A scenario-based stochastic programming model for the control or dummy wafers downgrading problem
The subject of this paper is to study a realistic planning environment in wafer fabrication for the control or dummy (C/D) wafers problem with uncertain demand. The demand of each product is assumed with a geometric Brownian motion and approximated by a finite discrete set of scenarios. A two‐stage...
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| Veröffentlicht in: | Applied stochastic models in business and industry Jg. 25; H. 3; S. 263 - 274 |
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Chichester, UK
John Wiley & Sons, Ltd
01.05.2009
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| ISSN: | 1524-1904, 1526-4025 |
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| Abstract | The subject of this paper is to study a realistic planning environment in wafer fabrication for the control or dummy (C/D) wafers problem with uncertain demand. The demand of each product is assumed with a geometric Brownian motion and approximated by a finite discrete set of scenarios. A two‐stage stochastic programming model is developed based on scenarios and solved by a deterministic equivalent large linear programming model. The model explicitly considers the objective to minimize the total cost of C/D wafers. A real‐world example is given to illustrate the practicality of a stochastic approach. The results are better in comparison with deterministic linear programming by using expectation instead of stochastic demands. The model improved the performance of control and dummy wafers management and the flexibility of determining the downgrading policy. Copyright © 2008 John Wiley & Sons, Ltd. |
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| AbstractList | The subject of this paper is to study a realistic planning environment in wafer fabrication for the control or dummy (C/D) wafers problem with uncertain demand. The demand of each product is assumed with a geometric Brownian motion and approximated by a finite discrete set of scenarios. A two‐stage stochastic programming model is developed based on scenarios and solved by a deterministic equivalent large linear programming model. The model explicitly considers the objective to minimize the total cost of C/D wafers. A real‐world example is given to illustrate the practicality of a stochastic approach. The results are better in comparison with deterministic linear programming by using expectation instead of stochastic demands. The model improved the performance of control and dummy wafers management and the flexibility of determining the downgrading policy. Copyright © 2008 John Wiley & Sons, Ltd. The subject of this paper is to study a realistic planning environment in wafer fabrication for the control or dummy (C/D) wafers problem with uncertain demand. The demand of each product is assumed with a geometric Brownian motion and approximated by a finite discrete set of scenarios. A two-stage stochastic programming model is developed based on scenarios and solved by a deterministic equivalent large linear programming model. The model explicitly considers the objective to minimize the total cost of C/D wafers. A real-world example is given to illustrate the practicality of a stochastic approach. The results are better in comparison with deterministic linear programming by using expectation instead of stochastic demands. The model improved the performance of control and dummy wafers management and the flexibility of determining the downgrading policy. |
| Author | Yang, Yi-Shu Chung, Shu-Hsing |
| Author_xml | – sequence: 1 givenname: Shu-Hsing surname: Chung fullname: Chung, Shu-Hsing organization: Department of Industrial Engineering and Management, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 300, Taiwan – sequence: 2 givenname: Yi-Shu surname: Yang fullname: Yang, Yi-Shu email: joanna@mail.dyu.edu.tw organization: Department of Industrial Engineering and Management, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 300, Taiwan |
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| Cites_doi | 10.1007/s00170-003-2031-1 10.1109/ISSM.2005.1513313 10.1016/j.ejor.2005.11.010 10.1111/j.2517-6161.1955.tb00191.x 10.1007/s00170-003-2028-9 10.1515/9781400830176 10.1109/IEMT.1994.404711 10.1007/s00170-003-1854-0 10.1287/mnsc.1.3-4.197 10.1109/66.778191 10.1109/ASMC.1997.630777 10.1109/ASMC.1998.731576 10.1007/978-3-642-61370-8_3 |
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| References | Chung SH, Kang HY, Pearn WL. A service level model for the control wafers safety inventory problem. The International Journal of Advanced Manufacturing and Technology 2005; 26:591-597. Benavides DL, Duley R, Johnson BE. As good as it gets: optimal fab design and deployment. IEEE Transactions on Semiconductor Manufacturing 1999; 12(3):281-287. Jarrow AR, Rudd A. Option Pricing. Irwin: Homewood, IL, 1983. Dixit AK, Pindyck RS. Investment under Uncertainty. Princeton University Press: Princeton, NJ, 1994. Kall P, Wallace SW. Stochastic Programming. Wiley: Chichester, U.K., 1994. Chung SH, Kang HY, Pearn WL. A linear programming model for the control wafers downgrading problem. The International Journal of Advanced Manufacturing and Technology 2005; 25:377-384. Dantzig GB. Linear programming under uncertainty. Management Science 1955; 1:197-206. Özelkan EC, Çakanyildirim M. Resource downgrading. European Journal of Operational Research 2007; 177:572-590. Lin YS, Chang YH, Chou YC. Application of stochastic programming to tool portfolio planning in semiconductor manufacturing. Journal of Management and Systems 2005; 12(4):1-15. Wu MC, Chien CS, Lu KS. Downgrade decision for control/dummy wafers in a fab. The International Journal of Advanced Manufacturing and Technology 2005; 26:585-590. Beale EML. On minimizing a convex function subject to linear inequalities. Journal of the Royal Statistical Society 1955; B17:173-184. 1999; 12 1994 1983 2005; 26 2007; 177 1955; 1 1955; B17 2005; 12 2005; 25 1988 Jarrow AR (e_1_2_1_17_2) 1983 Lin YS (e_1_2_1_15_2) 2005; 12 e_1_2_1_6_2 Kall P (e_1_2_1_12_2) 1994 e_1_2_1_7_2 e_1_2_1_4_2 e_1_2_1_5_2 e_1_2_1_2_2 Beale EML (e_1_2_1_11_2) 1955; 17 e_1_2_1_3_2 e_1_2_1_10_2 e_1_2_1_16_2 e_1_2_1_13_2 e_1_2_1_14_2 e_1_2_1_8_2 e_1_2_1_9_2 |
| References_xml | – reference: Wu MC, Chien CS, Lu KS. Downgrade decision for control/dummy wafers in a fab. The International Journal of Advanced Manufacturing and Technology 2005; 26:585-590. – reference: Beale EML. On minimizing a convex function subject to linear inequalities. Journal of the Royal Statistical Society 1955; B17:173-184. – reference: Benavides DL, Duley R, Johnson BE. As good as it gets: optimal fab design and deployment. IEEE Transactions on Semiconductor Manufacturing 1999; 12(3):281-287. – reference: Lin YS, Chang YH, Chou YC. Application of stochastic programming to tool portfolio planning in semiconductor manufacturing. Journal of Management and Systems 2005; 12(4):1-15. – reference: Jarrow AR, Rudd A. Option Pricing. Irwin: Homewood, IL, 1983. – reference: Chung SH, Kang HY, Pearn WL. A linear programming model for the control wafers downgrading problem. The International Journal of Advanced Manufacturing and Technology 2005; 25:377-384. – reference: Dantzig GB. Linear programming under uncertainty. Management Science 1955; 1:197-206. – reference: Chung SH, Kang HY, Pearn WL. A service level model for the control wafers safety inventory problem. The International Journal of Advanced Manufacturing and Technology 2005; 26:591-597. – reference: Dixit AK, Pindyck RS. Investment under Uncertainty. Princeton University Press: Princeton, NJ, 1994. – reference: Özelkan EC, Çakanyildirim M. Resource downgrading. European Journal of Operational Research 2007; 177:572-590. – reference: Kall P, Wallace SW. Stochastic Programming. Wiley: Chichester, U.K., 1994. – start-page: 298 end-page: 302 – volume: 26 start-page: 591 year: 2005 end-page: 597 article-title: A service level model for the control wafers safety inventory problem publication-title: The International Journal of Advanced Manufacturing and Technology – year: 1983 – volume: B17 start-page: 173 year: 1955 end-page: 184 article-title: On minimizing a convex function subject to linear inequalities publication-title: Journal of the Royal Statistical Society – start-page: 440 end-page: 443 – volume: 1 start-page: 197 year: 1955 end-page: 206 article-title: Linear programming under uncertainty publication-title: Management Science – year: 1988 – volume: 12 start-page: 1 issue: 4 year: 2005 end-page: 15 article-title: Application of stochastic programming to tool portfolio planning in semiconductor manufacturing publication-title: Journal of Management and Systems – start-page: 221 end-page: 225 – volume: 12 start-page: 281 issue: 3 year: 1999 end-page: 287 article-title: As good as it gets: optimal fab design and deployment publication-title: IEEE Transactions on Semiconductor Manufacturing – volume: 25 start-page: 377 year: 2005 end-page: 384 article-title: A linear programming model for the control wafers downgrading problem publication-title: The International Journal of Advanced Manufacturing and Technology – start-page: 123 end-page: 125 – volume: 177 start-page: 572 year: 2007 end-page: 590 article-title: Resource downgrading publication-title: European Journal of Operational Research – year: 1994 – volume: 26 start-page: 585 year: 2005 end-page: 590 article-title: Downgrade decision for control/dummy wafers in a fab publication-title: The International Journal of Advanced Manufacturing and Technology – ident: e_1_2_1_7_2 doi: 10.1007/s00170-003-2031-1 – ident: e_1_2_1_9_2 doi: 10.1109/ISSM.2005.1513313 – ident: e_1_2_1_8_2 doi: 10.1016/j.ejor.2005.11.010 – volume: 17 start-page: 173 year: 1955 ident: e_1_2_1_11_2 article-title: On minimizing a convex function subject to linear inequalities publication-title: Journal of the Royal Statistical Society doi: 10.1111/j.2517-6161.1955.tb00191.x – ident: e_1_2_1_4_2 doi: 10.1007/s00170-003-2028-9 – ident: e_1_2_1_16_2 doi: 10.1515/9781400830176 – volume-title: Stochastic Programming year: 1994 ident: e_1_2_1_12_2 – volume: 12 start-page: 1 issue: 4 year: 2005 ident: e_1_2_1_15_2 article-title: Application of stochastic programming to tool portfolio planning in semiconductor manufacturing publication-title: Journal of Management and Systems – volume-title: Option Pricing year: 1983 ident: e_1_2_1_17_2 – ident: e_1_2_1_2_2 doi: 10.1109/IEMT.1994.404711 – ident: e_1_2_1_6_2 doi: 10.1007/s00170-003-1854-0 – ident: e_1_2_1_10_2 doi: 10.1287/mnsc.1.3-4.197 – ident: e_1_2_1_14_2 doi: 10.1109/66.778191 – ident: e_1_2_1_3_2 doi: 10.1109/ASMC.1997.630777 – ident: e_1_2_1_5_2 doi: 10.1109/ASMC.1998.731576 – ident: e_1_2_1_13_2 doi: 10.1007/978-3-642-61370-8_3 |
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| SubjectTerms | control or dummy wafers downgrading scenario stochastic programming |
| Title | A scenario-based stochastic programming model for the control or dummy wafers downgrading problem |
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