a3ij − min  1ij xak1ij ¼ ak1ij −min ak1ij =Δmax   min k k k xa2ij ¼ a2ij −min a1ij =Δmax   min k k k xa3ij ¼ a3ij −min a1ij =Δmax min

j¼1

D¼AS

ð3Þ

Step 3: Compute factor total-influence matrix (T). T ¼ DðI−DÞ−1 I

ð4Þ

Normalization:

&

identity matrix

Step 4: Compute C, R, C+R, and R−C values and also set threshold value to obtain digraph of showing causal relations among criteria, where C and R denote the column sum and the row sum of matrix T, respectively.

ð5Þ

Compute left side (ls) and right side (rs) normalized values:   xlskij ¼ xak2ij = 1 þ xak2ij − xak1ij   xrskij ¼ xak3ij = 1 þ xak3ij − xak2ij

ð6Þ

2.2 Fuzzy DEMATEL method Qualitative factors that affect real-life facility layout problems cannot be fairly taken into consideration in most of the modeling approaches, while they can be modeled easily and effectively using fuzzy DEMATEL method. Steps of fuzzy DEMATEL method are presented in the following. Step 1: Compute average initial direct-relation matrix (A). In this study, we use the linguistic scale and corresponding triangular fuzzy numbers that are defined by Wang and Chang [39] and Chen [40] (see Table 1). The fuzzy numbers corresponding to expert’s assessment of facility pair with respect to each factor should be defuzzified. In this work, “Converting the Fuzzy data into Crips Scores” (CFCS) method, developed by Opricovic and Tzeng [41], is employed for the defuzzification process. CFCS method consists of the following four steps [42]. Let wkij =(ak1ij, ak2ij, and ak3ij), there exist k experts, wkij presents the fuzzy weight of ith criteria that affects the jth criteria evaluated by kth expert.

&

Compute total normalized crisp value:

xkij ¼ ½xlskij ð1 − xlskij Þ þ xrskij xlskij Š=½1 − xlskij þ xrskij Š ð7Þ &

Compute crisp values:

xkij ¼ min ak1ij þ xkij Δmax min

ð8Þ

Equation (1) is used to compute average initial directrelation matrix (A) after each fuzzy responds is defuzzified. Step 2: Compute the normalized initial direct-relation matrix (D) using Eqs. (2) and (3). Step 3: Compute factor total-influence matrix (T) using Eq. (4). Step 4: This step is exactly the same as step 4 of DEMATEL method.

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3 The proposed approach There exist basically two type of approaches for facility layout problem, namely, constructive type and improvement type [43, 44, 45]. Constructive-type approaches do not need any initial layout to establish facility’s location because these type of approaches are used when a layout is developed for the first time, while improvement-type approaches need an initial layout to improve that layout. The main aim of the constructive-type approaches is to find appropriate facility layout with respect to some

prespecified factors. Both of these approaches consist of two main stages. The first stage responds to which facility to be assigned with which order to facility layout. The second stage responds to which facility to be located with which area. A constructive-type approach that considers both qualitative and quantitative factors is proposed in this study. The proposed fuzzy DEMATEL-based approach can be implemented to facility layout problem in two stages. The first stage of the proposed approach consists of ten steps, which are presented in the following in a stepwise manner.

Step 1: Determine the factors that affect facility layout. Step 2: Establish linguistic description of the factors. Step 3: Compute matrix A for each qualitative factors by using expert’s assessment. Step 4: Compute matrix D for each qualitative factors. Step 5: Compute matrix T for each qualitative and also quantitative factor by using flow data. Step 6: Normalize the values of all T matrices to interval 0-1. Step 7: Weight all factors by using an appropriate method. Step 8: Multiply each normalized matrix T by corresponding factor weight. The final matrix is called matrix K. Step 9: Compute closeness ratio matrix C by summing all matrices of K . This step gives closeness ratings between the facilities. Step 10: Sort all facility pairs in descending order in terms of their closeness rating and add this ordered facility pairs to “list A” that denotes the order of allocation and stop.

Herein, the location factors could be weighted using subjective weighting methods such as analytic hierarchy process (AHP) and the simple multi-attribute rating technique (SMART). In the second stage of the proposed approach, we implement Altuntas and Selim’s [46] location algorithm for static facility layout problem. The algorithm can cope with difficulty in providing flexibility in assigning machine pairs to facility layout. In addition, it can be modified easily in handling static facility layout problem in cellular manufacturing systems. Therefore, Altuntas and Selim’s [46] location algorithm is employed in this study to assign machine pairs to facility layout. The algorithm applies four rules. Three of these rules, namely, “New facility cluster generation rule,” “Adoption rule,” and “Merging rule” are proposed by Chan et al. [47], and the last one, namely, “Final assembly rule” is proposed by Altuntas and Selim [46]. Details of these rules are presented in the following. –

New facility cluster generation rule: A facility pair is assigned to a new temporary layout (cluster) if there are not any connection between this facility pair and already located facility/facilities.

– –

–

Adoption rule: If the selected facility pair has relation with an already established layout, it is allocated adjacent to that layout to improve the closeness rating. Merging rule: If the selected facility pair has relation with two facility layouts, these two layouts are combined. When two facility clusters are merged, most related facilities have to be allocated as closely as possible. Final assembly rule: If there exist more than one layout when all facilities are located, the layouts have to be merged to obtain final layout. Herein, one of the layouts has to be determined as the main layout. The layout including the largest number of facility is selected as the main layout. In case of equal number of facilities, the facility location order is considered in determining the main layout. The other clusters called temporary clusters. Starting from the first facility pair, all facility pairs in the temporary clusters are located to appropriate locations in the main layout. Finally, a single cluster that is called “final facility layout” is obtained by applying final assembly rule. The algorithm is presented in the following.

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Step 1: Pick out the facility pair in the top of list A. Step 2: Is there more than one facility pair with the same value? If the answer is yes, select one of them randomly. Otherwise, go to step 3. Step 3: Has selected facility pair already been located to the same cluster in the workspace? If the answer is yes, go to step 9. Otherwise, go to step 4. Step 4: Is this first facility pair to be located in the workspace? If the answer is yes, go to step 5. Otherwise, go to step 6. Step 5: Locate this facility pair adjacently and go to step 9. Step 6: Is there a connection to any cluster in the workspace? If the answer is yes, apply “Adoption rule”. Otherwise, go to step 8. Step 7: Is there a connection to two facility clusters in the workspace? If the answer is yes, apply “Merging rule”. Otherwise, go to step 8. Step 8: Apply “New facility cluster generation rule”. Step 9: Have all facilities been located? If the answer is yes, go to step 10. Otherwise, go to step 1. Step 10: Are there two or more facility clusters in the workspace? If answer is yes, apply “Final assembly rule”. Otherwise, stop.

4 Case study To explore the viability of the proposed approach, a real world case study in the machinery industry is presented in this section. The manufacturing firm under concern produces twelve types of machine parts (products) for grouting machines using eleven types of totally 25 machines. Types and number of the machines are as follows: lathe (13 machines), honing (2 machines), gear shaper, milling (2 machines), drill, sanding, polishing, welder, sawing, grinding, and shaper. The current facility layout is illustrated in Fig. 1. Adjacency between the machines is represented by dashed arrows in the figure. There exist three different types of lathe machines, namely, CNC lathe, vertical lathe, and horizontal lathe, in the production system. Therefore, three different illustrations are used for lathe machines in Fig. 1. Currently, facility layout of the production system is not structured by a systematic approach. The routes, demand, and transfer batch size of the products are reported in Table 2. Application of the proposed approach is explained in a stepwise manner in the following. Initially, implementation of first stage is explained. Step 1: Six key location factors are determined in this application. These are material flow, information flow, personnel flow, equipment flow, environmental condition, and supervision of the personnel. Step 2: Descriptions of the location factors are presented in the following. Herein, explanation of the qualitative factors is based on Dweiri and Meier’s [21] study.

Material flow: Total material flow between facilities is a quantitative factor and it is computed by “demand/transfer batch size” formula. Information flow: Communication level between facilities can be used as a surrogate for information flow. Experts may evaluate the information flow by using linguistic variables such as no influence (NI) for no communication, very low influence (VLI) for very low communication, low influence (LI) for low communication, high influence (HI) for high communication, and very high influence (VHI) for very high communication. Personnel flow: It denotes the intensity of employees that perform tasks in both facilities under concern. Experts may evaluate personnel flow by using linguistic variables such as no influence (NI) for no personnel flow, very low influence (VLI) for very low personnel flow, low influence (LI) for low personnel flow, high influence (HI) for high personnel flow, and very high influence (VHI) for very high personnel flow. Equipment flow: It denotes the intensity of equipments used to perform task in both facilities under concern. Experts may evaluate equipment flow by using linguistic variables as in the same manner of the personnel flow. Environmental condition: It denotes the level of hazard or inconvenience involved such as high level of noise, temperature, and vibration. Experts may evaluate environmental condition by using linguistic variables such as no influence (NI) for very high hazard, very low influence (VLI) for high hazard, low influence (LI) for low

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Int J Adv Manuf Technol (2014) 73:749–771 HONING_1 LATHE_1

HONING_2

SANDING

LATHE_2

LATHE_3 GEAR SHAPER LATHE_5

LATHE_6

LATHE_7

POLISHING

SAWING

WELDER

LATHE_8

LATHE_4

MILLING_1

GRINDING LATHE_9

MILLING_2

SHAPER DRILL

CNC_LATHE

LATHE_10

LATHE_11

LATHE_12

Fig. 1 The current facility layout

hazard, high influence (HI) for very low hazard, and very high influence (VHI) for no hazard. Supervision of the personnel: It denotes the intensity of employees that come together under a common supervision. Experts may evaluate supervision of personnel by using linguistic variables such as no influence (NI) for no supervision of personnel, very low influence (VLI) for very low level of supervision, low influence (LI) for

low level of supervision, high influence (HI) for high level of supervision, and very high influence (VHI) for very high level of supervision. Explanations on the location factors expose that except material flow, all of the location factors are qualitative. Step 3: In our case, two experts evaluate association between the machines with respect to the location factors

Table 2 The routes, demand, and transfer batch size of the products Products

Routea

Product1 Product2 Product3

Lathe6 (6) Lathe11 (11) Sawing (23)

Honing1 (13) Honing1 (13) Lathe6 (6)

Lathe4 (4) Lathe4 (4) Honing1 (13)

Honing2 (14) Honing2 (14) Lathe10 (10)

Milling1 (15) Milling2 (16) Milling1 (15)

Product4 Product5 Product6 Product7 Product8 Product9 Product10 Product11 Product12

Lathe6 (6) Lathe6 (6) Lathe1 (1) Lathe5 (5) CNC Lathe (18) Lathe8 (8) Lathe3 (3) Lathe12 (12) Lathe12 (12)

Honing1 (13) Honing1 (13) Sanding (20) Grinding (24) Lathe9 (9) Milling1 (15) Milling2 (16) Milling2 (16) Drill (19)

Lathe7 (7) Shaper (25) Lathe2 (2) Sanding (20) Grinding (24) Grinding (24)

Lathe4 (4) Milling1 (15) Polishing (21) Polishing (21) Sanding (20) Gear Shaper (17)

Milling1 (15) Lathe4 (4)

Milling1(15)

Welder(22)

a

The numbers in the brackets denote the machine numbers

Polishing (21) Sanding (20)

Welder (22)

Polishing (21)

Demand

Transfer batch size

160 160 160

3 3 3

160 150 190 190 190 190 150 150 150

3 3 5 5 5 5 25 25 10

0 NI VLI NI NI NI NI LI NI NI NI NI NI NI

VLI VLI NI NI NI VLI VLI NI NI NI NI

1 2 3 4 5 6 7 8 9 10 11 12 13 14

15 16 17 18 19 20 21 22 23 24 25

1

VLI VLI NI NI NI VLI VLI NI NI NI NI

NI 0 VLI NI NI NI NI LI NI NI NI NI NI NI

2

VLI VLI NI NI NI VLI VLI NI NI NI NI

NI NI 0 NI VLI NI NI LI NI NI NI NI NI NI

3

VLI VLI NI NI NI VLI VLI NI NI NI NI

NI NI NI 0 VLI VLI VLI NI NI HI LI NI VLI VLI

4

VLI VLI NI NI NI VLI VLI NI NI NI NI

VLI LI VLI LI 0 NI NI NI NI NI NI NI NI NI

5

VLI VLI NI NI NI VLI VLI NI NI NI NI

NI LI VLI LI VLI 0 NI NI NI HI LI NI LI LI

6

Table 3 Expert1’s assessment for information flow

VLI VLI NI NI NI VLI VLI NI NI NI NI

NI LI VLI NI VLI NI 0 LI NI NI NI NI NI NI

7

VLI VLI NI NI NI VLI VLI NI NI NI NI

NI NI NI NI NI NI NI 0 NI NI NI NI NI NI

8

VLI VLI NI HI NI VLI VLI NI NI NI NI

NI NI NI NI NI NI NI HI 0 NI NI NI NI NI

9

VLI VLI NI NI NI VLI VLI NI NI NI VLI

NI NI NI LI VLI NI NI NI NI 0 VLI NI LI LI

10

VLI VLI NI NI NI VLI VLI NI NI NI VLI

NI VLI NI LI NI NI NI NI NI NI 0 NI NI NI

11

VLI VLI NI NI LI VLI VLI NI NI NI NI

NI NI NI NI NI NI NI NI NI NI NI 0 NI NI

12

VLI VLI NI NI NI NI NI NI NI NI VLI

NI VLI LI HI NI HI NI NI NI VLI VLI NI 0 HI

13

NI NI NI NI NI NI NI NI NI NI VLI

NI VLI LI HI NI HI NI NI NI VLI VLI NI HI 0

14

0 VHI NI NI VLI NI NI NI NI NI NI

NI VLI VLI VLI NI VLI LI VLI VLI NI VLI NI NI NI

15

VHI 0 NI NI VLI NI NI NI NI NI NI

NI VLI VLI VLI NI VLI LI VLI VLI NI VLI NI NI NI

16

NI NI 0 NI NI NI NI NI NI NI NI

NI NI VLI NI NI NI NI NI NI NI NI NI VHI VHI

17

NI NI NI 0 NI NI NI NI NI NI NI

NI NI NI NI NI NI NI VHI HI NI NI NI NI NI

18

LI LI NI NI 0 NI NI NI NI NI NI

NI NI NI NI NI NI NI NI NI NI NI LI NI NI

19

NI NI NI NI NI 0 NI NI NI NI NI

NI NI NI NI NI NI NI VLI LI NI NI NI NI NI

20

NI NI NI NI NI NI 0 NI NI NI NI

VLI NI NI NI NI NI NI NI NI NI NI NI NI NI

21

NI NI NI NI NI NI NI 0 NI NI NI

VLI NI NI VLI VLI NI NI NI NI NI NI NI NI NI

22

NI NI NI NI NI NI NI NI 0 VHI NI

NI NI NI NI NI NI NI NI NI NI NI NI NI NI

23

NI NI NI NI NI NI NI NI VHI 0 NI

VLI NI VLI NI NI NI VLI NI NI NI NI NI NI NI

24

NI NI NI NI NI NI NI NI NI NI 0

NI NI NI NI NI NI NI NI NI VLI VLI NI VLI VLI

25

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0 NI VLI NI NI NI NI VLI NI NI NI NI NI NI

LI LI NI NI NI NI NI NI NI VLI NI

1 2 3 4 5 6 7 8 9 10 11 12 13 14

15 16 17 18 19 20 21 22 23 24 25

1

LI LI NI NI NI NI NI NI NI NI NI

NI 0 VLI NI NI NI NI VLI NI NI NI NI NI NI

2

LI LI NI NI NI VLI NI NI NI VLI NI

NI NI 0 NI VLI NI NI VLI NI NI NI NI LI LI

3

LI LI NI NI NI NI NI NI NI NI NI

NI NI NI 0 VLI VLI VLI NI NI LI VLI NI VLI VLI

4

LI LI NI NI NI NI NI NI NI NI VLI

VLI LI LI HI 0 NI NI NI NI NI NI NI NI NI

5

LI LI NI NI NI NI LI LI NI NI NI

NI LI LI HI VLI 0 NI NI NI NI NI NI NI NI

6

Table 4 Expert2’s assessment for information flow

LI LI NI NI NI NI NI NI NI NI NI

NI HI VLI NI VLI NI 0 VLI NI NI NI NI NI NI

7

LI LI NI NI NI LI NI NI NI LI NI

NI NI NI NI NI NI VLI 0 NI NI NI NI VLI VLI

8

LI LI NI LI NI LI NI NI NI NI NI

NI NI NI NI NI NI NI LI 0 VLI NI NI VLI VLI

9

LI LI NI NI NI NI NI NI NI NI VLI

NI NI NI HI LI NI NI NI NI 0 NI NI NI NI

10

LI LI NI NI NI NI NI NI NI NI NI

NI LI NI LI NI NI NI NI NI NI 0 NI LI LI

11

LI LI NI NI NI NI NI NI NI NI NI

NI NI NI NI NI NI NI NI NI NI NI 0 NI NI

12

NI NI NI NI NI NI NI NI VLI NI VLI

NI VLI LI HI NI LI VLI NI NI LI LI NI 0 VHI

13

NI NI NI NI NI NI NI NI VLI NI VLI

NI VLI LI HI NI LI VLI NI NI LI LI NI VHI 0

14

0 VLI NI NI NI NI NI NI NI NI NI

NI VLI LI LI NI VLI LI VLI VLI VLI LI VLI NI NI

15

VLI 0 NI NI LI NI NI NI NI NI NI

NI VLI LI LI NI VLI LI VLI VLI VLI LI VLI NI NI

16

NI NI 0 NI LI NI NI NI NI NI NI

NI NI VLI NI NI NI NI VLI VLI NI NI NI LI LI

17

NI NI NI 0 NI NI NI NI NI NI NI

NI NI NI NI NI NI NI NI VHI NI NI NI NI NI

18

VLI VLI NI NI 0 NI NI NI NI NI NI

NI NI NI NI NI NI NI NI NI NI NI NI NI NI

19

NI NI NI NI NI 0 NI NI VLI NI NI

LI NI VLI NI NI NI NI LI LI NI NI NI NI NI

20

NI NI NI NI NI VLI 0 NI NI NI NI

NI NI VLI NI NI NI NI LI LI NI NI NI NI NI

21

NI NI NI NI NI NI NI 0 NI NI NI

VLI NI NI VLI HI VLI VLI NI NI NI NI NI NI NI

22

NI NI NI NI NI VLI NI NI 0 NI NI

NI NI NI NI NI NI NI NI NI NI NI NI NI NI

23

NI NI NI NI NI NI NI NI NI 0 NI

VLI NI VLI NI NI NI NI LI LI NI NI NI NI NI

24

NI NI NI NI NI NI NI LI NI NI 0

NI NI NI NI NI NI NI NI NI VLI VLI NI NI NI

25

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Table 5 The weights for the location factors

Step 4: Matrix D for information flow is presented in Table 8 in the Appendix. Step 5: Matrices T for material flow and information flow are presented in Tables 9 and 10 in the Appendix, respectively. As reported in Table 9, there is no material flow between most of the machine pairs (see Table 2). Step 6: Normalized T matrices for material flow and information flow are presented in Tables 11 and 12 in the Appendix, respectively. Step 7: We determine the weights of the location factors by averaging the weights assigned by the experts. The weights are reported in Table 5. Step 8: Matrices K for material flow and information flow are presented in Tables 13 and 14 in the Appendix, respectively. Step 9: Closeness rating matrix (matrix C) is reported in Table 15 in the Appendix. Step 10: List A that is obtained by sorting all machine pairs in descending order in terms of their closeness rating is presented in Table 6. The first 40 machine pairs that have the highest closeness rating are presented in the table. As recalled, list A responds to which facility to be assigned with which order to facility layout.

Factors

Assigned weight

Material flow Information flow Personnel flow Equipment flow Environmental condition Supervision of the personnel Total

Expert1

Expert2

0.30 0.20 0.10 0.25 0.05 0.10 1

0.40 0.15 0.15 0.10 0.10 0.10 1

Average weight

0.350 0.175 0.125 0.175 0.075 0.100 1

using linguistic variables. Corresponding triangular fuzzy numbers have already been presented in Table 1. To determine the associations between machines, a survey was conducted. In this regard, pairwise comparisons were made by the experts. To improve the readability and due to the space limitation, we only present the results on “information flow” and “material flow” in this study. Tables 3 and 4 report the experts’ assessment, while Table 7 presented in the Appendix presents “matrix A” for “information flow.” It should be recalled here that, matrix T for material flow is constructed using demand/transfer batch size formula. Table 6 Closeness rating of the machine pairs (list A)

P indicates that the machine pair is located adjacently in the proposed layout; C indicates that the machine pair is located adjacently in the current layout

Figure 2 illustrates the final facility layout obtained by the proposed approach. As stated before, dashed arrows in the figure represent adjacency between the machines. Due to the fuzzy

No

Machine pair

Closeness rating

No

Machine pair

Closeness rating

1 2 3 4 5 6 7 8 9 10 11 12 13 14

6–13 (P) 4–14 (P) 13–4 (P) 20–21 (P,C) 15–22 (P) 4–15 (P) 11–13 (P) 7–4 (P) 13–10 (P) 13–7 10–15 (P) 14–15 14–16 (P) 23–6 (P)

0.047960 0.027414 0.027007 0.019203 0.016290 0.014361 0.014282 0.014280 0.014163 0.014094 0.014081 0.014061 0.014041 0.013934

21 22 23 24 25 26 27 28 29 30 31 32 33 34

20–2 (P) 1–20 (P) 9–24 (P) 2–21 15–24 (C) 5–24 (P) 17–20 24–17 (P) 19–15 12–19 (P) 3–16 (P) 12–16 13–14 (C) 15–16 (C)

0.007231 0.007219 0.007205 0.007152 0.007131 0.007091 0.007061 0.007016 0.003649 0.003411 0.002426 0.002116 0.001944 0.001933

15 16 17 18

24–20 (P) 15–4 (P) 13–25 25–15 (P)

0.013040 0.009463 0.009142

35 36 37

14–13 (C) 4–6 16–15 (C)

0.001928 0.001923 0.001923

19 20

8–15 (C) 18–9 (P)

0.009062 0.007504 0.007327

38 39 40

4–5 (C) 8–9 (P, C) 4–13 (P)

0.001862 0.001835 0.001831

758

Int J Adv Manuf Technol (2014) 73:749–771 LATHE_3

LATHE_7

MILLING_2

HONING_1

LATHE_4

HONING_2

LATHE_10

MILLING_1

LATHE_11

SAWING

LATHE_6

DRILL LATHE_12

SHAPER

WELDER LATHE_8

LATHE_5

LATHE_9

LATHE_2

SANDING POLISHING

GRINDING

CNC_LATHE GEAR SHAPER

LATHE_1

Fig. 2 Facility layout obtained by the proposed approach

structure of the problem under concern, there does not exists an objective performance measure for evaluation of the facility layouts. In addition, different multicriteria decision making methods treat uncertainties distinctively. Therefore, we could not compare the results of the proposed method to the ones of other methods. However, we compare the current and proposed facility layouts using total closeness rating, the output of fuzzy DEMATEL method, of the adjacent machine pairs with respect to each layout. The results reveal that total closeness ratings of the current and proposed facility layouts are 0.1195 and 0.3822, respectively. It means that the proposed approach provides a considerably improved facility layout in terms of the aforementioned six location factors. The case study explores that the proposed fuzzy DEMATEL-based solution approach can effectively and straightforwardly be applied in real world facility layout problems under uncertainty.

5 Conclusion Facility layout is quite important for enterprises due to its direct effects on productivity and efficiency. However, facility layout in production systems is a difficult activity since both qualitative and quantitative factors affect the location decision. In addition, influence and causal relationship between these factors should be determined for a better location. In this respect, we demonstrated in this study that fuzzy DEMATEL method can effectively be used in handling facility layout problems in

practice. We take into account easily qualitative factors which are described by linguistic terms through the method. Fuzzy DEMATEL method is applied to various problems in practice. However, to the authors’ knowledge, DEMATEL or fuzzy DEMATEL methods have not been employed to solve facility layout problems. Considering this gap, a fuzzy DEMATEL-based solution approach for the facility layout problem is proposed in this study. The method is utilized to find the closeness ratings between the facilities to be located. The proposed approach takes both qualitative and quantitative location factors into account. To address the need in practice, six essential location factors are considered in this study. These are material flow, information flow, personnel flow, equipment flow, environmental condition, and supervision of the personnel. This study differs from the previous works in that it applies fuzzy DEMATEL method to the facility layout problem. To explore the viability of the proposed approach, a real world case study is presented. Results of the case study reveal that the proposed approach can effectively be used in solving practical facility layout problems. In addition, by means of the proposed approach, qualitative location factors can effectively be treated. As a future study, application of the proposed approach to dynamic or stochastic facility layout problems is of worth.

Acknowledgments The authors would like to thank the anonymous reviewers for their insightful comments and suggestions that have significantly improved the paper. The authors would also like to thank Fatih Dülgeroğlu for his help in conducting the survey.

0.000 0.125 0.310 0.125 0.125 0.125 0.125 0.405 0.125 0.125

0.125 0.125 0.125 0.125 0.405 0.405 0.125 0.125 0.125 0.217 0.217 0.125 0.125 0.217 0.125

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

1

0.125 0.125 0.125 0.125 0.405 0.405 0.125 0.125 0.125 0.217 0.217 0.125 0.125 0.125 0.125

0.125 0.000 0.310 0.125 0.125 0.125 0.125 0.405 0.125 0.125

2

0.125 0.125 0.313 0.313 0.405 0.405 0.125 0.125 0.125 0.310 0.217 0.125 0.125 0.217 0.125

0.125 0.125 0.000 0.125 0.310 0.125 0.125 0.405 0.125 0.125

3

0.405 0.125 0.310 0.310 0.405 0.405 0.125 0.125 0.125 0.217 0.217 0.125 0.125 0.125 0.125

0.125 0.125 0.125 0.000 0.310 0.310 0.310 0.125 0.125 0.595

4

0.125 0.125 0.125 0.125 0.405 0.405 0.125 0.125 0.125 0.217 0.217 0.125 0.125 0.125 0.217

0.310 0.500 0.405 0.595 0.000 0.125 0.125 0.125 0.125 0.125

5

Table 7 Matrix A for information flow

Appendix

0.313 0.125 0.313 0.313 0.405 0.405 0.125 0.125 0.125 0.217 0.405 0.313 0.125 0.125 0.125

0.125 0.500 0.405 0.595 0.310 0.000 0.125 0.125 0.125 0.408

6

0.125 0.125 0.125 0.125 0.405 0.405 0.125 0.125 0.125 0.217 0.217 0.125 0.125 0.125 0.125

0.125 0.595 0.310 0.125 0.310 0.125 0.000 0.405 0.125 0.125

7

0.125 0.125 0.217 0.217 0.405 0.405 0.125 0.125 0.125 0.405 0.217 0.125 0.125 0.313 0.125

0.125 0.125 0.125 0.125 0.125 0.125 0.217 0.000 0.125 0.125

8

0.125 0.125 0.217 0.217 0.405 0.405 0.125 0.595 0.125 0.405 0.217 0.125 0.125 0.125 0.125

0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.595 0.000 0.217

9

0.217 0.125 0.313 0.313 0.405 0.405 0.125 0.125 0.125 0.217 0.217 0.125 0.125 0.125 0.310

0.125 0.125 0.125 0.595 0.405 0.125 0.125 0.125 0.125 0.000

10

0.000 0.125 0.313 0.313 0.405 0.405 0.125 0.125 0.125 0.217 0.217 0.125 0.125 0.125 0.217

0.125 0.405 0.125 0.500 0.125 0.125 0.125 0.125 0.125 0.125

11

0.125 0.000 0.125 0.125 0.405 0.405 0.125 0.125 0.313 0.217 0.217 0.125 0.125 0.125 0.125

0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125

12

0.405 0.125 0.000 0.783 0.217 0.217 0.125 0.125 0.125 0.125 0.125 0.125 0.217 0.125 0.310

0.125 0.310 0.500 0.690 0.125 0.595 0.217 0.125 0.125 0.405

13

0.405 0.125 0.783 0.000 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.217 0.125 0.310

0.125 0.310 0.500 0.690 0.125 0.595 0.217 0.125 0.125 0.405

14

0.405 0.217 0.125 0.125 0.000 0.592 0.125 0.125 0.217 0.125 0.125 0.125 0.125 0.125 0.125

0.125 0.310 0.405 0.405 0.125 0.310 0.500 0.310 0.310 0.217

15

0.405 0.217 0.125 0.125 0.592 0.000 0.125 0.125 0.405 0.125 0.125 0.125 0.125 0.125 0.125

0.125 0.310 0.405 0.405 0.125 0.310 0.500 0.310 0.310 0.217

16

0.125 0.125 0.687 0.687 0.125 0.125 0.000 0.125 0.313 0.125 0.125 0.125 0.125 0.125 0.125

0.125 0.125 0.310 0.125 0.125 0.125 0.125 0.217 0.217 0.125

17

0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.000 0.125 0.125 0.125 0.125 0.125 0.125 0.125

0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.500 0.783 0.125

18

0.125 0.313 0.125 0.125 0.405 0.405 0.125 0.125 0.000 0.125 0.125 0.125 0.125 0.125 0.125

0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125

19

0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.000 0.125 0.125 0.217 0.125 0.125

0.313 0.125 0.217 0.125 0.125 0.125 0.125 0.405 0.500 0.125

20

0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.217 0.000 0.125 0.125 0.125 0.125

0.217 0.125 0.217 0.125 0.125 0.125 0.125 0.313 0.313 0.125

21

0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.000 0.125 0.125 0.125

0.310 0.125 0.125 0.310 0.500 0.217 0.217 0.125 0.125 0.125

22

0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.217 0.125 0.125 0.000 0.500 0.125

0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125

23

0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.500 0.000 0.125

0.310 0.125 0.310 0.125 0.125 0.125 0.217 0.313 0.313 0.125

24

0.310 0.125 0.217 0.217 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.313 0.125 0.125 0.000

0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.310

25

Int J Adv Manuf Technol (2014) 73:749–771 759

0.000 0.017 0.043 0.017 0.017 0.017 0.017 0.056 0.017 0.017 0.017 0.017 0.017 0.017

0.056 0.056 0.017 0.017 0.017 0.030 0.030 0.017 0.017 0.030 0.017

1 2 3 4 5 6 7 8 9 10 11 12 13 14

15 16 17 18 19 20 21 22 23 24 25

1

0.056 0.056 0.017 0.017 0.017 0.030 0.030 0.017 0.017 0.017 0.017

0.017 0.000 0.043 0.017 0.017 0.017 0.017 0.056 0.017 0.017 0.017 0.017 0.017 0.017

2

0.056 0.056 0.017 0.017 0.017 0.043 0.030 0.017 0.017 0.030 0.017

0.017 0.017 0.000 0.017 0.043 0.017 0.017 0.056 0.017 0.017 0.017 0.017 0.043 0.043

3

0.056 0.056 0.017 0.017 0.017 0.030 0.030 0.017 0.017 0.017 0.017

0.017 0.017 0.017 0.000 0.043 0.043 0.043 0.017 0.017 0.083 0.056 0.017 0.043 0.043

4

0.056 0.056 0.017 0.017 0.017 0.030 0.030 0.017 0.017 0.017 0.030

0.043 0.069 0.056 0.083 0.000 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017

5

Table 8 Matrix D for information flow

0.056 0.056 0.017 0.017 0.017 0.030 0.056 0.043 0.017 0.017 0.017

0.017 0.069 0.056 0.083 0.043 0.000 0.017 0.017 0.017 0.057 0.043 0.017 0.043 0.043

6

0.056 0.056 0.017 0.017 0.017 0.030 0.030 0.017 0.017 0.017 0.017

0.017 0.083 0.043 0.017 0.043 0.017 0.000 0.056 0.017 0.017 0.017 0.017 0.017 0.017

7

0.056 0.056 0.017 0.017 0.017 0.056 0.030 0.017 0.017 0.043 0.017

0.017 0.017 0.017 0.017 0.017 0.017 0.030 0.000 0.017 0.017 0.017 0.017 0.030 0.030

8

0.056 0.056 0.017 0.083 0.017 0.056 0.030 0.017 0.017 0.017 0.017

0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.083 0.000 0.030 0.017 0.017 0.030 0.030

9

0.056 0.056 0.017 0.017 0.017 0.030 0.030 0.017 0.017 0.017 0.043

0.017 0.017 0.017 0.083 0.056 0.017 0.017 0.017 0.017 0.000 0.030 0.017 0.043 0.043

10

0.056 0.056 0.017 0.017 0.017 0.030 0.030 0.017 0.017 0.017 0.030

0.017 0.056 0.017 0.069 0.017 0.017 0.017 0.017 0.017 0.017 0.000 0.017 0.043 0.043

11

0.056 0.056 0.017 0.017 0.043 0.030 0.030 0.017 0.017 0.017 0.017

0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.000 0.017 0.017

12

0.030 0.030 0.017 0.017 0.017 0.017 0.017 0.017 0.030 0.017 0.043

0.017 0.043 0.069 0.096 0.017 0.083 0.030 0.017 0.017 0.056 0.056 0.017 0.000 0.109

13

0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.030 0.017 0.043

0.017 0.043 0.069 0.096 0.017 0.083 0.030 0.017 0.017 0.056 0.056 0.017 0.109 0.000

14

0.000 0.082 0.017 0.017 0.030 0.017 0.017 0.017 0.017 0.017 0.017

0.017 0.043 0.056 0.056 0.017 0.043 0.069 0.043 0.043 0.030 0.056 0.030 0.017 0.017

15

0.082 0.000 0.017 0.017 0.056 0.017 0.017 0.017 0.017 0.017 0.017

0.017 0.043 0.056 0.056 0.017 0.043 0.069 0.043 0.043 0.030 0.056 0.030 0.017 0.017

16

0.017 0.017 0.000 0.017 0.043 0.017 0.017 0.017 0.017 0.017 0.017

0.017 0.017 0.043 0.017 0.017 0.017 0.017 0.030 0.030 0.017 0.017 0.017 0.095 0.095

17

0.017 0.017 0.017 0.000 0.017 0.017 0.017 0.017 0.017 0.017 0.017

0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.069 0.109 0.017 0.017 0.017 0.017 0.017

18

0.056 0.056 0.017 0.017 0.000 0.017 0.017 0.017 0.017 0.017 0.017

0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.043 0.017 0.017

19

0.017 0.017 0.017 0.017 0.017 0.000 0.017 0.017 0.030 0.017 0.017

0.043 0.017 0.030 0.017 0.017 0.017 0.017 0.056 0.069 0.017 0.017 0.017 0.017 0.017

20

0.017 0.017 0.017 0.017 0.017 0.030 0.000 0.017 0.017 0.017 0.017

0.030 0.017 0.030 0.017 0.017 0.017 0.017 0.043 0.043 0.017 0.017 0.017 0.017 0.017

21

0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.000 0.017 0.017 0.017

0.043 0.017 0.017 0.043 0.069 0.030 0.030 0.017 0.017 0.017 0.017 0.017 0.017 0.017

22

0.017 0.017 0.017 0.017 0.017 0.030 0.017 0.017 0.000 0.069 0.017

0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017

23

0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.069 0.000 0.017

0.043 0.017 0.043 0.017 0.017 0.017 0.030 0.043 0.043 0.017 0.017 0.017 0.017 0.017

24

0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.043 0.017 0.017 0.000

0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.017 0.043 0.043 0.017 0.030 0.030

25

760 Int J Adv Manuf Technol (2014) 73:749–771

Int J Adv Manuf Technol (2014) 73:749–771

761

Table 9 Matrix T for material flow 1

2

3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 a

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

38 38 6 160c

80 38

290b 80 38 38 80 80 6 160a

80

15

80

50 80

80 95f

50 38 38 15 114e

38

80+80=160

b

80+80+80+50=290

c

80+80=160

d

38+38=76

e

38+38+38=114

f

80+15=95

80 38 50

76d

38

0.039 0.072 0.105 0.087 0.062 0.067 0.069 0.118 0.068 0.068 0.071 0.053 0.075 0.068

0.132 0.132 0.048 0.053 0.058 0.080 0.074 0.051 0.055 0.069 0.055

1 2 3 4 5 6 7 8 9 10 11 12 13 14

15 16 17 18 19 20 21 22 23 24 25

1

0.130 0.130 0.048 0.052 0.057 0.079 0.073 0.051 0.053 0.056 0.055

0.055 0.054 0.104 0.086 0.061 0.066 0.068 0.117 0.067 0.067 0.070 0.053 0.074 0.067

2

0.140 0.140 0.052 0.057 0.062 0.097 0.079 0.056 0.060 0.073 0.061

0.061 0.081 0.073 0.100 0.091 0.076 0.075 0.124 0.074 0.075 0.079 0.057 0.106 0.099

3

0.155 0.155 0.057 0.063 0.068 0.093 0.088 0.062 0.065 0.065 0.070

0.067 0.093 0.101 0.101 0.102 0.108 0.107 0.096 0.080 0.148 0.126 0.063 0.117 0.110

4

0.148 0.148 0.054 0.059 0.065 0.089 0.083 0.058 0.061 0.063 0.075

0.087 0.132 0.130 0.162 0.055 0.077 0.079 0.094 0.076 0.081 0.083 0.060 0.086 0.079

5

Table 10 Matrix T for information flow

0.168 0.168 0.063 0.069 0.075 0.102 0.120 0.092 0.071 0.072 0.075

0.074 0.149 0.148 0.188 0.111 0.076 0.091 0.108 0.088 0.133 0.123 0.069 0.127 0.119

6

0.143 0.143 0.052 0.057 0.062 0.086 0.080 0.056 0.058 0.061 0.060

0.061 0.142 0.114 0.096 0.092 0.072 0.057 0.127 0.073 0.073 0.077 0.057 0.081 0.074

7

0.132 0.132 0.049 0.054 0.058 0.104 0.074 0.052 0.057 0.081 0.057

0.058 0.075 0.084 0.090 0.063 0.070 0.082 0.066 0.071 0.070 0.073 0.054 0.088 0.081

8

0.144 0.144 0.054 0.122 0.064 0.114 0.081 0.058 0.061 0.063 0.063

0.063 0.081 0.091 0.100 0.069 0.076 0.077 0.157 0.065 0.089 0.081 0.059 0.096 0.089

9

0.148 0.148 0.055 0.060 0.066 0.089 0.084 0.060 0.062 0.063 0.090

0.064 0.087 0.096 0.171 0.110 0.082 0.080 0.091 0.077 0.068 0.099 0.061 0.113 0.106

10

0.143 0.143 0.053 0.058 0.063 0.085 0.080 0.057 0.060 0.060 0.075

0.061 0.119 0.092 0.151 0.069 0.078 0.077 0.089 0.074 0.080 0.065 0.058 0.109 0.102

11

0.125 0.125 0.046 0.050 0.080 0.074 0.070 0.049 0.051 0.052 0.052

0.052 0.068 0.076 0.082 0.058 0.063 0.064 0.075 0.064 0.064 0.067 0.034 0.069 0.063

12

0.140 0.140 0.061 0.067 0.072 0.088 0.083 0.068 0.081 0.071 0.098

0.070 0.123 0.156 0.198 0.085 0.152 0.099 0.102 0.084 0.133 0.134 0.067 0.085 0.131

13

0.125 0.125 0.060 0.065 0.069 0.086 0.081 0.066 0.080 0.069 0.096

0.069 0.120 0.153 0.195 0.083 0.150 0.096 0.099 0.081 0.131 0.131 0.065 0.135 0.075

14

0.116 0.192 0.062 0.069 0.087 0.089 0.082 0.067 0.070 0.072 0.073

0.071 0.125 0.146 0.158 0.083 0.115 0.139 0.132 0.110 0.105 0.133 0.081 0.148 0.093

15

0.188 0.112 0.060 0.067 0.108 0.087 0.080 0.065 0.067 0.069 0.070

0.069 0.121 0.140 0.151 0.081 0.109 0.136 0.129 0.108 0.100 0.128 0.079 0.097 0.088

16

0.101 0.101 0.035 0.057 0.085 0.072 0.066 0.056 0.060 0.060 0.063

0.059 0.080 0.116 0.103 0.067 0.080 0.071 0.097 0.082 0.079 0.080 0.057 0.157 0.152

17

0.090 0.090 0.046 0.039 0.053 0.067 0.059 0.049 0.051 0.054 0.053

0.053 0.067 0.073 0.080 0.058 0.062 0.062 0.129 0.151 0.064 0.065 0.050 0.070 0.065

18

0.123 0.123 0.045 0.049 0.037 0.060 0.056 0.048 0.050 0.051 0.051

0.051 0.067 0.074 0.080 0.056 0.062 0.063 0.073 0.062 0.062 0.066 0.074 0.068 0.062

19

0.088 0.088 0.046 0.053 0.053 0.048 0.059 0.049 0.064 0.054 0.052

0.077 0.066 0.086 0.079 0.058 0.062 0.061 0.115 0.112 0.063 0.064 0.049 0.069 0.065

20

0.082 0.082 0.043 0.049 0.050 0.073 0.038 0.046 0.048 0.050 0.049

0.062 0.062 0.081 0.074 0.055 0.058 0.058 0.096 0.084 0.059 0.061 0.047 0.065 0.061

21

0.089 0.089 0.046 0.050 0.053 0.063 0.059 0.032 0.051 0.052 0.053

0.078 0.070 0.076 0.108 0.109 0.074 0.074 0.074 0.061 0.065 0.066 0.049 0.069 0.064

22

0.076 0.076 0.042 0.045 0.048 0.068 0.052 0.044 0.032 0.098 0.048

0.049 0.060 0.067 0.071 0.053 0.056 0.055 0.067 0.058 0.057 0.058 0.045 0.061 0.057

23

0.090 0.090 0.047 0.052 0.054 0.066 0.060 0.050 0.103 0.040 0.053

0.078 0.068 0.100 0.081 0.060 0.063 0.075 0.103 0.088 0.064 0.066 0.050 0.070 0.066

24

0.083 0.083 0.044 0.048 0.051 0.060 0.056 0.072 0.050 0.050 0.035

0.051 0.066 0.071 0.082 0.058 0.061 0.059 0.070 0.059 0.087 0.088 0.048 0.079 0.075

25

762 Int J Adv Manuf Technol (2014) 73:749–771

0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14

15 16 17 18 19 20 21 22 23 24 25

1

0 0 0 0 0 0.017 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

2

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

3

0.023 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0.037 0 0 0 0 0 0.073 0

4

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

5

0 0 0 0 0 0 0 0 0.037 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

6

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0.037 0

7

Table 11 Normalized T matrix for material flow

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

8

0 0 0 0.017 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

9

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0.037 0

10

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

11

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

12

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0.133 0 0 0 0 0.037 0 0 0

13

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0.073 0 0 0 0 0 0 0 0 0 0

14

0 0 0 0 0.007 0.000 0 0 0 0 0.023

0 0 0 0.037 0 0 0 0.017 0 0.037 0 0 0 0.037

15

0 0 0 0 0 0 0 0 0 0 0

0 0 0.003 0 0 0 0 0 0 0 0 0.003 0 0.037

16

0 0 0 0 0 0 0 0 0 0.017 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

17

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

18

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0.007 0 0

19

0 0 0.017 0 0 0 0 0 0 0.035 0

0.017 0 0 0 0 0 0 0 0 0 0 0 0 0

20

0 0 0 0 0 0.052 0 0 0 0 0

0 0.017 0 0 0 0 0 0 0 0 0 0 0 0

21

0.043 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

22

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

23

0.017 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0.017 0 0 0 0.017 0 0 0 0 0

24

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0.023 0

25

Int J Adv Manuf Technol (2014) 73:749–771 763

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

0.0014 0.0025 0.0029 0.0032 0.0017 0.0023 0.0028 0.0026 0.0022 0.0021 0.0027 0.0016 0.0030 0.0019 0.0023 0.0038

15

0.0008 0.0014 0.0021 0.0017 0.0012 0.0013 0.0014 0.0024 0.0014 0.0013 0.0014 0.0011 0.0015 0.0014 0.0026 0.0026 0.0010 0.0011 0.0011 0.0016 0.0015 0.0010 0.0011 0.0014 0.0011

1

0.0011 0.0011 0.0021 0.0017 0.0012 0.0013 0.0014 0.0023 0.0013 0.0013 0.0014 0.0010 0.0015 0.0013 0.0026 0.0026 0.0010 0.0010 0.0011 0.0016 0.0015 0.0010 0.0011 0.0011 0.0011

2

0.0014 0.0024 0.0028 0.0030 0.0016 0.0022 0.0027 0.0026 0.0021 0.0020 0.0026 0.0016 0.0019 0.0018 0.0037 0.0022

16

0.0012 0.0016 0.0015 0.0020 0.0018 0.0015 0.0015 0.0025 0.0015 0.0015 0.0016 0.0011 0.0021 0.0020 0.0028 0.0028 0.0010 0.0011 0.0012 0.0019 0.0016 0.0011 0.0012 0.0014 0.0012

3

0.0012 0.0016 0.0023 0.0021 0.0013 0.0016 0.0014 0.0019 0.0016 0.0016 0.0016 0.0011 0.0031 0.0030 0.0020 0.0020

17

0.0013 0.0019 0.0020 0.0020 0.0020 0.0022 0.0021 0.0019 0.0016 0.0029 0.0025 0.0013 0.0023 0.0022 0.0031 0.0031 0.0011 0.0012 0.0014 0.0018 0.0018 0.0012 0.0013 0.0013 0.0014

4

Table 12 Normalized T matrix for information flow

0.0011 0.0013 0.0015 0.0016 0.0012 0.0012 0.0012 0.0026 0.0030 0.0013 0.0013 0.0010 0.0014 0.0013 0.0018 0.0018

18

0.0017 0.0026 0.0026 0.0032 0.0011 0.0015 0.0016 0.0019 0.0015 0.0016 0.0017 0.0012 0.0017 0.0016 0.0030 0.0030 0.0011 0.0012 0.0013 0.0018 0.0017 0.0012 0.0012 0.0012 0.0015

5

0.0010 0.0013 0.0015 0.0016 0.0011 0.0012 0.0013 0.0014 0.0012 0.0012 0.0013 0.0015 0.0014 0.0012 0.0025 0.0025

19

0.0015 0.0030 0.0029 0.0037 0.0022 0.0015 0.0018 0.0021 0.0018 0.0027 0.0025 0.0014 0.0025 0.0024 0.0034 0.0034 0.0013 0.0014 0.0015 0.0020 0.0024 0.0018 0.0014 0.0014 0.0015

6 0.0012 0.0028 0.0023 0.0019 0.0018 0.0014 0.0011 0.0025 0.0015 0.0015 0.0015 0.0011 0.0016 0.0015 0.0028 0.0028 0.0010 0.0011 0.0012 0.0017 0.0016 0.0011 0.0012 0.0012 0.0012

7

0.0015 0.0013 0.0017 0.0016 0.0012 0.0012 0.0012 0.0023 0.0022 0.0013 0.0013 0.0010 0.0014 0.0013 0.0018 0.0018

20

0.0011 0.0015 0.0017 0.0018 0.0012 0.0014 0.0016 0.0013 0.0014 0.0014 0.0015 0.0011 0.0017 0.0016 0.0026 0.0026 0.0010 0.0011 0.0012 0.0021 0.0015 0.0010 0.0011 0.0016 0.0011

8

0.0012 0.0012 0.0016 0.0015 0.0011 0.0012 0.0011 0.0019 0.0017 0.0012 0.0012 0.0009 0.0013 0.0012 0.0016 0.0016

21

0.0013 0.0016 0.0018 0.0020 0.0014 0.0015 0.0015 0.0031 0.0013 0.0018 0.0016 0.0012 0.0019 0.0018 0.0029 0.0029 0.0011 0.0024 0.0013 0.0023 0.0016 0.0011 0.0012 0.0013 0.0013

9

0.0016 0.0014 0.0015 0.0022 0.0022 0.0015 0.0015 0.0015 0.0012 0.0013 0.0013 0.0010 0.0014 0.0013 0.0018 0.0018

22

0.0013 0.0017 0.0019 0.0034 0.0022 0.0016 0.0016 0.0018 0.0015 0.0013 0.0020 0.0012 0.0023 0.0021 0.0030 0.0030 0.0011 0.0012 0.0013 0.0018 0.0017 0.0012 0.0012 0.0012 0.0018

10

0.0010 0.0012 0.0013 0.0014 0.0010 0.0011 0.0011 0.0013 0.0011 0.0011 0.0012 0.0009 0.0012 0.0011 0.0015 0.0015

23

0.0012 0.0024 0.0018 0.0030 0.0014 0.0016 0.0015 0.0018 0.0015 0.0016 0.0013 0.0012 0.0022 0.0020 0.0028 0.0028 0.0011 0.0012 0.0013 0.0017 0.0016 0.0011 0.0012 0.0012 0.0015

11 0.0010 0.0014 0.0015 0.0016 0.0012 0.0013 0.0013 0.0015 0.0013 0.0013 0.0013 0.0007 0.0014 0.0013 0.0025 0.0025 0.0009 0.0010 0.0016 0.0015 0.0014 0.0010 0.0010 0.0010 0.0010

12

0.0016 0.0014 0.0020 0.0016 0.0012 0.0012 0.0015 0.0021 0.0018 0.0013 0.0013 0.0010 0.0014 0.0013 0.0018 0.0018

24

0.0014 0.0024 0.0031 0.0040 0.0017 0.0030 0.0020 0.0020 0.0017 0.0027 0.0027 0.0013 0.0017 0.0026 0.0028 0.0028 0.0012 0.0013 0.0014 0.0018 0.0017 0.0014 0.0016 0.0014 0.0020

13

0.0010 0.0013 0.0014 0.0016 0.0012 0.0012 0.0012 0.0014 0.0012 0.0017 0.0018 0.0009 0.0016 0.0015 0.0017 0.0017

25

0.0014 0.0024 0.0030 0.0039 0.0017 0.0030 0.0019 0.0020 0.0016 0.0026 0.0026 0.0013 0.0027 0.0015 0.0025 0.0025 0.0012 0.0013 0.0014 0.0017 0.0016 0.0013 0.0016 0.0014 0.0019

14

764 Int J Adv Manuf Technol (2014) 73:749–771

17 18 19 20 21 22 23 24 25

0.0012 0.0014 0.0017 0.0018 0.0016 0.0013 0.0014 0.0014 0.0015

15

Table 12 (continued)

0.0012 0.0013 0.0022 0.0017 0.0016 0.0013 0.0013 0.0014 0.0014

16 0.0007 0.0011 0.0017 0.0014 0.0013 0.0011 0.0012 0.0012 0.0013

17 0.0009 0.0008 0.0011 0.0013 0.0012 0.0010 0.0010 0.0011 0.0011

18 0.0009 0.0010 0.0007 0.0012 0.0011 0.0009 0.0010 0.0010 0.0010

19 0.0009 0.0011 0.0011 0.0010 0.0012 0.0010 0.0013 0.0011 0.0010

20 0.0009 0.0010 0.0010 0.0014 0.0008 0.0009 0.0010 0.0010 0.0010

21 0.0009 0.0010 0.0010 0.0013 0.0012 0.0006 0.0010 0.0010 0.0011

22 0.0008 0.0009 0.0010 0.0014 0.0010 0.0009 0.0006 0.0019 0.0009

23 0.0009 0.0010 0.0011 0.0013 0.0012 0.0010 0.0020 0.0008 0.0011

24

0.0009 0.0010 0.0010 0.0012 0.0011 0.0014 0.0010 0.0010 0.0007

25

Int J Adv Manuf Technol (2014) 73:749–771 765

0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14

15 16 17 18 19 20 21 22 23 24 25

1

0 0 0 0 0 0.006 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

2

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

3

0.008 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0.013 0 0 0 0 0 0.026 0

4

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

5

Table 13 Matrix K for material flow

0 0 0 0 0 0 0 0 0.013 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

6

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0.013 0

7

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

8

0 0 0 0.006 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

9

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0.013 0

10

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

11

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

12

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0.046 0 0 0 0 0.013 0 0 0

13

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0.026 0 0 0 0 0 0 0 0 0 0

14

0 0 0 0 0.002 0 0 0 0 0 0.008

0 0 0 0.013 0 0 0 0.006 0 0.013 0 0 0 0.013

15

0 0 0 0 0 0 0 0 0 0 0

0 0 0.001 0 0 0 0 0 0 0 0 0.001 0 0.013

16

0 0 0 0 0 0 0 0 0 0.006 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

17

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

18

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0.002 0 0

19

0 0 0.006 0 0 0 0 0 0 0.012 0

0.006 0 0 0 0 0 0 0 0 0 0 0 0 0

20

0 0 0 0 0 0.018 0 0 0 0 0

0 0.006 0 0 0 0 0 0 0 0 0 0 0 0

21

0.015 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

22

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0

23

0.006 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0.006 0 0 0 0.006 0 0 0 0 0

24

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0.008 0

25

766 Int J Adv Manuf Technol (2014) 73:749–771

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

0.00025 0.00044 0.00051 0.00055 0.00029 0.00040 0.00049 0.00046 0.00038 0.00037 0.00046 0.00028 0.00052 0.00032 0.00040 0.00067

15

0.00014 0.00025 0.00037 0.00030 0.00022 0.00023 0.00024 0.00041 0.00024 0.00024 0.00025 0.00019 0.00026 0.00024 0.00046 0.00046 0.00017 0.00018 0.00020 0.00028 0.00026 0.00018 0.00019 0.00024 0.00019

1 0.00021 0.00028 0.00026 0.00035 0.00032 0.00026 0.00026 0.00043 0.00026 0.00026 0.00027 0.00020 0.00037 0.00035 0.00049 0.00049 0.00018 0.00020 0.00022 0.00034 0.00027 0.00019 0.00021 0.00025 0.00021

3

0.00024 0.00042 0.00049 0.00053 0.00028 0.00038 0.00047 0.00045 0.00038 0.00035 0.00045 0.00028 0.00034 0.00031 0.00065 0.00039

16

0.00019 0.00019 0.00036 0.00030 0.00021 0.00023 0.00024 0.00041 0.00023 0.00023 0.00025 0.00018 0.00026 0.00023 0.00045 0.00045 0.00017 0.00018 0.00020 0.00027 0.00025 0.00018 0.00019 0.00019 0.00019

2

Table 14 Matrix K for information flow

0.00021 0.00028 0.00040 0.00036 0.00023 0.00028 0.00025 0.00034 0.00029 0.00027 0.00028 0.00020 0.00055 0.00053 0.00035 0.00035

17

0.00023 0.00033 0.00035 0.00035 0.00036 0.00038 0.00037 0.00033 0.00028 0.00051 0.00044 0.00022 0.00041 0.00038 0.00054 0.00054 0.00020 0.00022 0.00024 0.00032 0.00031 0.00022 0.00023 0.00023 0.00024

4

0.00018 0.00023 0.00026 0.00028 0.00020 0.00022 0.00022 0.00045 0.00053 0.00022 0.00023 0.00017 0.00024 0.00023 0.00031 0.00031

18

0.00030 0.00046 0.00045 0.00057 0.00019 0.00027 0.00027 0.00033 0.00027 0.00028 0.00029 0.00021 0.00030 0.00027 0.00052 0.00052 0.00019 0.00021 0.00023 0.00031 0.00029 0.00020 0.00021 0.00022 0.00026

5

0.00018 0.00023 0.00026 0.00028 0.00020 0.00022 0.00022 0.00025 0.00021 0.00022 0.00023 0.00026 0.00024 0.00022 0.00043 0.00043

19

0.00026 0.00052 0.00052 0.00066 0.00039 0.00026 0.00032 0.00038 0.00031 0.00046 0.00043 0.00024 0.00044 0.00041 0.00059 0.00059 0.00022 0.00024 0.00026 0.00036 0.00042 0.00032 0.00025 0.00025 0.00026

6 0.00021 0.00050 0.00040 0.00033 0.00032 0.00025 0.00020 0.00044 0.00026 0.00025 0.00027 0.00020 0.00028 0.00026 0.00050 0.00050 0.00018 0.00020 0.00022 0.00030 0.00028 0.00019 0.00020 0.00021 0.00021

7

0.00027 0.00023 0.00030 0.00028 0.00020 0.00021 0.00021 0.00040 0.00039 0.00022 0.00022 0.00017 0.00024 0.00023 0.00031 0.00031

20

0.00020 0.00026 0.00029 0.00031 0.00022 0.00024 0.00029 0.00023 0.00025 0.00024 0.00026 0.00019 0.00031 0.00028 0.00046 0.00046 0.00017 0.00019 0.00020 0.00036 0.00026 0.00018 0.00020 0.00028 0.00020

8

0.00022 0.00022 0.00028 0.00026 0.00019 0.00020 0.00020 0.00034 0.00029 0.00021 0.00021 0.00016 0.00023 0.00021 0.00028 0.00028

21

0.00022 0.00028 0.00032 0.00035 0.00024 0.00027 0.00027 0.00055 0.00023 0.00031 0.00028 0.00021 0.00034 0.00031 0.00050 0.00050 0.00019 0.00043 0.00022 0.00040 0.00028 0.00020 0.00021 0.00022 0.00022

9

0.00027 0.00024 0.00026 0.00038 0.00038 0.00026 0.00026 0.00026 0.00021 0.00023 0.00023 0.00017 0.00024 0.00022 0.00031 0.00031

22

0.00022 0.00030 0.00033 0.00060 0.00038 0.00029 0.00028 0.00032 0.00027 0.00024 0.00035 0.00021 0.00039 0.00037 0.00052 0.00052 0.00019 0.00021 0.00023 0.00031 0.00029 0.00021 0.00022 0.00022 0.00031

10 0.00018 0.00024 0.00026 0.00029 0.00020 0.00022 0.00022 0.00026 0.00022 0.00022 0.00023 0.00012 0.00024 0.00022 0.00044 0.00044 0.00016 0.00017 0.00028 0.00026 0.00024 0.00017 0.00018 0.00018 0.00018

12

0.00017 0.00021 0.00023 0.00025 0.00018 0.00019 0.00019 0.00024 0.00020 0.00020 0.00020 0.00016 0.00021 0.00020 0.00026 0.00026

23

0.00021 0.00041 0.00032 0.00053 0.00024 0.00027 0.00027 0.00031 0.00026 0.00028 0.00023 0.00020 0.00038 0.00035 0.00050 0.00050 0.00018 0.00020 0.00022 0.00030 0.00028 0.00020 0.00021 0.00021 0.00026

11

0.00027 0.00024 0.00035 0.00028 0.00021 0.00022 0.00026 0.00036 0.00031 0.00022 0.00023 0.00018 0.00024 0.00023 0.00031 0.00031

24

0.00025 0.00043 0.00054 0.00069 0.00030 0.00053 0.00035 0.00036 0.00029 0.00047 0.00047 0.00023 0.00029 0.00046 0.00049 0.00049 0.00021 0.00023 0.00025 0.00031 0.00029 0.00024 0.00028 0.00025 0.00034

13

0.00018 0.00023 0.00025 0.00029 0.00020 0.00021 0.00021 0.00024 0.00021 0.00030 0.00031 0.00017 0.00028 0.00026 0.00029 0.00029

25

0.00024 0.00042 0.00053 0.00068 0.00029 0.00052 0.00033 0.00035 0.00028 0.00046 0.00046 0.00023 0.00047 0.00026 0.00043 0.00043 0.00021 0.00023 0.00024 0.00030 0.00028 0.00023 0.00028 0.00024 0.00034

14

Int J Adv Manuf Technol (2014) 73:749–771 767

17 18 19 20 21 22 23 24 25

0.00022 0.00024 0.00030 0.00031 0.00029 0.00023 0.00024 0.00025 0.00026

15

Table 14 (continued)

0.00021 0.00023 0.00038 0.00030 0.00028 0.00023 0.00023 0.00024 0.00024

16 0.00012 0.00020 0.00030 0.00025 0.00023 0.00019 0.00021 0.00021 0.00022

17 0.00016 0.00014 0.00019 0.00023 0.00021 0.00017 0.00018 0.00019 0.00018

18 0.00016 0.00017 0.00013 0.00021 0.00020 0.00017 0.00017 0.00018 0.00018

19 0.00016 0.00018 0.00018 0.00017 0.00020 0.00017 0.00022 0.00019 0.00018

20 0.00015 0.00017 0.00017 0.00025 0.00013 0.00016 0.00017 0.00017 0.00017

21 0.00016 0.00017 0.00018 0.00022 0.00021 0.00011 0.00018 0.00018 0.00018

22 0.00015 0.00016 0.00017 0.00024 0.00018 0.00015 0.00011 0.00034 0.00017

23 0.00016 0.00018 0.00019 0.00023 0.00021 0.00017 0.00036 0.00014 0.00019

24

0.00015 0.00017 0.00018 0.00021 0.00019 0.00025 0.00017 0.00017 0.00012

25

768 Int J Adv Manuf Technol (2014) 73:749–771

1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

0.1202 0.1421 0.1488 1.4361 0.1236 0.1349 0.1432 0.7504 0.1348 1.4081 0.1402 0.1163

15

0.1160 0.1513 0.1581 0.1523 0.1336 0.1355 0.1362 0.1549 0.1374 0.1323 0.1361 0.1244 0.1270 0.1230 0.1396 0.1393 0.1137 0.1001 0.1071 0.1152 0.1099 0.1071 0.1048 0.1056 0.1057

1

0.1426 0.1241 0.1577 0.1520 0.1334 0.1352 0.1358 0.1545 0.1370 0.1320 0.1358 0.1242 0.1267 0.1228 0.1392 0.1389 0.1135 0.0998 0.1069 0.7231 0.1097 0.1069 0.1044 0.1011 0.1054

2

0.1193 0.1404 0.2426 0.1529 0.1224 0.1326 0.1418 0.1409 0.1336 0.1259 0.1383 0.2116

16

0.1397 0.1490 0.1294 0.1557 0.1432 0.1378 0.1376 0.1563 0.1387 0.1343 0.1380 0.1252 0.1371 0.1330 0.1417 0.1414 0.1141 0.1009 0.1079 0.1205 0.1109 0.1078 0.1058 0.1064 0.1070

3

Table 15 Closeness rating matrix (×10−2)

0.1111 0.1218 0.1337 0.1342 0.1127 0.1181 0.1143 0.1250 0.1199 0.1140 0.1177 0.1040

17

0.1346 0.1465 0.1531 0.1400 0.1517 0.1516 1.4280 0.1454 0.1399 0.1587 0.1580 0.1265 2.7007 0.1358 0.9463 0.1458 0.1153 0.1021 0.1093 0.1184 0.1135 0.1094 0.1070 0.1031 0.1093

4

0.0995 0.1068 0.1086 0.1130 0.1005 0.1021 0.1019 0.1267 0.1343 0.0999 0.1023 0.0926

18

0.1447 0.1633 0.1666 0.1862 0.1216 0.1462 0.1408 0.1478 0.1416 0.1381 0.1418 0.1280 0.1327 0.1285 0.1468 0.1465 0.1176 0.1036 0.1111 0.1199 0.1146 0.1202 0.1084 0.1048 0.1151

5

0.0988 0.1067 0.1087 0.1131 0.0999 0.1020 0.1023 0.1070 0.1031 0.0992 0.1026 0.3411

19

0.1411 0.1702 0.1783 0.1923 0.1588 0.1313 0.1462 0.1536 0.1469 0.1573 0.1567 0.1321 0.1484 0.1438 0.1549 0.1545 0.1219 0.1078 0.1156 0.1255 0.1445 0.1242 1.3934 0.1090 0.1152

6 0.1346 0.1743 0.1549 0.1512 0.1440 0.1374 0.1214 0.1640 0.1452 0.1342 0.1380 0.1259 1.4094 0.1250 0.1435 0.1431 0.1151 0.1016 0.1087 0.1175 0.1120 0.1086 0.1062 0.1029 0.1074

7

0.7219 0.1127 0.1190 0.1192 0.1060 0.1077 0.1073 0.1275 0.1266 0.1052 0.1081 0.0980

20

0.1349 0.1524 0.1460 0.1511 0.1353 0.1379 0.1482 0.1281 0.1548 0.1343 0.1382 0.1260 0.1335 0.1295 0.1412 0.1408 0.1159 0.1017 0.1089 0.1254 0.1117 0.1091 0.1071 0.1113 0.1078

8

0.1042 0.7152 0.1138 0.1131 0.1007 0.1113 0.1018 0.1169 0.1125 0.0997 0.1025 0.0929

21

0.1351 0.1450 0.1471 0.1525 0.1363 0.1389 0.1453 0.1835 0.1267 0.1399 0.1394 0.1267 0.1348 0.1306 0.1439 0.1436 0.1159 0.7327 0.1096 0.1272 0.1127 0.1095 0.1072 0.1038 0.1085

9

0.1126 0.1126 0.1141 0.1277 0.1225 0.1107 0.1102 0.1118 0.1074 0.1043 0.1082 0.0965

22

0.1313 0.1417 0.1446 0.1770 0.1462 0.1366 0.1360 0.1412 0.1363 0.1171 0.1474 0.1235 1.4163 0.1317 0.1412 0.1409 0.1120 0.0992 0.1060 0.1148 0.1097 0.1063 0.1039 0.1001 0.1143

10

0.1039 0.1105 0.1125 0.1165 0.1042 0.1057 0.1053 0.1111 0.1076 0.1030 0.1060 0.0965

23

0.1294 0.1519 0.1421 0.1647 0.1313 0.1347 0.1341 0.1396 0.1345 0.1376 0.1179 0.1220 0.1336 0.1294 0.1385 0.1382 0.1103 0.0977 0.1044 0.1129 0.1079 0.1046 0.1023 0.0985 0.1081

11 0.1246 0.1325 0.1347 0.1390 0.1256 0.1277 0.1280 0.1331 0.1292 0.1250 0.1284 0.1004 0.1181 0.1139 0.1303 0.1300 0.1101 0.0932 0.1082 0.1072 0.1024 0.1001 0.0975 0.0939 0.0987

12

0.1083 0.1072 0.1178 0.1132 0.7091 0.1022 0.1063 0.1176 0.7205 0.0998 0.1025 0.0927

24

0.1270 0.1488 0.1601 0.1831 0.1309 4.7959 0.1359 0.1391 0.1325 0.1442 1.4282 0.1180 0.1339 0.1928 0.1428 0.1423 0.1510 0.1049 0.1129 0.1182 0.1140 0.1132 0.1147 0.1064 0.1209

13

0.1048 0.1129 0.1144 0.1208 0.1063 0.1080 0.1067 0.1121 0.1084 0.1135 0.1259 0.0976

25

0.1254 0.1468 0.1579 2.7414 0.1293 0.1530 0.1338 0.1370 0.1306 0.1425 0.1458 0.1164 0.1944 0.1288 0.1366 0.1362 0.1459 0.1038 0.1115 0.1168 0.1127 0.1120 0.1135 0.1052 0.1197

14

Int J Adv Manuf Technol (2014) 73:749–771 769

0.1081 0.0984 0.0863 0.0923 0.0954 0.0919 0.1260 0.0907 0.0870 0.0808 0.1164 0.0919 0.0815 0.0741 0.0899 0.0865 0.0869 0.0851 0.0822 0.0860

0.1093 0.7061 0.0874 0.0922 0.0859 0.0920 0.0990 0.1173 1.3040 0.0918

0.1036 0.0935 0.0830 0.0881 1.9203 0.0752 0.0882 0.0864 0.0835 0.0871

0.1083 0.0967 0.0852 0.0911 0.0946 0.0912 0.0802 0.0893 0.0861 0.1127

0.1049 0.0966 0.0848 0.0905 0.1266 0.0897 0.0917 0.0790 0.1030 0.0897

0.1047 0.0926 0.0828 0.0878 0.0919 0.0876 0.0876 0.1035 0.0706 0.0868

References

The results are multiplied by 100 in order to improve readability

0.1047 0.0924 0.0702 0.0877 0.0923 0.0876 0.0874 0.0857 0.0833 0.0866 0.1179 0.0984 0.0926 0.1078 0.1033 0.0991 0.0996 0.0980 0.7016 0.0996 0.1923 0.1118 0.1001 0.3649 0.1123 0.1076 0.1061 0.1043 0.1010 0.9061 16 17 18 19 20 21 22 23 24 25

0.1233 0.1109 0.0991 0.1282 0.1111 0.1064 0.1051 0.1031 0.1000 0.1045

0.1040 0.1016 0.7131 0.1068 0.1045 0.1052 0.1081 0.1056 1.6290 0.1042 0.1019 0.1040 0.1094 0.1070 0.1096 0.1033 0.1003 0.1167 0.1040 0.1015 0.1050 0.1740 0.1659 0.1183 0.1280 1.4041 0.1933 0.1460 1.4061 0.1253 13 14 15

24 23 22 21 20 19 18 17 16 15

Table 15 (continued)

0.9142 0.1117 0.1084

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25

770

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