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Control of a Single-Server Tandem Queueing System with Setups

Author

Listed:
  • Izak Duenyas

    (University of Michigan, Ann Arbor, Michigan)

  • Diwakar Gupta

    (University of Michigan, Ann Arbor, Michigan)

  • Tava Lennon Olsen

    (University of Michigan, Ann Arbor, Michigan)

Abstract

This paper considers the control of a single-server tandem queueing system with setups. Jobs arrive to the system according to a Poisson process and are produced to order. A single server must perform a number of different operations on each job. There is a setup time for the server to switch between different operations. We assume that there is a holding cost at each operation, which is nondecreasing in operation number (i.e., as value is added to a job, it becomes more expensive to hold). The control problem is to decide which job the server should process at each point in time.We formulate this control problem as a Markov-Decision Process. We partially characterize the optimal policy, develop an exact analysis of exhaustive and gated polling policies, and develop an effective heuristic policy. The results of a simulation study, which tests the performance of the policies considered, are reported. These computational results indicate that our heuristic is effective for a wide variety of cases.

Suggested Citation

  • Izak Duenyas & Diwakar Gupta & Tava Lennon Olsen, 1998. "Control of a Single-Server Tandem Queueing System with Setups," Operations Research, INFORMS, vol. 46(2), pages 218-230, April.
    • Handle: RePEc:inm:oropre:v:46:y:1998:i:2:p:218-230
    DOI: 10.1287/opre.46.2.218
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    References listed on IDEAS

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    1. Steven A. Lippman, 1975. "Applying a New Device in the Optimization of Exponential Queuing Systems," Operations Research, INFORMS, vol. 23(4), pages 687-710, August.
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    Cited by:

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    3. Yi‐Chun Tsai & Nilay Tanık Argon, 2008. "Dynamic server assignment policies for assembly‐type queues with flexible servers," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(3), pages 234-251, April.
    4. Yun Fong Lim & Bingnan Lu & Rowan Wang & Wenjia Zhang, 2020. "Flexibly Serving A Finite Number of Heterogeneous Jobs in A Tandem System," Production and Operations Management, Production and Operations Management Society, vol. 29(6), pages 1431-1447, June.
    5. Seyed M. Iravani & Mark P. Van Oyen & Katharine T. Sims, 2005. "Structural Flexibility: A New Perspective on the Design of Manufacturing and Service Operations," Management Science, INFORMS, vol. 51(2), pages 151-166, February.
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    7. S.M.R. Iravani & J.A. Buzacott & M.J.M. Posner, 2005. "A robust policy for serial agile production systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(1), pages 58-73, February.
    8. Eser Kırkızlar & Sigrún Andradóttir & Hayriye Ayhan, 2012. "Flexible Servers in Understaffed Tandem Lines," Production and Operations Management, Production and Operations Management Society, vol. 21(4), pages 761-777, July.
    9. Seyed M. R. Iravani & John A. Buzacott & Morton J. M. Posner, 2003. "Operations and Shipment Scheduling of a Batch on a Felxible Machine," Operations Research, INFORMS, vol. 51(4), pages 585-601, August.
    10. Samuli Aalto & Ziv Scully, 2022. "On the Gittins index for multistage jobs," Queueing Systems: Theory and Applications, Springer, vol. 102(3), pages 353-371, December.
    11. Wallace J. Hopp & Seyed M. R. Iravani & Biying Shou, 2005. "Serial Agile Production Systems with Automation," Operations Research, INFORMS, vol. 53(5), pages 852-866, October.
    12. Gregory Dobson & Hsiao-Hui Lee & Arvind Sainathan & Vera Tilson, 2012. "A Queueing Model to Evaluate the Impact of Patient "Batching" on Throughput and Flow Time in a Medical Teaching Facility," Manufacturing & Service Operations Management, INFORMS, vol. 14(4), pages 584-599, October.
    13. Ramesh Arumugam & Maria Mayorga & Kevin Taaffe, 2009. "Inventory based allocation policies for flexible servers in serial systems," Annals of Operations Research, Springer, vol. 172(1), pages 1-23, November.
    14. Gabriel Zayas-Cabán & Jingui Xie & Linda V. Green & Mark E. Lewis, 2016. "Dynamic control of a tandem system with abandonments," Queueing Systems: Theory and Applications, Springer, vol. 84(3), pages 279-293, December.
    15. Wallace J. Hopp & Seyed M.R. Iravani & Biying Shou & Robert Lien, 2009. "Design and control of agile automated CONWIP production lines," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(1), pages 42-56, February.
    16. Tuğçe Işık & Sigrún Andradóttir & Hayriye Ayhan, 2022. "Dynamic Control of Non‐Collaborative Workers When Reassignment Is Costly," Production and Operations Management, Production and Operations Management Society, vol. 31(3), pages 1332-1352, March.
    17. Eser Kırkızlar & Sigrún Andradóttir & Hayriye Ayhan, 2010. "Robustness of efficient server assignment policies to service time distributions in finite‐buffered lines," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(6), pages 563-582, September.
    18. Soroush Saghafian & Wallace J. Hopp & Mark P. Van Oyen & Jeffrey S. Desmond & Steven L. Kronick, 2012. "Patient Streaming as a Mechanism for Improving Responsiveness in Emergency Departments," Operations Research, INFORMS, vol. 60(5), pages 1080-1097, October.
    19. Dimitrios Pandelis, 2007. "Optimal use of excess capacity in two interconnected queues," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(1), pages 179-192, February.

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