# Solution

Τεχνίτη Νοημοσύνη και Ρομποτική

25 Νοε 2013 (πριν από 4 χρόνια και 7 μήνες)

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Question number (1):

a) For the part
-
machine matrix shown below, apply a clustering technique to form the GT cells of
machines.

b)
Three
machines

from the seven above

will constitute a GT cell. The F
rom
-
To data for the machines
are shown in the table below.

To

FROM

A

B

D

A

0

10

0

B

0

0

85

D

70

0

0

1.

Determine the most logical sequence of machines for this data, according to Hollier

Method 1,
and construct the flow diagram for the data, showing where and how many parts enter and exit
the system.

Solution:

FROM

A

B

D

From sums

A

0

10

0

10

B

0

0

85

85

D

70

0

0

70

To sums

70

10

85

165

The minimum
To sum is 10 for machine B

and the same 10 is the minimum
from sum for
machine A
,
So according to tie breaker
3
rd

rule, both machines with the minimum To ( B ) is first
and minimum From ( A) is last.

Then the sequence is B

D
-

A

From

B 85 part exit and 10 enter from A, So the system starts with 75 parts
enter directly
to the first machine B (85 exit

10 enter = 75 should enter at B).

85 parts enter to D and only 70 exit to A, So Machine D ships 15 parts to
the exit (70+15
exit=85enter)

Machine A has 70 parts enter from machine D and 10 exit to B, the remaining parts are
60 parts exit.

Note that the system has 75 parts enter and finally 75 parts exit to the shipping 60 from A
and 15 from D.

2.

Repeat (1) using

Hollier Method 2.

FROM

A

B

D

From sums

From/To
ratio

A

0

10

0

10

1/7

B

0

0

85

85

8.5

D

70

0

0

70

0.82

To sums

70

10

85

165

The sequence is B

D

A (the same as Hollier 1).

3.

Compute the percentage of in
-
sequence moves and the percentage of backtracking moves in the
solution for the two methods. Which
sequence

is better, according to these measures?

For method 1 and 2 the same : percent of in
-
sequence moves

= [(85+70)
/
(85+70+10)] *100%

=
93.93
%

Percent

of backtracking moves

= [(10)
/
(85+70+10)] *100%

=
6.06
%

B

D

A

7
5

8
5

70

60

10

15

Question number (
2
):

a) For the part
-
machine matrix shown below, apply
the rank order
clustering technique to form the GT
cells of machines.

Part
s

‘Number’

䵡捨i湥
s

N

2

3

4

5

6

A

N

N

B

N

N

C

N

N

D

N

N

N

b

N

N

N

If w攠獵灰潳攠t桡h t桥h

m慣桩湥n will 捯湳tit畴攠愠GT 捥ll⸠T桥h䙲潭
-
T漠摡d愠f潲 t桥h
m慣桩湥n⁡ 攠e桯h渠n渠n桥⁴慢a攠扥l潷⸠

TO

FROM

1

2

3

4

5

1

0

40

110

0

0

2

0

0

0

115

0

3

0

0

0

0

0

4

100

0

50

0

0

5

0

105

0

50

0

1.

Determine the most logical sequence of machines for this data, according to Hollier Method 1,
and construct the flow diagram for the data, showing where and how many parts enter and exit
the system.

2.

Repeat (1) using Hollier Method 2.

3.

Compute the percentage

of in
-
sequence moves and the percentage of backtracking moves in the
solution for the two methods. Which
sequence

is better, according to these measures?

Solution

for Hollier method
:

TO

FROM

1

2

3

4

5

SUM

1

0

10

80

0

0

90

2

0

0

0

85

0

85

3

0

0

0

0

0

0

4

70

0

20

0

0

90

5

0

75

0

20

0

95

SUM

70

85

100

105

0

TO

FROM

1

2

4

5

SUM

1

0

10

0

0

10

2

0

0

85

0

85

4

70

0

0

0

70

5

0

75

20

0

95

SUM

70

85

105

0

TO

FROM

1

2

4

SUM

1

0

10

0

10

2

0

0

85

85

4

70

0

0

90

SUM

70

10

85

2 4 1

TO

FROM

2

4

SUM

2

0

85

85

4

0

0

0

SUM

0

85

Accordingly, the machines' flow will take the sequence
: 5 _ 2 _ 4 _ 1 _ 3

(b) Repeat step (a) only using Hollier Method 2.

TO

FROM

1

2

3

4

5

SUM

Ratio

1

0

10

80

0

0

90

9/7

2

0

0

0

85

0

85

1

3

0

0

0

0

0

0

0

4

70

0

20

0

0

90

9/10.5

5

0

75

0

20

0

95

SUM

70

85

100

105

0

Accordingly
, the machines'
flow will take the sequence
: 5 _
1

_
2

_
4

_ 3

5

2

4

1

3

95

7
5

8
5

70

80

100

20

15

20

20

10

(c) Compute the percentage of in
-
sequence moves and the percentage of backtracking moves in the
solution for the two methods. Which method is better, according to these measures?

In
-
sequence
moves
percentage

considers moves

between adjacent machines in the flow direction

implied by the machine sequence

So, for method 1: percent of in
-
sequence moves

= [(75+85+70+80)
/

(
75
+85+70+80+10+20+20)] *100%

= 86.1%

For method 2, percent of in
-
sequence moves

=

[ (10+85+20)
/

(

10+85+20+80+70+75+20) ]* 100%

= 32%

Similarly for the backtracking percentage, it is computed by dividing the values of backtracked moves
between adjacent points by the total number of moves.

In the two cases there is no backtracks betwee
n two adjacent nodes. That is, the percentage of
backtracking moves equal
zero

in both alternatives. However, there is another performance measure
called percentage of backward moves which consider all the backward moves regardless to cells'
adjacency. Thi
s percentage will equal 10/360 = 2.8% in method 1 and 70/360 = 19.4% in the second.

The percentage of in
-
sequence moves in the first alternative is grater than that of the second whereas
the percentage of the backward moves in the second is greater than t
he first. So, the
machine sequence
resulted in Hollier method 1 is better

than the sequence in the
second method.