4. Experimental Results
4.2 Case Study
4.2.1 Production Line Allocation Module
4.2.1.1.2 Rough Cycle time Approximation
In this section, the machine group PI Exposure and product family 2 is considered as the default example.
Step 1. Calculate the average number of dedicated machines for each product family of each machine group, ANDMg,f .
Case 1: for each product family f and each machine group g which has to setup for different product families.
⎡
g f g⎤
f
g DPP NTM
ANDM , = , × , (7)
Case 2: for each product family f and each machine group g which does not have to setup for different product families.
g f
g NTM
ANDM , = , (8)
For example, because PI Exposure has to setup for different product families, it belongs to case 1. ANDM4,2 =
⎡
0.375×6⎤
=3. However, because IQC do not have to setup for different product families, it belongs to case 2. ANDM1,2 =8Table 4-10 list the average number of dedicated machines for each machine group and product family.
Table 4-10 The average number of dedicated machines
Machine group g ANDMg,1 ANDMg,2 ANDMg,3 ANDMg,4
IQC 1 8 8 8 8
Scrubber-1 2 9 9 9 9
PI Coating 3 0 4 3 4
PI Exposure 4 0 3 2 3
PI Developing 5 0 4 3 4
Plasma Ash-PI 6 0 3 2 4
Sputter 7 2 2 2 2
Photo Coating 8 12 12 12 12
Photo Exposure 9 17 17 17 17
Photo Developing 10 11 11 11 11
Plating 11 11 11 11 11
Stripping 12 9 9 9 9
Scrubber-2 13 9 9 9 9
FI 14 8 8 8 8
OQC 15 8 8 8 8
Step 2. Calculate the service rate of each machine group g for product family f during the planning horizon, SRg,f.
f g
g f
g f
g g f
g ANDM
NTM DPP
P SR B
, , ,
,
× ×
= , (9)
for each machine group g and product family f.
For example, 0.13636
3 6 375 . 0 5 . 5
1
2 ,
4 = × × =
SR .
Table 4-11 lists the service rate of all machine groups and product families.
Table 4-11 Service rate of each machine group and product family Machine group g SRg,1 SRg,2 SRg,3 SRg,4
IQC 1 0.25 0.25 0.25 0.25
Scrubber-1 2 0.2 0.2 0.2 0.2
PI Coating 3 0 0.1534 0.1318 0.1568
PI Exposure 4 0 0.1364 0.1318 0.1394 PI Developing 5 0 0.1688 0.145 0.1725 Plasma Ash-PI 6 0 0.25 0.2417 0.1917
Sputter 7 1.528 1.677 1.0807 1.7143
Photo Coating 8 0.1538 0.1538 0.1538 0.1538
Photo Exposure 9 0.1 0.1 0.1 0.1
Photo Developing 10 0.2 0.2 0.2 0.2 Plating 11 0.1538 0.1538 0.1538 0.1538
Stripping 12 0.2 0.2 0.2 0.2
Scrubber-2 13 0.2 0.2 0.2 0.2
FI 14 0.2222 0.2222 0.2222 0.2222
OQC 15 0.2 0.2 0.2 0.2
Step 3. Calculate the lot arrival rate of each machine group g for product family f during the planning horizon, ARg,f.
Case 1: for each machine group g which does not have to setup for different product families.
( )
D NP DPQ
AR f
f g f f
g ×
×
=
∑
24
,
, , (10)
Case 2: for each product family f and machine group g which has to setup for different product families.
D NP ARg f DPQf g f
×
= ×
24
,
, , (11)
For example, because PI Exposure has to setup for different product families, it belongs to case 2. 0.3571
63 24
1 540
2 ,
4 =
×
= ×
AR . However, because IQC does not have to setup for different product families, it belongs to case 1.
0952
Table 4-12 lists all the arrival rate of each machine group g for product family f during the planning horizon.
Table 4-12 The arrival rates
Machine group g ARg,1 ARg,2 ARg,3 ARg,4
Step 4. Calculate the utilization of each machine group g for product family f,
f
for each machine group g and product family f.
For example, 0.8726
Table 4-13 lists the utilization of each machine group g for product family f.
Table 4-13 The utilizations
Step 5. Calculate the probability that there is no WIP of product family f before machine group g, PZg,f .
for each machine group g and product family f.
For example,
( ) ( ) ( )
Table 4-14 lists the probability that there is no WIP in front of each machine group g for product family f.
Table 4-14 The probability that there is no WIP in front of machine groups Machine group g PZg,1 PZg,2 PZg,3 PZg,4
for each machine group g and product family f.
For example,
( )
Table 4-15 lists the WIP level for each machine group g for product family f.
Table 4-15 The WIP levels
Machine group g LQg,1 LQg,2 LQg,3 LQg,4
Step 7. Calculate the queue time of the product family f in front of machine group g caused by load factors, QTLg,f.
Table 4-16 lists the queue time of the product family f in front of machine group g caused by load factors.
Table 4-16 The queue time caused by load factor
where πf is a set which contains all the machine groups that product family f should go through to complete its processes.
Take product family 2 for example,
5
Step 9. Calculate the mean queue time of each product family f before the batch machine caused by batch factor, QTBg,'f .
( )
machine group with least spare capacity whose operation lies before g.Take product family 2 for example, g=7 and g'=4
Step 10. Calculate the mean queue time of each product family f caused by the peak load due to the batch process, QTPg,f .
where g’ is the batch machine group and g is the critical serial machine group whose route is after the batch machine group.
Take product family 2 for example, g=11 and g'=7
Step 11. Calculate the total queue time of each product family f before machine group
for all product family f; where g’ is the batch machine group, and g’’ is the critical machine group whose route is after the batch machine group.
Take product family 2 for example, g'=7 and g''=11
Step 12. Calculate the estimated cycle time of product family f, CTf .
f
4.1.1.1.1 Dedicated and Mixed VPLs Allocation
Step 1. Calculate the number of bottleneck machines which is allocated for dedicated VPLs, NDBMf .
⎣
BMGf BMG⎦
f DPP NTM
NDBM = , × , for each product family f. (21)
Take product family 2 for example, NDCM2 =
⎣
0.375×6⎦ ⎣
= 2.25⎦
=21 =0 NDCM
3 =1 NDCM
4 =2 NDCM
Step 2. Calculate the number of bottleneck machines which is allocated for mixed VPLs.
∑
−
=
f
f
BMG NDBM
NTM
NBMV , (22)
(
0 2 1 2)
16− + + + =
=
NBMV .
4.1.1.1.2 Non-bottleneck Machines Allocation
Step 1. Set the normalized spare capacity, NSpareg,m , equal to 1 for all machine m in all machine group g.
Step 2. For each non-bottleneck machine group g that need to setup for different product families, do Step 3 through Step 8, else do nothing and start allocating the next machine group. If all machine groups are assigned, stop this algorithm.
Step 3. Sort all product families according to NNMg,f in descending order. Where
f
NNMg, is given below.
f g f
g f
g DPP NTM
NNM , = , × , , for each f and g. (23)
Take PI Coating and product family 2 for example, NNM3,2 =0.38×9=34.2. Table 4-17 list the expected number of non-bottleneck machines that is allocated for product family f during the planning horizon.
Table 4-17 Expected number of non-bottleneck machines
Machine group g NNMg,1 NNMg,2 NNMg,3 NNMg,4
PI Coating 3 0 3.42 2.16 3.42
PI Developing 5 0 3.42 2.16 3.42
Plasma Ash-PI 6 0 3.04 1.92 3.04
Sputter 7 1.5 1.68 1.08 1.74
Step 4. Pick product families one by one according to the order obtained in Step 3, do Step 5 through Step 8 for each product family. If all product families are assigned, go back to Step 2 for next machine group.
Follow the steps, the allocation of non-bottleneck machines is obtained as Table 4-18 shows.
Table 4-18 The allocation of non-bottleneck machines Machine
group g m Assign for f = 1
Assign for f = 2
Assign for f = 3
Assign for f = 4
1 ˇ
2 ˇ
3 ˇ
4 ˇ ˇ
5 ˇ
6 ˇ
7 ˇ
8 ˇ ˇ
PI Coating 3
9 ˇ
1 ˇ
2 ˇ
3 ˇ
4 ˇ ˇ
5 ˇ
6 ˇ
7 ˇ
8 ˇ ˇ
PI
Developing 5
9 ˇ
1 ˇ
2 ˇ
3 ˇ
4 ˇ ˇ
5 ˇ
6 ˇ
7 ˇ
Plasma
Ash-PI 6
8 ˇ ˇ
1 ˇ
2 ˇ ˇ
3 ˇ
4 ˇ ˇ
5 ˇ
Sputter 7
6 ˇ ˇ
Step 5. Search for the machine m in machine group g that has the most normalized spare capacity left.
Step 6. If the normalized spare capacity of the machine m is larger or equal to
f
NNMg, , go to Step 7, else go to Step 8.
Step 7. Assign the capacity of machine m to the product family f, and substrate the capacity of the machine m by NNMg,f . Put the product family f into τg ,m. Go back to Step 4 for the next product family.
Step 8. Assign all the spare capacity of the machine m to product family f, and set the normalized spare capacity of the machine m to 0. Put the product family f into τg ,m. Substrate NNMg,f by the capacity assigned to it, and go to Step 5 to allocate the unassigned demand of product family f.