Sheet 6 Solu.docx

Faculty of Engineering Industrial Engineering Department,3rd year Sheet 5 Work Sampling

1- pply the rank order clustering technique to the part-machine incidence matrix in the following table to identify logical part families and machine groups. Parts are identified by letters, and machines are identified numerically. Parts Machines

A

1

1

B

2

C

D

E

1

3

1

1

1

4

1

1

5

1

Solution: Step 1 A 1

C

D

E

1

2 3

B

Step 2

1

1

1

4

1 1

1

5

1

Rank

A

B

2

3

1

4

1

1

1

4

1

3

2

1

5

5 Rank

D

3

1

1

1

1

B

4

1

2

1

5

1

D

E

1

1 1 1

1

3

Step 3 A

C

4

2

5

B

C

E

1

Step 4 C

E

1 1

Rank

A

D 1

1

3

1

2

1

1

4

5

5

4

1

3

2

1

1

Part families and machine groups: I = (A, D) and (3,1,5), II = (B, C, E) and (4, 2).

1

2- Apply the rank order clustering technique to the part-machine incidence matrix in the following table to identify logical part families and machine groups. Parts are identified by letters, and machines are identified numerically. Parts Machines

A

1

1

B

C

D

E 1

2

1

3

F

1

1

1

4

1

5

1

1

6

1 1

1

1

Solution: Step 1 A 1

B

C

1

E

1 1

1

1

4

1

5

F

1

2 3

D

Step 2

1

1

6

1 1

1

1

Rank

A

B 1

C

D

2

3

1

6

1

1

1

5

5

6

1

1

3

4

1

1

4

2 Rank

E

1 1

1 1

1 1

2

5

4

1 3

Step 3 A

B

3

1

1

1

1

5

1

E

D

C

F

Rank

Part families and machine groups:

1

I = (A, B, E) and (3, 1, 5)

1

2

II = (D, C, F) and (6, 4, 2)

1

3

6

1

1

4

1

1

2

1

1

4 5

1

6

F

6

3- Apply the rank order clustering technique to the part-machine incidence matrix in the following table to identify logical part families and machine groups. Parts are identified by letters, and machines are identified numerically. Parts Machines

A

1

1

B

C

D

E

F

G

H

1

2

1

1

3

1

4

1

1

1

1

5

1

1

1

6

1

7

I

1

1

1

8

1

1

Solution: Step 1 A 1

B

C

D

E

F

G

H

1

2

1

3

1

1

5

I

Rank

1

2

7

1

4

1

1

5

4

1

3

2

1

7

3

1

1

8

8

1

1

1

5

1

6

6

1 1

4

1 1

1

1

1

6 7

Step 2

1 1

1

1

8

1

1

A

Rank

1

B

C

D

D

7

1

1

1

1

I

G

B

1

1

2

1

1

F

C

E

H

1

3

1

1

8

1

1

5

1

6

1

G

H

I

1

5

1

1 1

7

1

1

2

8

1

1

6

4

9

3

C

E

H

1

Step 4

1

4

F

1

Step 3 A

E

1

1

1

Rank

A

D 1

I

G

B

F

1

1

7

1

2

1

1

3

4

1

1

4

2

1

1

6

6

1

7

3

1

1

8

8

1

1

5

5

1

Rank

1

1

2

3

4

Part families and machine groups: I = (A, D, I) and (7, 1) II = (G, B, F) and (4, 2, 6) III = (C, E, H) and (3, 8, 5)

1

5

6

7

1 8

9

4- The following table lists the weekly quantities and routings of ten parts that are being considered for cellular manufacturing in a machine shop. Parts are identified by letters and machines are identified numerically. For the data given, (a) develop the part-machine incidence matrix, and (b) apply the rank order clustering technique to the part-machine incidence matrix to identify logical part families and machine groups. Part A B

Weekly quantity 50 20

C D

75 10

E

12

Machine routing 327 61 65 651 3274

Part F G

Weekly quantity 60 5

Machine routing

H I

100 40

3 2  4  7

J

15

51 3 2  4 247 561

Solution: (a) See step 1. (b) See steps 1 through 4. Step 1

Step 2

A B C D E F G H I 1

1

1

1

2 1

1

1

1

3 1

1

1

1

4

1

1

1

5

1

1

6

1 1

1

7 1

Ran k

1

5

2 1

1

1

1 1

1

3 1

1

1

1

2

7 1

1

7

6

1

1

6

1

1

1

4

5

3

4

1

1

1

1

J

1

1

A B C D E

1

A

G

I

2

1

1

1

1

1

3

1

1

1

1

7

1

1

1

D

1

1

1

1

1

1

9 6

J

B

1

1

1

1

1

1

5

1

1

1

C

F

1

1

1 1

4

2

5

E

H

A

G

I

7

1

D

J

B

C

1

2

1

1

1

1

2

3

1

1

1

1

3

7

1

1

1

5

4

1

1

1

6

6

1

1

1

1

7

1

1

1

1

4

5

1

1

6

7

1

1

Rank 1

1 1

1

10

1

1

Step 4

6

4

1 1

1 8

J

1

Step 3 H

G H I

1

1

Ran 3 k

E

F

Rank

1

2

1 1

3

F

4

1

5

Part families and machine groups: I = (E, H, A, G, I) and (2, 3, 7, 4) II = (D, J, B, C, F) and (6, 1, 5)

8

1 1

1

9

10