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Multiproduct Systems with Both Setup Times and Costs: Fluid Bounds and Schedules

Author

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  • Wei-Min Lan

    (Industrial and Operations Engineering Department, University of Michigan, 1205 Beal Avenue, Ann Arbor, Michigan 48109-2117)

  • Tava Lennon Olsen

    (John M. Olin School of Business, Washington University in St. Louis, One Brookings Drive, St. Louis, Missouri 63130-4899)

Abstract

This paper considers a multiproduct, single-server production system where both setup times and costs are incurred whenever the server changes product. The system is make-to-order with a per unit backlogging cost. The objective is to minimize the long-run average cost per unit time. Using a fluid model, we provide a closed-form lower bound on system performance. This bound is also shown to provide a lower bound for stochastic systems when scheduling is local or static, but is only an approximation when scheduling is global or dynamic. The fluid bound suggests both local and global scheduling heuristics, which are tested for the stochastic system via a simulation study.

Suggested Citation

  • Wei-Min Lan & Tava Lennon Olsen, 2006. "Multiproduct Systems with Both Setup Times and Costs: Fluid Bounds and Schedules," Operations Research, INFORMS, vol. 54(3), pages 505-522, June.
    • Handle: RePEc:inm:oropre:v:54:y:2006:i:3:p:505-522
    DOI: 10.1287/opre.1060.0298
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    References listed on IDEAS

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    1. Tava Lennon Olsen, 1999. "A Practical Scheduling Method for Multiclass Production Systems with Setups," Management Science, INFORMS, vol. 45(1), pages 116-130, January.
    2. Dimitris Bertsimas & José Niño-Mora, 1999. "Optimization of Multiclass Queueing Networks with Changeover Times Via the Achievable Region Approach: Part II, The Multi-Station Case," Mathematics of Operations Research, INFORMS, vol. 24(2), pages 331-361, May.
    3. Salah E. Elmaghraby, 1978. "The Economic Lot Scheduling Problem (ELSP): Review and Extensions," Management Science, INFORMS, vol. 24(6), pages 587-598, February.
    4. David M. Markowitz & Lawrence M. Wein, 2001. "Heavy Traffic Analysis of Dynamic Cyclic Policies: A Unified Treatment of the Single Machine Scheduling Problem," Operations Research, INFORMS, vol. 49(2), pages 246-270, April.
    5. S. W. Fuhrmann & Robert B. Cooper, 1985. "Stochastic Decompositions in the M / G /1 Queue with Generalized Vacations," Operations Research, INFORMS, vol. 33(5), pages 1117-1129, October.
    6. Dimitris Bertsimas & José Niño-Mora, 1999. "Optimization of Multiclass Queueing Networks with Changeover Times Via the Achievable Region Approach: Part I, The Single-Station Case," Mathematics of Operations Research, INFORMS, vol. 24(2), pages 306-330, May.
    7. J. G. Dai & Gideon Weiss, 2002. "A Fluid Heuristic for Minimizing Makespan in Job Shops," Operations Research, INFORMS, vol. 50(4), pages 692-707, August.
    8. Dimitris Bertsimas & David Gamarnik & Jay Sethuraman, 2003. "From Fluid Relaxations to Practical Algorithms for High-Multiplicity Job-Shop Scheduling: The Holding Cost Objective," Operations Research, INFORMS, vol. 51(5), pages 798-813, October.
    9. David M. Markowitz & Martin I. Reiman & Lawrence M. Wein, 2000. "The Stochastic Economic Lot Scheduling Problem: Heavy Traffic Analysis of Dynamic Cyclic Policies," Operations Research, INFORMS, vol. 48(1), pages 136-154, February.
    10. Awi Federgruen & Ziv Katalan, 1998. "Determining Production Schedules Under Base-Stock Policies in Single Facility Multi-Item Production Systems," Operations Research, INFORMS, vol. 46(6), pages 883-898, December.
    11. J. G. Dai & O. B. Jennings, 2004. "Stabilizing Queueing Networks with Setups," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 891-922, November.
    12. Boxma, O. J. & Down, D. G., 1997. "Dynamic server assignment in a two-queue model," European Journal of Operational Research, Elsevier, vol. 103(3), pages 595-609, December.
    13. Sox, Charles R. & Jackson, Peter L. & Bowman, Alan & Muckstadt, John A., 1999. "A review of the stochastic lot scheduling problem," International Journal of Production Economics, Elsevier, vol. 62(3), pages 181-200, September.
    14. Izak Duenyas & Mark P. Van Oyen, 1996. "Heuristic Scheduling of Parallel Heterogeneous Queues with Set-Ups," Management Science, INFORMS, vol. 42(6), pages 814-829, June.
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    Cited by:

    1. Alexey Matveev & Varvara Feoktistova & Ksenia Bolshakova, 2016. "On Global Near Optimality of Special Periodic Protocols for Fluid Polling Systems with Setups," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 1055-1070, December.
    2. Zhao, Yaping & Xu, Xiaoyun & Li, Haidong & Liu, Yanni, 2016. "Prioritized customer order scheduling to maximize throughput," European Journal of Operational Research, Elsevier, vol. 255(2), pages 345-356.
    3. Carri W. Chan & Mor Armony & Nicholas Bambos, 2016. "Maximum weight matching with hysteresis in overloaded queues with setups," Queueing Systems: Theory and Applications, Springer, vol. 82(3), pages 315-351, April.
    4. uit het Broek, Michiel A.J. & Van der Heide, Gerlach & Van Foreest, Nicky D., 2020. "Energy-saving policies for temperature-controlled production systems with state-dependent setup times and costs," European Journal of Operational Research, Elsevier, vol. 287(3), pages 916-928.
    5. Niv Buchbinder & Tracy Kimbrel & Retsef Levi & Konstantin Makarychev & Maxim Sviridenko, 2013. "Online Make-to-Order Joint Replenishment Model: Primal-Dual Competitive Algorithms," Operations Research, INFORMS, vol. 61(4), pages 1014-1029, August.
    6. Rappold, James A. & Yoho, Keenan D., 2014. "Setting safety stocks for stable rotation cycle schedules," International Journal of Production Economics, Elsevier, vol. 156(C), pages 146-158.

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