Contoh Model OMAX-Fuzzy Logic

Proceeding, International Seminar on Industrial Engineering and Management

ISSN: 1978-774X

Productivity Measurement Using OMAX

Nofi Erni E67

PRODUCTIVITY MEASUREMENT USING OMAX

AND FUZZY LOGIC AT PT. AMD

Nofi Erni

Industrial Engineering Department , Indonusa Esa Unggul University Email: [email protected]

ABSTRACT

This research conduct to seeks of application fuzzy logic in determining weight of criteria for measurement productivity using OMAX method. Verification this research are used by production data at PT. AMD. Linguistic value are used to measure importance level and relationship each criteria, through implementation of fuzzification, defuzification and fuzzy arithmetic, the data able to convert as a quantitative value that represent weight of criteria.

The criteria based on weight that affect to productivity level at PT. AMD are minimize product defect (0.32), raw material usage efficiency (0.32), efficiency of labor usage (0.16), minimize late delivery (0.12) optimize production capacity(0.08). Using OMAX method, productivity index shown unstable with highest value was achieved in August 2008 as 237%, and the lowest in October 2008 as 13%. The main factor that affect the productivity achievement are product defect and quality of raw material. Keywords : Productivity, OMAX, Fuzzy Logic, Triangular Fuzzy Number

1. INTRODUCTION

The internal factor is one of the factors that can affect the competitive advantage, these factors tend to be controlled rather than the company’s external factors. In general the internal factors are the factors thats affecting the performance of the inputs or resources used to produce the output. Ratio of output produced to resources consumed, commonly determined as productivity.Many different approaches to measuring productivity have been adopted by industry for different purposes. The productivity measure must define each of parameter (criteria) of the model in a way that suits the intended use. Parameters that can be used is the level of productivity of a system ( Card, 2006) The Obejctive Matrix (OMAX) is one of productivity measurement method would able to combine all of productivity criteria. This method is designed by James L. Riggs, which ability to mesure productivity as parsial or the whole of system. Each of criteria has different weighted, and calculation of productivity index has a result

of circumtances base certain period. Analysis of productivity measurement can be identified all the shortcomings, improvements can be done correctly and directed. The measurement results can be used as a planning target for the next productivity period (Summanth, 1984). Under many condition, human judgement including preferences are often vague and cannot estimate with an exact numerical number. A more realistic approach may be to use linguistic assesments instead of numerical value. The ratings and weights of the criteria in the problem are assessed by means of linguistic variables ( Herrera et al, 2000). Considering the fuzzines in decision data and group decision making process, linguistic variables are used to assess the weight of all criteria and the rating of each alternative with respect to each criteria (Chen et.al, 2005). The fuzzy number have used to express linguistic variables. Fuzzy number is a set fuzzy set A in a universe of discourse X is charaterized by a membership function wich associates with each element x in X a real number in the interval [0,1]. The function value is termed the grade


Inna Kuta Beach Hotel, Bali December 10th-11th ,2009 ISSN: 1978-774X

E68 Productivity Measurement Using OMAX Nofi Erni

membership of x in A (Kaufman and Gupta, 1991) The purpose of this research is how to application fuzzy logic in order measurement rating and weight that expressed by linguistic value, which used to develop objective matrix (OMAX). This research was verified by using data from PT. AMD in order measure productivity index. PT. AMD is a company engaged in the printing industry. The company in this case have need to measure the productivity level in production and determine the factors that affect performance and productivity of those company.

2. RESEARCH METHOD In this research fuzzy logic were developed for determining rating and weight in application OMAX to measure productivity index. The linguistic value were expressed to determine the important and relationship criteria in order measuring productivity. According Shen (2000) the fuzzification and defuzzification process using membership function Triangular Fuzzy Number. The measurement productivity index were processed according the step and formula was developed in OMAX method. Research was done in production department of PT. AMD in Jakarta. Data were collected by direct observation, interviews and focus group discussion with management. In this research to propose productivity index in production department, the data obtained from production record, while productivity during January – December 2007 as a base to calculation productivity index in January – December 2008 . 3. RESULT AND DISCUSSION 3.1. Developing potential objective Based on observation and focus group discussion with General Manager, Head Operational, Production Supervisor

are summarised that there are 5 potensial objective that important to measure. The potensial objective will describe through some criteria. The criteria will be measure using the quantitaive production data. Many formula to calculate the productivity index using Objective Matrix (OMAX) as shown at Table 1.

Table1. Potential Objective and Criteria

Potential ObjectiveNo Measurement Criteria

1

5

4

3

2

Minimize Product Defect

Optimize Production Capacity

Labor Usage Efficiency

Raw Material Usage Efficiency

Number of Defect Product

Late Deliveries

Actual Production

Production Capacity

Number of Deliveries

Labor Working Time

Raw Material Quantity

Minimize Late Delivery

Actual Production

Actual Production

Actual Production

3.2. Data Collection PT. AMD has printing machine which production capacity as 9.450 rim paper . During research period the machine only produce less than production capacity. The production depend on order from customer. Table 2. shown the printing production and number of delivery during January – December 2007. Production and delivery order during January – December 2008 shown at Table 3.

Table 2. Production and Delivery Order January – December 2007

Month

Actual Production (rim)

Defect Product (rim)

Number of delivery (order)

Number of late delivery (order)

Jan 2.303 6 227 22

Feb 3.235 5 320 35

March 4.388 4 435 27

April 3.775 3 374 28


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May 4.783 9 475 22

June 4.963 5 493 35

July 3.700 4 367 27

Augst 4.848 9 481 27

Sept 2.700 5 267 28

Oct 1.845 4 181 22

Nov 2.338 3 230 35

Dec 3.845 5 381 30

Table 3. Production and Delivery Order

January – December 2008

Month

Actual

Production (rim)

Defect product (rim)

Number of delivery (order)

Number of late delivery (order)

Jan 2.353 5 235 15

Feb 3.285 3 328 10

March 4.438 8 443 7

April 3.825 7 382 21

May 4.833 9 483 22

June 5.013 6 501 35

July 3.750 5 375 27

Augst 4.898 4 489 28

Sept 2.750 3 275 25

Oct 1.895 5 189 33

Nov 2.388 7 238 17

Dec 3.895 9 389 25

Actual production is number of printing product that produced each month. Defect product is total product does not meet quality standar. Delivery is all of order that received by customer include the late delivery. Labor attendance measure in hour as shown employee printing attendance. Another data that used to measure productivity is raw material quantity and labor attendance as shown at Table 4.

Table 4. Raw material and labor attendance

during 2007 - 2008

3.3. Developing Initial Table of OMAX

After determining potensial objective and criteria, the matrix will develop. The base value as a standar of measurement and

target will achieve would be arranged in matrix. OMAX method provide matrix cell will describe achievement score. Scoring range from (0-10), which is 0 as represent the lowest achievement and 10 as target of productivity index. Using formula in Table 1, the ratio determine as a comparison between of output produced to resources consumed during January – December 2007. Base of period determine at level 3.Table as format of objective matrix have developed as shown Table 5. These initial table will be use as base to calculate the matrix for each month during January – December 2008.

Table 5. Objective Matrix Table Format

Criteria

1 2 3 4 5

Performance

0 0.4709 0 9.361 1 10

0.0003 0.4571 0.0123 9.1383 0.9993 9

0.0005 0.4437 0.0248 8.9154 0.9989 8

0.0007 0.4303 0.0373 8.6925 0.9985 7

Month

Raw Material

Labor Attendance

(hours) Quantity (rim)

2007

2008

2007

2008

Jan 2.314 2.363 465 465

Feb 3.245 3.293 420 420

March 4.397 4.451 465 465

April 3.783 3.837 450 450

May 4.797 4.847 465 465

June 4.973 5.024 450 450

July 3.709 3.760 465 465

Augst 4.862 4.907 465 465

Sept 2.710 2.758 450 450

Oct 1.854 1.905 465 465

Nov 2.346 2.400 450 450

Dec 3.855 3.909 465 465




0.0009 0.4169 0.0498 8.4696 0.9981 6

0.0011 0.4035 0.0623 8.2467 0.9977 5

0.0013 0.3901 0.0748 8.0238 0.9973 4

0.0015 0.3767 0.0873 7.8009 0.9969 3

0.002 0.3162 0.109 6.5231 0.9963 2

0.0023 0.2557 0.1306 5.2454 0.9957 1

-0.0003 0.1952 0.1522 3.9677 0.9951 0

Score

Weight

Grade

Achievement Indicator

Basic Current Period Index

Period (%)

300

3.4. Weight determination Having obtained the matrix as base productivity value, the next step is to determine the relative importance of potential objectives. Each criteria have different impact in determination productivity at production department. The importance level each criteria is defined using weighted. Usually OMAX provide scoring (1 - 10 scale) to measure importance level. In this research, weight determination using application fuzzy logic. The management judgement use linguistic assessment to describe their judgement based on their knowledge in printing business. Determination weight was made to give priority of each criteria. In this research weighting is calculated using

fuzzy logic. Value and importance level of each criteria have defined in linguistic data. Fuzzy numbers used in this study refers to research by Shen et.al.(2000) for each linguistic data and its relationship.The importance level of each criteria, linguistic label and fuzzy number defined as shown at Table 6. Linguistic value and membership function using Triangular Fuzzy Number (TFN). Relationship between importance level of each criteria with the productivity measurement is obtained by brainstorming. Any relationship that occurs is described in linguistic data to be more precise in its use, compared with the use of numbers. The type of the relationship language used fuzzy number shown at Table 7.

Table 6. The importance level and fuzzy

number

Table 7. Relationship level and fuzzy number

Relationship Triangular Fuzzy

Number (TFN)

None [ 0 0 0,1 ]

Weak [ 0 0,2 0,4 ]

Moderat [ 0,2 0,5 0,8 ]

Strong [ 0,6 1 1 ]

Level Linguistic Label

Triangular Fuzzy Number (TFN)

1 Not important [ 0 0 0,3 ]

2 Some important [ 0 0,25 0,5 ]

3 Moderately important [ 0,3 0,5 0,7 ]

4 Important [ 0,5 0,75 1 ]

5 Very Important [ 0,7 1 1 ]


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Based on focus group discussion had done with management the importance level and relationship judgement in linguistic value shown at Table 8. Their jugdement

represent the criteria minimize product, labor and raw material usage efficiency are very important.

Table 8. Importance level of criteria and relationship

Fuzzyfication the importance level and the relationship criteria to potensial objective using linguistic data are converted to crisp value as a membership of Triangular Fuzzy Number. The fuzzy numbers used in this study refers to research by Shen (2000) for each linguistic data and its relationship. After all fuzzyfication processes have been performed, then continued with the fuzzy arithmetic process. This fuzzy arithmetic process actually resembles the ordinary arithmetic, only we use fuzzy numbers, not ordinary numbers (crisp). Fuzzy arithmetic formula is:

IMPORTANCE (define the importance level)

CORRELATION (define the relationship between importance level and productivity measurement )

j 1j 1) 2j 2)

........ nj n); j ε {1,2,3,.....,m} Defuzzyfication method using MoM (Mean of Maximum) is conduct by looking at the maximum membership of a fuzzy number. In this research we use TFN, the results is the second value of the fuzzy number domain because that is what gives the maximum degree of membership. Calculation using fuzzy arithmetic results can be seen in the table 10. The formula of calculating the relative importance rate is :

Weight of criteria were obtained as result from process fuzzyfication, defuzzification, fuzzy arithmetic. The minimize product defect and raw material usage efficiency have the highest weight as value 0.32. It means the parameter number of defect product and raw material quantity that important to improve in order increase productivity.

No Criteria Importance

level Relationship

1 Minimize product defect

very important

strong

2 Optimize production capacity

moderatly important

moderate

3 Minimize late delivery

important moderate

4 Labor usage efficiency

very important

moderat

5

Raw material usage efficiency

very important

strong

ImportanceAbsolute

ImportanceAbsoluteImportanceRelative




Table 9.Absolute importance rate with MoM method

Attribute Triangular Fuzzy Number

(TFN) Absolute

Importance Rate Weight of criteria

Minimize product defect [ 0,42 1 1 ] 1

0.32

Optimize production capacity [ 0.06 0,25 0,56 ] 0,25

0.08

Minimize late delivery [ 0,1 0,38 0,8 ] 0,38

0.12

Labor usage efficiency [ 0,02 0, 5 0,8 ] 0, 5

0.16

Raw material usage efficiency [ 0,42 1 1 ] 1

0.32

3.5. Measuring productivy index Based on production data and weigted of criteria, the OMAX table is formed to measure productivity index during January – December 2008. From the initial (base) objective matrix table (Table 5), the performance and productivity index is calculated. Having obtained the value of performance, the next step is to determine the score. The steps that must be done is : a. If the performance value equal to the

value of achieving a certain score on the line, then the score is the score achieved

b. If the performance values are among the top 2 scores, then the calculations used the method of interpolation.

For example, keeping score on criteria minimize product defect at January 2008, we obtained performance values is 0.0021. This value lies in the matrix blocks between 1 and 2, so the score is 0.0023 and 0.0020, how to calculate the score is:

0.0020 – 0.0023 2 – 1 -------------------- = ------- 0.0020 – 0.0021 2 – x

- 0.0003 1 ---------- = ------- - 0.0001 2 – x - 0.0006 + 0.0003 x = - 0.0001 x = 1.66

The value of each criteria is multiply weight to the score. Performance indicators is summarize of value, and written in the current period. According to calculation in January 2008 achievement productivity as 170%, it means productivity in January lower than the base period (300%). The productivity index (PI) is calculated by :

indicator achievment Base

monthIndicator/AchievmentPI

Productivity Index for each value in Janaury 2008 shown at Table 10. In the same way productivity index for another month had calculate. Comparison between productivity index for each month shown at Table 11. The change of productivity index shown that the productivity at PT. AMD unstable. The highest productivity index was achieve in August, and the lowest October 2008. Many factors affect the productivity achievement, such as man, material, method, machine. The unskill operator, and loss of process control are the factor that relation with man. In other side quality of material influence printing process.. The parameter of raw material such as paper, ink must be under control.


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Tabel 10. Objective Matrix Januari 2008

Criteria

1 2 3 4 5

0.0021 0.2490 0.0638 5.0602 0.9958 Performance

0 0.4709 0 9.361 1 10

0.0003 0.4571 0.0123 9.1383 0.9993 9

0.0005 0.4437 0.0248 8.9154 0.9989 8

0.0007 0.4303 0.0373 8.6925 0.9985 7

0.0009 0.4169 0.0498 8.4696 0.9981 6

0.0011 0.4035 0.0623 8.2467 0.9977 5

0.0013 0.3901 0.0748 8.0238 0.9973 4

0.0015 0.3767 0.0873 7.8009 0.9969 3

0.002 0.3162 0.109 6.5231 0.9963 2

0.0023 0.2557 0.1306 5.2454 0.9957 1

-0.0003 0.1952 0.1522 3.9677 0.9951 0

1.66 0.89 4.88 0.85 1.16 Score

0.32 0.08 0.12 0.16 0.32 Weight

0.53 0.07 0.59 0.14 0.37 Grade

Achievement Indicator

Basic Period

Current Period

Index (%) 57

300 170

Table 11. Productivity index

Month

Productivity index (%)

Index changes

(%)

January 57 -

February 168 112

March 178 100

April 126 - 51

May 166 40

June 202 35

July 137 -65

August 237 100

September 115 -121

October 13 -103

November 38 26

December 98 60

Improvement suggestion to increase productivity are maintain the quality of raw materials, control production priorities so that the machine set up is as minimum as posibble, conduct regular training for employees that increasing their ability in processing raw materials

4. CONCLUSION This study seeks to way of possible application of fuzzy logic in determining weight of criteria to measure productivity index using OMAX method. Reffer to developing fuzzy logic by Shen et.al. (2000) the importance and relationship criteria with productivity in linguistic value have convert in a crisp value. This value is used as weight in measuring productivity using OMAX method. Verified this method by used production data at PT. AMD during 2007 - 2008. The criteria that affect the productivity level in this company is minimize defect products, optimize production capacity, minimize late delivery, efficiency of labor usage, raw material usage efficiency. Productivity index PT AMD shown aunstable. The highest value was achieved in August 2008 as 237%, and the lowest in October 2008 as 13%. Many factor affect the

productivity achievement, the main factor are product defect and quality of raw material .




5. REFERENCES

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Decision Making in A Fuzzy Environtment. Management Science 17 (4)

b. Card, D.N. 2006. The Challenge of

Productivity Measurement. Proceedings : Pacific Northwest Sotfware Quality Conference

c. Chen et. al. 2006. A Fuzzy Approach for

supplier Evaluation and Selection in Supply Chain Management. International Journal Of Production Economics 102 (www. sciencedirect.com).

d. Herrera et. al., 2000. Linguistic decision

analysis : Step for solving Problems Under Linguistic Information. Journal of Fuzzy sets and Systems 115.

e. Kaufmann, A., Gupta, M.M.1991.

Introduction to Fuzzy Aritmetic : Theory and Applications. Van Nostrand Reinhold, New York.

f. Shen et.al, 2000. The Implementation Of

Quality Funtion Development Based On Linguistik Data. Journal Of Intelligent Manufacturing. Vol 12. Departemen of Industrial And System Engineering. National University Of Singapore.

g. Sri Kusuma Dewi. 2002. Analisis &

Desain Fuzzy Menggunakan Tol Box Matlab. Cetakan Pertama. Graha Ilmu. Yogyakarta.

h. Summanth, D.J. 1984. Productivity

Engineering Productivity Engineering And Management. McGraw-Hil l. N e w Y o r k .

i. Susanto, D & Sugiarto, D. 2004.

Penerapan Metode Quality Function Development Yang Berbasis Data Linguistic Pada Produk Permen Karet Chewing Gum (Studi Kasus Di PT. Batman Kencana). Vol 3. Jurnal Inovisi, Jurusan Teknik Industri. Universitas Indonusa Esa Unggul

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Contoh Model OMAX-Fuzzy Logic