Planning_formulations - Formulating Semiconductor...

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3/2/04 RCL - Semiconductor Production Planning 1 Formulating Semiconductor Formulating Semiconductor Production Planning Models Production Planning Models Rob Leachman Director, Competitive Semiconductor Manufacturing Program University of California at Berkeley 2 March, 2004
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3/2/04 RCL - Semiconductor Production Planning 2 Agenda • Introduction to semiconductor production planning problem • Textbook formulation • Step-by-step modification to a realistic formulation • Trends and state of the art in the industry
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3/2/04 RCL - Semiconductor Production Planning 3 Reference • “Semiconductor Production Planning,” in Handbook of Applied Optimization , Pardolos and Resende (eds.), Oxford University Press, 2001.
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3/2/04 RCL - Semiconductor Production Planning 4 Semiconductor Manufacturing • 100s of process steps performed by tens of machine types on discrete lots • 20-80 lots started per day, 5-50 device types • Long flow times: – Wafer fabrication: 40-60 days – Electrical die sort: 5 days – Chip packaging, final testing and packing: 5 days • Capital intensity – Wafer fab for advanced digital devices > $2 billion – New equipment required every few years
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3/2/04 RCL - Semiconductor Production Planning 5 Problem complexities • “Re-entrant” process: re-visit same machine type interspersed with visits to others • Steep learning curves for yields, flow times, process times, equipment efficiencies • Uncertainties in yields, flow times, capacities • Non-homogeneous machines and tooling • Product structure with many-to-many relationships • Huge size (1000s of products)
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3/2/04 RCL - Semiconductor Production Planning 6 Types of planning calculations Incremental – a large portion of the plan is fixed and plans for production of one or several devices are updated Regenerative – the plans for all devices are re-evaluated and updated
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3/2/04 RCL - Semiconductor Production Planning 7 Related optimization problems • Capacity planning • Establishing short-term factory floor targets • Short-term release scheduling • Our problem (production planning): plan rates of product release and rates of output in periods such as days, weeks or months
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3/2/04 RCL - Semiconductor Production Planning 8 Naïve (textbook) formulation • Variables x i,t = release quantity of device i in period t –I i,t and BO i,t = inventory and backorders of device i at end of period t • Parameters b i = yield of device i b ij = yield up to step j of device i a kij = process time at step j on equipment type k d it = demand for device i in period t r i = release cost h i , s i = holding cost, shortage cost
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3/2/04 RCL - Semiconductor Production Planning 9 Textbook formulation (cont.) () t i i t i i t i i N i T t BO s I h x r Minimize , , , 11 + + ∑∑ = = . ,..., 1 , ,..., 1 , 0 , 0 , 1 , , , 1 , T t N i BO I d BO I x b I i i t i t i t i t L i i i = = + = + = = τ . ,..., 1 , ,..., 1 , , 1 1 T t K k c x b a kt L t i N j ij kij N i ij i I = = = = . ,..., 1 , ,..., 1 , 0 , 0 , 0 T t N i BO I x I it it it = = Subject to
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  • Spring '11
  • Subramanainajolly
  • Periodic function, Noble gas, Emoticon, Planning permission, Semiconductor Production Planning

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Planning_formulations - Formulating Semiconductor...

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