Semiconductor integrated circuit manufacturing: Very complex process Hundreds of operations Several hundred sets of tools Price of tools is very high

($1- $10 million) Accurate capacity planning is

very critical

Chemical Clean Oxidation Photolithography Chemical Etch Ion Implant Metal/Insulator

Deposition Anneal

Need to plan capacity one year in advance of the expected demand

Find the best product mix with existing capacity

Assessing tool capacity by product mix (a complex process)

Current planning approach not very efficient (spreadsheets, simulations)

Helps identify tool capacity required to meet the demand

Helps volume mix of products to maximize profit

Solver: IBM Optimization Solutions and Library (OSL) on a Unix server

Graphical User Interface on a PC client Input data automatically formatted and

downloaded from tool-planning database Variables: 3,500 – 5,500 Constraints: 1,600 – 2,400 Products: 1 – 40 Solution time: 18 – 30 seconds

Many scenarios can be analysed in hours versus days

10s of millions of Dollars in savings Comprehensive reports enabling

analysis Enables a quick utilization of

scenarios to maximum capacity

50 Products, each 400 to 600 operations Tools; same operations, different speeds 100s Tool Groups (identical tools) Parallel, unrelated T.G. T.G. with common operations: Cascade T.G. w/o common operations: NonCascade Identify bottlenecks or gating T.G. Preferred order of T.G. in C.G.

TG 1

TG 2

TG 3

1, 2

, 7, 8

1, 2, 5, 6

1, 2, 3, 4

9, 10

11

12

TG 4

13, 15, 18, 19 14, 16,

17

TG 5

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Maxs.t.

# Cascade Tool Groups = 3 # Operations in C.G. = 12 (1,…, 12) # Non-Cascade Tools = 2 # Operation in N-C.G = 7 (13,…, 19) # Products = 3 Available time = 480 Min./Day # Variables = 306 # Constraints = 109 Solution Time < 1.0 Sec.

Cascade Gr. Index

Operation Cascade Gr.

Tool Cascade Gr.

1 1, 2 T1, T2, T3

2 3, 4 T1, T2

3 5, 6 T1, T3

4 7, 8 T2, T3

5 9, 10 T1

6 11 T2

7 12 T3

Operation Group index

TG 1 ratio

TG 2 ratio

TG 3ratio

1 1 1 1.8 2

2 1 1 1.5 2.25

3 2 1 0.5

4 2 1 2

5 3 1 1.5

6 3 1 0.75

7 4 1 1.67

8 4 1 1.25

9 5 1

10 5 1

11 6 1

12 7 1

Operation Product 1 Product 2 Product 3

1 10 - -

2 12 8 20

3 - 7 14

4 - 5 18

5 15 10 -

6 - 8 -

7 6 - -

8 4 - 9

9 - 11 6

10 - 8 -

11 - - 10

Operation Product 1 Product 2 Product 3

13 7 - 10

14 8 6 10

15 - 4 2

16 10 12 16

17 - 5 -

18 9 - -

19 - - 8

Tool 1

Tool 2

Tool 3

Tool 4

Tool 5

No. 3 6 13 7 5

Opt.No.

3 6 13 7 5

Forecast Demand

24 40 20 Total

Min. Demand

16 30 18 -

Max. Demand

50 80 40 -

Optimal Demand

16 68 18 -

Forecast Profit

192 360 120 672

Opt. Profit

128 612 108 848

Tool Util. Comparison

1.00

0

1.00

0

0.24

0

0.28

1

0.83

0

1.00

0

1.00

0

0.55

8

0.26

4

1.00

0

0

0.2

0.4

0.6

0.8

1

1.2

Tool1 Tool 2 Tool 3 Tool 4 Tool 5

Tool Groups

Utili

lizat

ion

First Run Optimum

Tool 1

Tool 2

Tool 3

Tool 4

Tool 5

No. 3 6 13 7 5

Rq.No.

6 6 13 7 8

Forecast Demand

34 64 50 Total

Min. Demand

25 48 34 -

Max. Demand

45 80 65 -

Optimal Demand

45 80 37 -

Forecast Profit

272 576 300 1148

Opt. Profit

360 720 223 1303

Tool Util. Comparison

1.75

9

1.00

1

1.00

1

0.53

6

1.48

1

1.00

0

1.00

0

0.51

6

0.53

6

0.92

6

1.00

0

1.00

0

0.66

0

0.53

0

1.00

0

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Tool1 Tool 2 Tool 3 Tool 4 Tool 5

Tool Groups

Utilil

izatio

n

First Run Second Run Optimum

Tool 1

Tool 2

Tool 3

Tool 4

Tool 5

No. 3 6 13 7 5

Opt.No.

3 6 13 7 6

Forecast Demand

25 48 34 Total

Min. Demand

20 43 30 -

Max. Demand

60 80 65 -

Optimal Demand

24.99 66.32 30 -

Forecast Profit

200 432 204 836

Opt. Profit

199.9 596.8 180 976.7

Tool Util. Comparison

1.00

0

1.00

0

0.70

6

0.37

9

1.06

8

1.00

0

1.00

0

0.71

0

0.37

9

0.89

01.00

0

1.00

0

0.95

3

0.37

7

1.00

0

0

0.2

0.4

0.6

0.8

1

1.2

Tool1 Tool 2 Tool 3 Tool 4 Tool 5

Tool Groups

Utilil

izatio

n

First Run Second Run Optimum

Tool 1

Tool 2

Tool 3

Tool 4

Tool 5

No. 3 6 13 7 5

Opt.No.

4 6 13 7 7

Forecast Demand

30 55 40 Total

Min. Demand

30 55 40 -

Max. Demand

60 100 80 -

Optimal Demand

30 91.7 40 -

Forecast Profit

240 495 240 975

Opt. Profit

240 825 240 1305

Tool Util. Comparison

1.07

8

1.00

1

1.00

1

0.44

6

1.24

8

1.00

0

1.00

0

0.18

8

0.44

6

0.78

0

1.00

0

1.00

0

0.66

8

0.49

0

1.00

0

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Tool1 Tool 2 Tool 3 Tool 4 Tool 5

Tool Groups

Utilil

izatio

n

First Run Second Run Optimum

Scenario ProductUnit

ProfitFixed

DemandFixedProfit

MinDemand

OptDemand

MaxDemand

OptProfit

1 P1 8 24 192 16 16 50 128

1 P2 9 40 360 30 68 80 612

1 P3 6 20 120 18 18 40 108

2 P1 8 34 272 25 45 45 360

2 P2 9 64 576 48 80 80 720

2 P3 6 50 300 34 37 65 223

Scenario ProductUnit

ProfitFixed

DemandFixedProfit

MinDemand

OptDemand

MaxDemand

OptProfit

3 P1 8 25 200 20 24.99 60 199.9

3 P2 9 48 432 43 66.32 80 596.8

3 P3 6 34 204 30 30 65 180

4 P1 8 30 240 30 30 60 240

4 P2 9 55 495 55 91.7 100 825

4 P3 6 40 240 40 40 80 240

Does not consider: Inventory Stochastic demand