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Dynamic Control of a Make-to-Order, Parallel-Server System with Cancellations

Author

Listed:
  • Melanie Rubino

    (Wolverine Trading LLC, Chicago, Illinois 60604)

  • Barış Ata

    (Kellogg School of Management, Northwestern University, Evanston, Illinois 60208)

Abstract

Motivated by make-to-order production systems, we consider a dynamic control problem for a multiclass, parallel-server queueing system. The production system serves multiple classes of customers who require rigid due-date lead times and may cancel their order subject to a cancellation penalty. To meet the due-date constraints, a system manager may outsource orders when the backlog of work is judged excessive, thereby incurring outsourcing costs. The system manager strives to minimize long-run average costs by dynamically making outsourcing and resource allocation decisions. Under heavy-traffic conditions, the scheduling problem is approximated by a Brownian control problem. Interpreting the solution of the Brownian control problem in the context of the original queueing system, a nongreedy outsourcing and resource allocation policy is proposed. A simulation experiment is performed to demonstrate the effectiveness of this policy.

Suggested Citation

  • Melanie Rubino & Barış Ata, 2009. "Dynamic Control of a Make-to-Order, Parallel-Server System with Cancellations," Operations Research, INFORMS, vol. 57(1), pages 94-108, February.
    • Handle: RePEc:inm:oropre:v:57:y:2009:i:1:p:94-108
    DOI: 10.1287/opre.1080.0532
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Baris Ata & Deishin Lee & Mustafa Hayri Tongarlak, 2024. "A diffusion model of dynamic participant inflow management," Queueing Systems: Theory and Applications, Springer, vol. 108(3), pages 383-414, December.
    2. Barış Ata & Xiaoshan Peng, 2020. "An Optimal Callback Policy for General Arrival Processes: A Pathwise Analysis," Operations Research, INFORMS, vol. 68(2), pages 327-347, March.
    3. Xinshang Wang & Van-Anh Truong, 2018. "Multi-Priority Online Scheduling with Cancellations," Operations Research, INFORMS, vol. 66(1), pages 104-122, January.
    4. Amy R. Ward & Mor Armony, 2013. "Blind Fair Routing in Large-Scale Service Systems with Heterogeneous Customers and Servers," Operations Research, INFORMS, vol. 61(1), pages 228-243, February.
    5. Özkan, Erhun & Tan, Barış, 2025. "Asymptotically optimal energy consumption and inventory control in a make-to-stock manufacturing system," European Journal of Operational Research, Elsevier, vol. 320(2), pages 375-388.
    6. Josh Reed & Bo Zhang, 2017. "Managing capacity and inventory jointly for multi-server make-to-stock queues," Queueing Systems: Theory and Applications, Springer, vol. 86(1), pages 61-94, June.
    7. Baris Ata & Xiaoshan Peng, 2018. "An Equilibrium Analysis of a Multiclass Queue with Endogenous Abandonments in Heavy Traffic," Operations Research, INFORMS, vol. 66(1), pages 163-183, January.
    8. Jeunghyun Kim & Ramandeep S. Randhawa & Amy R. Ward, 2018. "Dynamic Scheduling in a Many-Server, Multiclass System: The Role of Customer Impatience in Large Systems," Manufacturing & Service Operations Management, INFORMS, vol. 20(2), pages 285-301, May.
    9. Adan, Ivo J.B.F. & Boon, Marko A.A. & Weiss, Gideon, 2019. "Design heuristic for parallel many server systems," European Journal of Operational Research, Elsevier, vol. 273(1), pages 259-277.
    10. Rami Atar & Anat Lev-Ari, 2018. "Workload-Dependent Dynamic Priority for the Multiclass Queue with Reneging," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 494-515, May.
    11. Dongyuan Zhan & Gideon Weiss, 2018. "Many-server scaling of the N-system under FCFS–ALIS," Queueing Systems: Theory and Applications, Springer, vol. 88(1), pages 27-71, February.
    12. Mustafa Akan & Barı ş Ata & Tava Olsen, 2012. "Congestion-Based Lead-Time Quotation for Heterogenous Customers with Convex-Concave Delay Costs: Optimality of a Cost-Balancing Policy Based on Convex Hull Functions," Operations Research, INFORMS, vol. 60(6), pages 1505-1519, December.
    13. Barιş Ata & Deishin Lee & Erkut Sönmez, 2019. "Dynamic Volunteer Staffing in Multicrop Gleaning Operations," Operations Research, INFORMS, vol. 67(2), pages 295-314, March.
    14. Shuangchi He & Dacheng Yao & Hanqin Zhang, 2017. "Optimal Ordering Policy for Inventory Systems with Quantity-Dependent Setup Costs," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 979-1006, November.
    15. Baris Ata & Peter W. Glynn & Xiaoshan Peng, 2017. "An equilibrium analysis of a discrete-time Markovian queue with endogenous abandonments," Queueing Systems: Theory and Applications, Springer, vol. 86(1), pages 141-212, June.
    16. Samim Ghamami & Amy R. Ward, 2013. "Dynamic Scheduling of a Two-Server Parallel Server System with Complete Resource Pooling and Reneging in Heavy Traffic: Asymptotic Optimality of a Two-Threshold Policy," Mathematics of Operations Research, INFORMS, vol. 38(4), pages 761-824, November.
    17. Cao, Ping & Zhong, Zhiheng, 2025. "Asymptotically optimal routing of a many-server parallel queueing system with long-run average criterion," European Journal of Operational Research, Elsevier, vol. 321(2), pages 462-475.
    18. Amir A. Alwan & Baris Ata & Yuwei Zhou, 2024. "A queueing model of dynamic pricing and dispatch control for ride-hailing systems incorporating travel times," Queueing Systems: Theory and Applications, Springer, vol. 106(1), pages 1-66, February.

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