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Forming and scheduling jobs with capacitated containers in semiconductor manufacturing: Single machine problem

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  • Fehmi Tanrisever
  • Erhan Kutanoglu

Abstract

We study a scheduling problem motivated by the challenges observed in the newest semiconductor manufacturing wafer fabrication facilities. As wafers are larger and heavier in these wafer fabs, it is becoming more common to use specialized material handling containers that carry multiple orders coming from different customers and to schedule the containers as jobs in the fab. The system performance is a function of the completion times of orders, which ultimately depend on both (1) how the orders are assigned to such containers (“job formation”), and (2) how the containers are scheduled in the fab (“job scheduling”). The overall problem is to find the best way to form and schedule the jobs subject to complicating constraints, including the restrictions on the number of containers that can be used at one time and on the number of wafers the containers can carry. We focus on the single machine job formation and scheduling problem with the total completion time objective. We show that this problem is quite different from conventional parallel and serial batching scenarios and prove that the uncapacitated special case is polynomially solvable and the capacitated case is strongly NP-hard. We use a dynamic programming algorithm to solve the uncapacitated problem, which not only provides tight lower bounds for the capacitated problem, but also becomes a basis for a heuristic approach for the capacitated problem. The computational results show that this approach is very effective, leading to small optimality gaps that get even smaller as the problems become larger. Copyright Springer Science+Business Media, LLC 2008

Suggested Citation

  • Fehmi Tanrisever & Erhan Kutanoglu, 2008. "Forming and scheduling jobs with capacitated containers in semiconductor manufacturing: Single machine problem," Annals of Operations Research, Springer, vol. 159(1), pages 5-24, March.
    • Handle: RePEc:spr:annopr:v:159:y:2008:i:1:p:5-24:10.1007/s10479-007-0273-2
    DOI: 10.1007/s10479-007-0273-2
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    References listed on IDEAS

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    1. Gregory Dobson & Ramakrishnan S. Nambimadom, 2001. "The Batch Loading and Scheduling Problem," Operations Research, INFORMS, vol. 49(1), pages 52-65, February.
    2. Jolai Ghazvini, Fariborz & Dupont, Lionel, 1998. "Minimizing mean flow times criteria on a single batch processing machine with non-identical jobs sizes," International Journal of Production Economics, Elsevier, vol. 55(3), pages 273-280, August.
    3. Edward G. Coffman & Ardavan Nozari & Mihalis Yannakakis, 1989. "Optimal Scheduling of Products with Two Subassemblies on a Single Machine," Operations Research, INFORMS, vol. 37(3), pages 426-436, June.
    4. Potts, Chris N. & Kovalyov, Mikhail Y., 2000. "Scheduling with batching: A review," European Journal of Operational Research, Elsevier, vol. 120(2), pages 228-249, January.
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    Cited by:

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    3. Lin-Hui Sun & Kai Cui & Ju-Hong Chen & Jun Wang & Xian-Chen He, 2013. "Some results of the worst-case analysis for flow shop scheduling with a learning effect," Annals of Operations Research, Springer, vol. 211(1), pages 481-490, December.

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