An overview Company

Company chosen for this research study is a famous open frame manufacturing industry located in the United States California. The company planned to improve the quality of the product. They planned to purchase the quality raw material at low cost and at a short duration of time. Instead of purchasing the material from the single supplier they noted that five alternative suppliers, namely supplier 1 (S1), supplier 2 (S2), supplier 3 (S3), supplier 4 (S4), and supplier 5 (S5) were taken into consideration. Top manager of te company needs to decide to choose the most preferred supplier among these suppliers based on the quality and the fuzzy sample data. Let us consider the fuzzy sample data of the light transmission rate with size 20 have been collected from each supplier listed in Table 4.

Table 4: Triangular fuzzy data collected from the suppliers (unit: %)

S1 S2 S3 S4 S5

( 87, 90, 93 ) ( 90, 93, 94 ) ( 88, 91, 92 ) ( 89, 90, 91 ) ( 88, 91, 92 ) ( 88, 92, 93 ) ( 91, 92, 95 ) ( 89, 90, 93 ) ( 91, 92, 94 ) ( 89, 91, 93 ) ( 89, 92, 95 ) ( 88, 91, 95 ) ( 86, 89, 92 ) ( 87, 89, 91 ) ( 86, 89, 92 ) ( 90, 91, 92 ) ( 90, 91, 92 ) ( 90, 91, 92 ) ( 85, 89, 97 ) ( 89, 90, 91 ) ( 86, 90, 93 ) ( 91, 92, 95 ) ( 89, 90, 93 ) ( 90, 92, 93 ) ( 88, 91, 93 ) ( 88, 91, 92 ) ( 92, 93, 94 ) ( 90, 91, 92 ) ( 85, 89, 97 ) ( 90, 91, 92 ) ( 90, 93, 94 ) ( 92, 94, 95 ) ( 80, 82, 83 ) ( 91, 92, 93 ) ( 91, 92, 93 ) ( 90, 91, 92 ) ( 91, 93, 94 ) ( 89, 91, 92 ) ( 88, 89, 96 ) ( 89, 91, 92 )

15

( 88, 91, 93 ) ( 91, 93, 94 ) ( 89, 91, 92 ) ( 90, 91, 95 ) ( 90, 91, 92 ) ( 88, 92, 93 ) ( 90, 91, 92 ) ( 88, 89, 90 ) ( 77, 79, 83 ) ( 88, 89, 90 ) ( 89, 90, 93 ) ( 91, 92, 93 ) ( 89, 90, 91 ) ( 92, 93, 94 ) ( 82, 86, 88 ) ( 93, 94, 95 ) ( 93, 94, 96 ) ( 91, 92, 94 ) ( 91, 92, 95 ) ( 90, 91, 92 ) ( 88, 90, 92 ) ( 89, 91, 93 ) ( 87, 89, 91 ) ( 90, 91, 95 ) ( 88, 90, 91 ) ( 86, 89, 90 ) ( 87, 91, 92 ) ( 85, 89, 90 ) ( 90, 91, 92 ) ( 85, 89, 90 ) ( 91, 93, 94 ) ( 92, 94, 95 ) ( 90, 92, 93 ) ( 91, 92, 95 ) ( 91, 92, 94 ) ( 88, 89, 92 ) ( 88, 91, 94 ) ( 86, 89, 92 ) ( 92, 93, 94 ) ( 88, 89, 92 ) ( 90, 92, 93 ) ( 93, 94, 95 ) ( 91, 92, 93 ) ( 92, 94, 95 ) ( 90, 92, 93 ) ( 89, 91, 92 ) ( 90, 91, 92 ) ( 88, 89, 90 ) ( 91, 93, 94 ) ( 89, 90, 91 ) ( 89, 91, 93 ) ( 90, 93, 94 ) ( 88, 91, 92 ) ( 91, 93, 94 ) ( 89, 90, 92 ) ( 80,85, 89 ) ( 79, 81, 85 ) ( 77, 79, 83 ) ( 90, 91, 92 ) ( 87, 89, 90 )

The upper and lower specification limits of light transmission rate are set as USL = 95%

and LSL = 85% respectively. And the target value is set at τ= 90%. Then the estimates of statistics

x

_iα^L ,

s

_i^L_α , cˆ^L_pmiα

x

_i^U_α ,

s

_i^U_α , and cˆ^U_pmiα in the α-level sense of the five suppliers are shown in Table 5.

Table 5: The α-level estimates of C_pmi S1

α-level ^L

xi_α s_i^L_α cˆ^L_pmiα x_i^U_α s_i^U_α cˆ^U_pmiα

0.0 88.35 2.56 0.44 92.65 1.42 0.55

0.1 88.60 2.48 0.48 92.47 1.45 0.58

0.2 88.85 2.40 0.54 92.29 1.48 0.61

0.3 89.10 2.32 0.59 92.11 1.51 0.64

0.4 89.35 2.24 0.65 91.93 1.56 0.66

0.5 89.60 2.17 0.71 91.75 1.60 0.68

0.6 89.85 2.11 0.77 91.57 1.65 0.69

0.7 90.10 2.05 0.80 91.39 1.71 0.70

0.8 90.35 1.99 0.78 91.21 1.77 0.71

0.9 90.60 1.94 0.75 91.03 1.83 0.72

1.0 90.85 1.90 0.73 90.85 1.90 0.73

S2

α-level ^L

xi_α s_i^L_α cˆ^L_pmiα x_i^U_α s_i^U_α cˆ^U_pmiα

0.0 89.90 3.02 0.54 93.45 2.33 0.22

0.1 90.09 2.99 0.55 93.28 2.36 0.24

0.2 90.27 2.96 0.53 93.11 2.39 0.26

0.3 90.46 2.92 0.52 92.94 2.43 0.28

0.4 90.64 2.90 0.50 92.77 2.47 0.30

0.5 90.83 2.87 0.48 92.60 2.51 0.32

0.6 91.01 2.85 0.47 92.43 2.56 0.33

0.7 91.20 2.83 0.45 92.26 2.61 0.35

0.8 91.38 2.81 0.43 92.09 2.67 0.36

0.9 91.57 2.80 0.41 91.92 2.73 0.38

1.0 91.75 2.79 0.39 91.75 2.79 0.39

S3

α-level ^L

xi_α s_i^L_α cˆ^L_pmiα x_i^U_α s_i^U_α cˆ^U_pmiα

0.0 87.50 3.50 0.24 91.00 2.94 0.45

0.1 87.69 3.47 0.26 90.84 2.96 0.47

0.2 87.87 3.43 0.28 90.67 2.98 0.48

0.3 88.06 3.40 0.30 90.51 3.00 0.50

0.4 88.24 3.37 0.32 90.34 3.03 0.51

0.5 88.43 3.35 0.34 90.18 3.06 0.53

0.6 88.61 3.32 0.36 90.01 3.09 0.54

0.7 88.80 3.30 0.38 89.85 3.13 0.52

0.8 88.98 3.28 0.40 89.68 3.16 0.49

0.9 89.17 3.26 0.43 89.52 3.21 0.47

1.0 89.35 3.25 0.45 89.35 3.25 0.45

S4

α-level ^L

xi_α s_i^L_α c^ˆLpmi_α x_i^U_α s_i^U_α c^ˆUpmi_α

0.0 89.15 3.53 0.39 93.50 3.00 0.17

0.1 89.31 3.48 0.41 93.23 2.93 0.20

16

0.2 89.47 3.44 0.43 92.95 2.88 0.24

0.3 89.63 3.39 0.45 92.68 2.84 0.27

0.4 89.79 3.35 0.48 92.40 2.83 0.31

0.5 89.95 3.32 0.50 92.13 2.84 0.34

0.6 90.11 3.28 0.50 91.85 2.86 0.37

0.7 90.27 3.25 0.49 91.58 2.91 0.39

0.8 90.43 3.22 0.47 91.30 2.98 0.41

0.9 90.59 3.19 0.46 91.03 3.06 0.43

1.0 90.75 3.16 0.45 90.75 3.16 0.45

S5

α-level ^L

xi_α s_i^L_α cˆ^L_pmiα x_i^U_α s_i^U_α cˆ^U_pmiα

0.0 88.35 2.13 0.52 91.65 1.39 0.81

0.1 88.54 2.05 0.57 91.51 1.38 0.85

0.2 88.72 1.97 0.63 91.36 1.37 0.89

0.3 88.91 1.89 0.69 91.22 1.37 0.92

0.4 89.09 1.82 0.75 91.07 1.37 0.96

0.5 89.28 1.74 0.82 90.93 1.37 0.99

0.6 89.46 1.67 0.89 90.78 1.38 1.02

0.7 89.65 1.61 0.96 90.64 1.39 1.05

0.8 89.83 1.55 1.04 90.49 1.40 1.07

0.9 90.02 1.49 1.12 90.35 1.42 1.10

1.0 90.20 1.44 1.11 90.20 1.44 1.11

5.3 Result Analysis

Using the commercial software MATLAB, can calculate the α-level sets, the graphs of membership functions of fuzzy estimates ˆ

c

_pmi for i =1 ,…, 5 can be constructed and shown as Fig. 8.

After pair-wise comparisons were obtained and entered into data matrices. The value of Δ and ij Δ are tabulated in the 2nd and 3rd column in Table 7, and the values of the fuzzy _ji preference relation FPR

( ^c

^ˆpmi,

^c

^ˆpmj

)

^{and FPR}

( ^c

^ˆpmj,

^c

^ˆpmi

)

^{=1- FPR}

( ^c

^ˆpmi,

^c

^ˆpmj

)

for i =1,2,3,4 and i

< j are tabulated in the 4th and 5th column in Table 7.

Table 7 : Value of the fuzzy preference relation

Pairwise Comparison

Δij Δ_ji FPR

(

^{cˆpmi,cˆpmj}

)

^FPR

(

^{cˆpmj,cˆpmi}

)

S1 and S2 ( i=1 and j=2 ) 0.7635 0.0373 0.9534 0.0466 S1 and S3 ( i=1 and j=3 ) 0.7623 0.0343 0.9569 0.0431 S₁ and S₄ ( i=1 and j=4 ) 0.7509 0.0287 0.9632 0.0368 S₁ and S₅ ( i=1 and j=5 ) 0.1047 1.0211 0.0930 0.9070 S2 and S3 ( i=2 and j=3 ) 0.1664 0.1646 0.5028 0.4972

0.4 0.6 0.8 1 1.2 1.4 1.6

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Cpm

Figure 8 : The membership functions of fuzzy estimates of 5 suppliers S1 S5

S2 S3

S4

α

S1 S2

S4 S5 S3

17

S₂ and S₄ ( i=2 and j=4 ) 0.1589 0.1629 0.4938 0.5062 S2 and S5 ( i=2 and j=5 ) 0.0105 1.3105 0.0079 0.9921 S3 and S4 ( i=3 and j=4 ) 0.1492 0.1550 0.4904 0.5096 S₃ and S₅ ( i=3 and j=5 ) 0.0098 1.3117 0.0074 0.9926 S₄ and S₅ ( i=4 and j=5 ) 0.0060 1.3021 0.0046 0.9954

(1) After finding the values of the fuzzy preference relation FPR

( ^c

^ˆpmi,

^c

^ˆpmj

)

^and

FPR

( ^c

^ˆpmj,

^c

^ˆpmi

)

^{=1- FPR}

( ^c

^ˆpmi,

^c

^ˆpmj

)

for i =1,2,3,4 and i < j. We draw an analogy of the value of

γ

is set to be 0.50. In the light of Step 2 in the above procedure, the sequence of suppliers arranged by considering the preference of selection is given by { S5,S1,S4,S2,S3 }. On the basis of the result of the sorting we are convinced that Supplier 5 is the most preferred choice and Supplier 3 is the worst choice among all five suppliers with the preference degree 0.50.

(2) Furthermore, if the value of

γ

is set to be 0.65, then the sequence goes for { ( S2,S3 ), ( S2,S4 ), ( S3,S4 )}, in which S2 is indifferent fromS3, S2 is indifferent fromS4, and S3 is indifferent fromS4 with indifference degrees (0.65,0.35), that can be written as below.

0.35≤ FPR

( ^c

^ˆpm2,

^c

^ˆpm3

)

≤ 0.65 and 0.35 ≤ FPR

( ^c

^ˆpm3,

^c

^ˆpm2

)

^{≤ 0.65}

and

0.35≤ FPR

( ^c

^ˆpm2,

^c

^ˆpm4

)

≤ 0.65 and 0.35 ≤ FPR

( ^c

^ˆpm4,

^c

^ˆpm2

)

^{≤ 0.65}

and

0.35≤ FPR

( ^c

^ˆpm3,

^c

^ˆpm4

)

≤ 0.65 and 0.35 ≤ FPR

( ^c

^ˆpm4,

^c

^ˆpm3

)

^{≤ 0.65}

In other words, supplier S5 and supplier S1 is still the most preferred supplier with the preference degree 0.65. In this case, the manger may randomly select one of supplier S5 and supplier S1 as the most preferred supplier, or provide some other criteria to select the most preferred supplier form supplier S5 and supplier S1. Surely, if the company is allowed to select more than one supplier to supply this particular touch screen for manufacturing, then both suppliers S5 and supplier S1 are the most preferred supplier.

6. Conclusions

Fuzzy logic is a powerful problem-solving methodology with a myriad of applications in embedded control and information processing. Fuzzy provides a remarkably simple way to draw definite conclusions from vague, ambiguous or imprecise information. In a sense, fuzzy logic resembles human decision making with its ability to work from approximate data and find precise solutions. This paper proposed an approach for the selection of suppliers, which model is capable of handling fuzzy data and was not seriously treated by the researchers.

The quality-based supplier selection and evaluation using the imprecise sample data has been applied for supplier selection. A general method is proposed to obtain the fuzzy estimate of the capability index

C

_pmi of supplier i using “resolution identity” in fuzzy sets theory.

In order to derive the membership degree of any given

γ

of fuzzy estimate ˆ

c

_pmi , the original problem is transformed into the optimization problems. After obtaining the fuzzy

18

estimates

{ ^c

^ˆpm1,...,

^c

^ˆpmq

}

of respective supplier

{ S

1,..., q

S }

, we follow the ranking method proposed by Yuan (1991) to choose the most preferred supplier. The application model/case study taken from the touch screen application is provided illustrated the applicability of the proposed methodology.

The results show that the model has the capability to be flexible and deal with fuzzy data to choose their supplier. The final priority of each alternative will lead to a recommended best option. It can be concluded that the model could facilitate decision making. The approach could help in reduced time consuming efforts in the supplier selection process.

Reference:

[1] Accenture Consulting, 2005. Supply chain mastery in the global marketplace. In:

16th POMS annual conference, April 29-May 2; 2005, Chicago.

[2] Anderson, E.L. Jr., 1994. Evaluate critical suppliers. Purchasing, 117(1), 53-56.

[3] Benion, M.L. and Redmond, W.H., 1994. Modeling customer response in an industrial commodity product market. Industrial Marketing Management, 23, 383-392.

[4] Buckley, J.J., 2003. Fuzzy Probabilities: New Approach and Application, Physica-Verlag, Heidelberg.

[5] Chaudhry, S., Forst, F., and Zydiak, J., 1993. Vendor selection with price breaks.

European Journal of Operational Research, 70(1), 52-56.

[6] Chen, J.K., Chen I.S., 2009. TQM measurement model for the biotechnology industry in Taiwan. Expert Systems with Applications, 36(5), 8789-8798.

[7] Dickson, G.W., 1966. An analysis of vendor selection systems and decisions. Journal of Purchasing, 2, 5-17.

[8] Filzmoser, R. and Vertl, R., 2004. Testing hypotheses with fuzzy data: the fuzzy p-value. Metrika, 59, 21-29.

[9] Garvin, D.A., 1988 Managing quality: The strategic and competitive edge. New York: Free Press.

[10] Gregory, R.E., 1986. Source selection: a matrix approach. Journal of Purchasing and Materials Management, 24-29.

[11] Gulbay, M. and Kahraman, C., 2007. An alternative approach to fuzzy control charts:

Direct fuzzy approach. Information Sciences, 177, 1463-1480.

[12] Hong, D.H., 2004. A note on Cpk index estimation using fuzzy numbers. European Journal of Operational Research, 158(2), 529-532.

[13] Hsiang, T.C. and Taguchi, G., 1985. A tutorial on quality control and assurance the Taguchi methods. ASA Annual Meeting, Las Vegas, Nevada, U.S.A.

[14] Houshyar, A. and David, L., 1992. A systematic selection procedure. Computers and

19

Industrial Engineering, 23(1-4), 173-176.

[15] Hsu, B.M. and Shu, M.H., 2008. Fuzzy inference to assess manufacturing process capability with imprecise data. European Journal of Operational Research, 186, 652-670

[16] Kane, V.E., 1986. Process capability indices. Journal of Quality Technology, 18(1), 41-52.

[17] Lee, A.H.I., 2009. A fuzzy supplier selection model with the consideration of benefits, opportunities, costs and risks. Expert Systems with Applications, 36(2), Part 2, 2879-2893.

[18] Lee, H.T., 2001. Cpk index estimation using fuzzy numbers. European Journal of Operational Research, 129(3), 683-688.

[19] Lau, H.S. and Lau, A.H.J., 1994. Coordinating two suppliers with offsetting lead time and price performance. Journal of Operations Management, 11(4), 327-337.

[20] Lambert, D.M., Ronald, J.A. and Margaret, A.E., 1997. Supplier selection criteria in the healthcare industry: a comparison of importance and performance. International Journal of Purchasing and Materials, 16-22.

[21] Maani, K.E., 1989. Productivity and profitability through quality-myth and reality.

International Journal of Quality & Reliability Management, 6(3), 11-23.

[22] Parchami, A. and Mashinchi, M., 2007. Fuzzy estimation for process capability indices. Information Sciences, 177, 1452-1462.

[23] Pearn, W.L. and Shu, M.H., 2003. Manufacturing capability control for multiple power distribution switch processes based on modified MPPAC. Microelectronics &

Reliability, 43(6), 963-975.

[24] Phillips, L.W., Chang, D.R. and Buzzell, R.D., 1983. Product quality, cost position and business performance: A test of some key hypotheses, Journal of Marketing, 47(2), 26-43.

[25] Prasad, S. and Calis, A., 1999. Capability indices for material balance accounting.

European Journal of Operational Research, 114(1), 93-104.

[26] Patton, W. E., 1996. Use of human judgement models in industrial buyers' vendor selection decisions. Industrial Marketing Management, 25, 135-149.

[27] Pearson, J.N. and Ellram, L.M., 1995. Supplier selection and evaluation in small versus large electronics frms. Journal of Small Business Management, 53-65.

[28] Pacheco, P.L., 1989. Satisfaction guaranteed: A marketing research approach to measuring customer satisfaction and identifying competitive opportunities. Journal of Business and Industrial Marketing, 4(2), 5-6.

[29] Pearson, J.N., and Ellram, L.M., 1995. Supplier selection and evaluation in small versus large electronics firms. Journal of Small Business Management, 33(4), 53-65.

20

[30] Sugano, N., 2006. Fuzzy set theoretical approach to achromatic relevant color on the natural color system. International Journal of Innovative Computing, Information and Control, 2(1), 193-203.

[31] Swift, C.O., 1995. Preference for single sourcing and supplier selection criteria.

Journal of Business Research, 32(2), 105-111.

[32] Shiau, J.H., Chiang, C.T., and Hung, H.N., 1999. A Bayesian procedure for process capability assessment. Quality and Reliability Engineering International, 15, 369-378.

[33] Viertl, R. and Hareter, D., 2004. Fuzzy estimation and imprecise probability. Journal of Applied Mathematics and Mechanics, 84(10-11), 731-739.

[34] Voehl, F., Jackson, P., and Ashton, D., 1994 ISO 9000: An Implementation Guide for Small to Mid-sized Business, St. Lucie Press.

[35] Weber, C.A., Current, J.R. and Benton, W.C., 1991. Vendor selection criteria and methods. European Journal of Operational Research, 50, 2-18.

[36] Wilson, E.J., 1994, The relative importance of supplier selection criteria: A review and update. International Journal of Purchasing and Materials Management, 30(4), 35-41.

[37] Wagner, J., Ettenson, R. and Parrish, J., 1989. Vendor selection among retail buyers:

An analysis by merchandise division. Journal Retailing, 65, 58-77.

[38] Weber, C. L., Current, J.R., Benton, W.C., 1991. Vendor selection criteria and methods. European Journal of Operational Research, 50(1), 2–18

[39] Xekalaki, E. and Perakis, M., 2004. A new method for constructing confidence intervals for the index Cpm. Quality and Reliability Engineering International,20, 651-665.

[40] Yuan, Y., 1991. Criteria for evaluation fuzzy ranking methods. Fuzzy Set and System. 43, 139-157.

[41] Zimmer, L.S., Hubele, N.F., and Zimmer, W.J., 2001. Confidence intervals and sample size determination for Cpm. Quality Reliability Engineering international, 17, 51-68.

[42] Zadeh, 1965. Fuzzy sets, Information and Control, 8, 338-353.

[43] Zhang, Z. and Chu, X., 2009. Fuzzy group decision-making for multi-format and multi-granularity linguistic judgments in quality function deployment. Expert Systems with Applications, 36(5), 9150-9158.

在文檔中 具有多重機遇原因變異的奈米科技製程其整合製程監控與績效量測之研究 (頁 56-63)