Using Constraint Satisfaction Approach to Solve the Capacity Allocation Problem for Photolithography Area

  • Shu-Hsing Chung
  • Chun-Ying Huang
  • Amy Hsin-I Lee
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3982)


This paper addresses the capacity allocation problem for photo- lithography area (CAPPA) under an advanced technology environment. The CAPPA problem has two characteristics: process window and machine dedication. Process window means that a wafer needs to be processed on machines that can satisfy its process capability (process specification). Machine dedication means that after the first critical layer of a wafer lot is being processed on a certain machine, subsequent critical layers of this lot must be processed on the same machine to ensure good quality of final products. A production plan, constructed without considering the above two characteristics, is difficult to execute and to achieve its production targets. Thus, we model the CAPPA problem as a constraint satisfaction problem (CSP), which uses an efficient search algorithm to obtain a feasible solution. Additionally, we propose an upper bound of load unbalance estimation to reduce the search space of CSP for searching an optimal solution. Experimental results show that the proposed model is useful in solving the CAPPA problem in an efficient way.


Process Capability Constraint Satisfaction Problem Planning Period Critical Layer Wafer Fabrication 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Akçali, E., Nemoto, K., Uzsoy, R.: Cycle-Time Improvements for Photolithography Process in Semiconductor Manufacturing. IEEE Transactions on Semiconductor Manufacturing 14(1), 48–56 (2001)CrossRefGoogle Scholar
  2. 2.
    Brailsford, S.C., Potts, C.N., Smith, B.M.: Constraint Satisfaction Problems: Algorithms and Applications. European Journal of Operational Research 119(3), 557–581 (1999)MATHCrossRefGoogle Scholar
  3. 3.
    Chung, S.H., Huang, C.Y., Lee, A.H.I.: Capacity Allocation Model for Photolithography Workstation with the Constraints of Process Window and Machine Dedication. Production Planning and Control (2006) (accepted)Google Scholar
  4. 4.
    Freuder, E.C., Wallace, R.J.: Constraint Programming and Large Scale Discrete Optimization. American Mathematical Society, Providence (2001)MATHGoogle Scholar
  5. 5.
    Hung, Y.F., Cheng, G.J.: Hybrid Capacity Modeling for Alternative Machine Types in Linear Programming Production Planning. IIE Transactions 34(2), 157–165 (2002)Google Scholar
  6. 6.
    ILOG Inc.: ILOG OPL Studio 3.5. ILOG Inc., France (2001)Google Scholar
  7. 7.
    Kim, S., Yea, S.H., Kim, B.: Shift Scheduling for Steppers in the Semiconductor Wafer Fabrication Process. IIE Transactions 34(2), 167–177 (2002)Google Scholar
  8. 8.
    Kishimoto, M., Ozawa, K., Watanabe, K., Martin, D.: Optimized Operations by Extended X-Factor Theory Including Unit Hours Concept. IEEE Transactions on Semiconductor Manufacturing 14(3), 187–195 (2001)CrossRefGoogle Scholar
  9. 9.
    Leachman, R.C., Carmon, T.F.: On Capacity Modeling for Production Planning with Alternative Machine Types. IIE Transactions 24(4), 62–72 (1992)CrossRefGoogle Scholar
  10. 10.
    Lee, Y.H., Park, J., Kim, S.: Experimental Study on Input and Bottleneck Scheduling for a Semiconductor Fabrication Line. IIE Transactions 34(2), 179–190 (2002)MathSciNetGoogle Scholar
  11. 11.
    Lustig, I.J., Puget, J.-F.P.: Program Does Not Equal Program: Constraint Programming and Its Relationship to Mathematical Programming. Interfaces 31(6), 29–53 (2001)Google Scholar
  12. 12.
    Toktay, L.B., Uzsoy, R.: A Capacity Allocation Problem with Integer Side Constraints. European Journal of Operational Research 109(1), 170–182 (1998)MATHCrossRefGoogle Scholar
  13. 13.
    Uzsoy, R., Lee, C.-Y., Martin-Vega, L.A.: A Review of Production Planning and Scheduling Models in the Semiconductor Industry (I): System Characteristics, Performance Evaluation and Production Planning. IIE Transactions 24(4), 47–60 (1992)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Uzsoy, R., Lee, C.-Y., Martin-Vega, L.A.: A Review of Production Planning and Scheduling Models in the Semiconductor Industry (II): Shop-Floor Control. IIE Transactions 26(5), 44–55 (1994)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Shu-Hsing Chung
    • 1
  • Chun-Ying Huang
    • 1
  • Amy Hsin-I Lee
    • 2
  1. 1.Department of Industrial Engineering and ManagementNational Chiao Tung UniversityHsinchuTaiwan, R.O.C.
  2. 2.Department of Industrial ManagementChung Hua UniversityHsinchuTaiwan, R.O.C.

Personalised recommendations