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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

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Chemical Clean Oxidation Photolithography Chemical Etch Ion Implant Metal/Insulator Deposition Anneal

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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)

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Helps identify tool capacity required to meet the demand Helps volume mix of products to maximize profit

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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

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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

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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.

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TG 1 TG 2 TG 3 1, 2, 7, 8 1, 2, 5, 6 1, 2, 3, 4 9, 10 11 12

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TG 4 13, 15, 18, 19 14, 16, 17 TG 5

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Max s.t.

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# 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.

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Cascade Gr. Index Operation Cascade Gr. Tool Cascade Gr. 11, 2T1, T2, T3 23, 4T1, T2 35, 6T1, T3 47, 8T2, T3 59, 10T1 611T2 712T3

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Operation Group index TG 1 ratio TG 2 ratio TG 3 ratio 1111.82 2111.52.25 3210.5 4212 5311.5 6310.75 7411.67 8411.25 951 1051 1161 1271

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OperationProduct 1Product 2Product 3 110-- 212820 3-714 4-518 51510- 6-8- 76-- 84-9 9-116 10-8- 11--10

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OperationProduct 1Product 2Product 3 137-10 148610 15-42 16101216 17-5- 189-- 19--8

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Tool 1 Tool 2 Tool 3 Tool 4 Tool 5 No.361375 Opt. No. 361375 Forecast Demand 244020Total Min. Demand 163018- Max. Demand 508040- Optimal Demand 166818- Forecast Profit 192360120672 Opt. Profit 128612108848

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Tool 1 Tool 2 Tool 3 Tool 4 Tool 5 No.361375 Rq. No. 661378 Forecast Demand 346450Total Min. Demand 254834- Max. Demand 458065- Optimal Demand 458037- Forecast Profit 2725763001148 Opt. Profit 3607202231303

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Tool 1 Tool 2 Tool 3 Tool 4 Tool 5 No.361375 Opt. No. 361376 Forecast Demand 254834Total Min. Demand 204330- Max. Demand 608065- Optimal Demand 24.9966.3230- Forecast Profit 200432204836 Opt. Profit 199.9596.8180976.7

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Tool 1 Tool 2 Tool 3 Tool 4 Tool 5 No.361375 Opt. No. 461377 Forecast Demand 305540Total Min. Demand 305540- Max. Demand 6010080- Optimal Demand 3091.740- Forecast Profit 240495240975 Opt. Profit 2408252401305

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ScenarioProduct Unit Profit Fixed Demand Fixed Profit Min Demand Opt Demand Max Demand Opt Profit 1P182419216 50128 1P2940360306880612 1P362012018 40108 2P18342722545 360 2P29645764880 720 2P3650300343765223

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ScenarioProduct Unit Profit Fixed Demand Fixed Profit Min Demand Opt Demand Max Demand Opt Profit 3P18252002024.9960199.9 3P29484324366.3280596.8 3P363420430 65180 4P183024030 60240 4P29554955591.7100825 4P364024040 80240

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Does not consider: Inventory Stochastic demand

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