IDEAS home Printed from https://ideas.repec.org/a/spr/queues/v86y2017i1d10.1007_s11134-017-9519-0.html
   My bibliography  Save this article

Managing capacity and inventory jointly for multi-server make-to-stock queues

Author

Listed:
  • Josh Reed

    (Leonard N. Stern School of Business, Kaufman Management Center)

  • Bo Zhang

    (IBM T.J. Watson Research Center)

Abstract

We consider joint capacity–inventory management for multi-server make-to-stock queues operating under a base stock policy. The number of servers corresponds to the capacity decision, and the base stock level is the inventory decision. Our goal is to minimize a combination of capacity, inventory, and backordering costs. We develop a square-root rule for the joint decision and justify the rule analytically in a many-server queue asymptotic framework. We demonstrate the accuracy of the square-root rule, first via our derivation and numerical assessment of a novel corrected diffusion approximation and then more directly by conducting extensive numerical experiments. Finally, we provide operational insights into the trade-offs involved in such joint management problems, through various analysis based on the square-root rule as well as a comparison with analogous results for single-server make-to-stock queues.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:queues:v:86:y:2017:i:1:d:10.1007_s11134-017-9519-0
    DOI: 10.1007/s11134-017-9519-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11134-017-9519-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11134-017-9519-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. M. R. Rao, 1976. "Optimal Capacity Expansion with Inventory," Operations Research, INFORMS, vol. 24(2), pages 291-300, April.
    2. Bo Zhang & Bert Zwart, 2013. "Steady-State Analysis for Multiserver Queues Under Size Interval Task Assignment in the Quality-Driven Regime," Mathematics of Operations Research, INFORMS, vol. 38(3), pages 504-525, August.
    3. Bo Zhang & Johan S. H. van Leeuwaarden & Bert Zwart, 2012. "Staffing Call Centers with Impatient Customers: Refinements to Many-Server Asymptotics," Operations Research, INFORMS, vol. 60(2), pages 461-474, April.
    4. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(1), pages 193-194, February.
    5. Shlomo Halfin & Ward Whitt, 1981. "Heavy-Traffic Limits for Queues with Many Exponential Servers," Operations Research, INFORMS, vol. 29(3), pages 567-588, June.
    6. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(2), pages 541-545, April.
    7. Paul Glasserman, 1997. "Bounds and Asymptotics for Planning Critical Safety Stocks," Operations Research, INFORMS, vol. 45(2), pages 244-257, April.
    8. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(4), pages 1007-1017, August.
    9. Saif Benjaafar & Mohsen ElHafsi & Francis de Véricourt, 2004. "Demand Allocation in Multiple-Product, Multiple-Facility, Make-to-Stock Systems," Management Science, INFORMS, vol. 50(10), pages 1431-1448, October.
    10. James R. Bradley & Peter W. Glynn, 2002. "Managing Capacity and Inventory Jointly in Manufacturing Systems," Management Science, INFORMS, vol. 48(2), pages 273-288, February.
    11. 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.
    12. Erica L. Plambeck & Stefanos A. Zenios, 2003. "Incentive Efficient Control of a Make-to-Stock Production System," Operations Research, INFORMS, vol. 51(3), pages 371-386, June.
    13. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1461-1465, December.
    14. Jodlbauer, Herbert & Altendorfer, Klaus, 2010. "Trade-off between capacity invested and inventory needed," European Journal of Operational Research, Elsevier, vol. 203(1), pages 118-133, May.
    15. Eberly, Janice C. & Van Mieghem, Jan A., 1997. "Multi-factor Dynamic Investment under Uncertainty," Journal of Economic Theory, Elsevier, vol. 75(2), pages 345-387, August.
    16. Jan A. Van Mieghem & Nils Rudi, 2002. "Newsvendor Networks: Inventory Management and Capacity Investment with Discretionary Activities," Manufacturing & Service Operations Management, INFORMS, vol. 4(4), pages 313-335, August.
    17. Ward Whitt, 1992. "Understanding the Efficiency of Multi-Server Service Systems," Management Science, INFORMS, vol. 38(5), pages 708-723, May.
    18. Achal Bassamboo & Ramandeep S. Randhawa & Assaf Zeevi, 2010. "Capacity Sizing Under Parameter Uncertainty: Safety Staffing Principles Revisited," Management Science, INFORMS, vol. 56(10), pages 1668-1686, October.
    19. Sem Borst & Avi Mandelbaum & Martin I. Reiman, 2004. "Dimensioning Large Call Centers," Operations Research, INFORMS, vol. 52(1), pages 17-34, February.
    20. Nasuh Buyukkaramikli & J. Bertrand & Henny Ooijen, 2013. "Flexible hiring in a make to order system with parallel processing units," Annals of Operations Research, Springer, vol. 209(1), pages 159-178, October.
    21. Lawrence M. Wein, 1992. "Dynamic Scheduling of a Multiclass Make-to-Stock Queue," Operations Research, INFORMS, vol. 40(4), pages 724-735, August.
    22. René Caldentey & Lawrence M. Wein, 2003. "Analysis of a Decentralized Production-Inventory System," Manufacturing & Service Operations Management, INFORMS, vol. 5(1), pages 1-17, November.
    23. Mincsovics, Gergely & Tan, Tarkan & Alp, Osman, 2009. "Integrated capacity and inventory management with capacity acquisition lead times," European Journal of Operational Research, Elsevier, vol. 196(3), pages 949-958, August.
    24. van Leeuwaarden, Johan S.H. & Knessl, Charles, 2011. "Transient behavior of the Halfin-Whitt diffusion," Stochastic Processes and their Applications, Elsevier, vol. 121(7), pages 1524-1545, July.
    25. Alexandar Angelus & Evan L. Porteus, 2002. "Simultaneous Capacity and Production Management of Short-Life-Cycle, Produce-to-Stock Goods Under Stochastic Demand," Management Science, INFORMS, vol. 48(3), pages 399-413, March.
    26. Ronald W. Wolff, 1982. "Poisson Arrivals See Time Averages," Operations Research, INFORMS, vol. 30(2), pages 223-231, April.
    27. Itai Gurvich, 2014. "Validity of Heavy-Traffic Steady-State Approximations in Multiclass Queueing Networks: The Case of Queue-Ratio Disciplines," Mathematics of Operations Research, INFORMS, vol. 39(1), pages 121-162, February.
    28. A. J. E. M. Janssen & J. S. H. van Leeuwaarden & Bert Zwart, 2011. "Refining Square-Root Safety Staffing by Expanding Erlang C," Operations Research, INFORMS, vol. 59(6), pages 1512-1522, December.
    29. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(5), pages 1273-1289, October.
    30. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(3), pages 819-821, June.
    31. Avishai Mandelbaum & Sergey Zeltyn, 2009. "Staffing Many-Server Queues with Impatient Customers: Constraint Satisfaction in Call Centers," Operations Research, INFORMS, vol. 57(5), pages 1189-1205, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Nha-Nghi Cruz & Hans Daduna, 2019. "Optimal capacity allocation in a production–inventory system with base stock," Annals of Operations Research, Springer, vol. 277(2), pages 329-344, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Frank Karsten & Marco Slikker & Geert-Jan van Houtum, 2015. "Resource Pooling and Cost Allocation Among Independent Service Providers," Operations Research, INFORMS, vol. 63(2), pages 476-488, April.
    2. Cambier, Adrien & Chardy, Matthieu & Figueiredo, Rosa & Ouorou, Adam & Poss, Michael, 2022. "Optimizing subscriber migrations for a telecommunication operator in uncertain context," European Journal of Operational Research, Elsevier, vol. 298(1), pages 308-321.
    3. Libura, Marek, 2007. "On the adjustment problem for linear programs," European Journal of Operational Research, Elsevier, vol. 183(1), pages 125-134, November.
    4. Christophe Loussouarn & Carine Franc & Yann Videau & Julien Mousquès, 2021. "Can General Practitioners Be More Productive? The Impact of Teamwork and Cooperation with Nurses on GP Activities," Health Economics, John Wiley & Sons, Ltd., vol. 30(3), pages 680-698, March.
    5. Tschakert, Petra, 2016. "Shifting Discourses of Vilification and the Taming of Unruly Mining Landscapes in Ghana," World Development, Elsevier, vol. 86(C), pages 123-132.
    6. Isabelle Boutron & Peter John & David J. Torgerson, 2010. "Reporting Methodological Items in Randomized Experiments in Political Science," The ANNALS of the American Academy of Political and Social Science, , vol. 628(1), pages 112-131, March.
    7. Ben Slimane, Faten & Padilla Angulo, Laura, 2019. "Strategic change and corporate governance: Evidence from the stock exchange industry," Journal of Business Research, Elsevier, vol. 103(C), pages 206-218.
    8. Weijun Xie & Yanfeng Ouyang & Sze Chun Wong, 2016. "Reliable Location-Routing Design Under Probabilistic Facility Disruptions," Transportation Science, INFORMS, vol. 50(3), pages 1128-1138, August.
    9. Natalia Nikolaevna Natocheeva* & Yuri Alexandrovich Rovensky & Yuri Yuryevich Rusanov & Tatiana Viktorovna Belyanchikova & Anna Anatolevna Staurskaya, 2018. "Optimizing Variability of Approaches to Regulatory Financing of Higher Education Services," The Journal of Social Sciences Research, Academic Research Publishing Group, pages 221-227:3.
    10. Sahar Validi & Arijit Bhattacharya & P. J. Byrne, 2020. "Sustainable distribution system design: a two-phase DoE-guided meta-heuristic solution approach for a three-echelon bi-objective AHP-integrated location-routing model," Annals of Operations Research, Springer, vol. 290(1), pages 191-222, July.
    11. Andy Hall, 2005. "Capacity development for agricultural biotechnology in developing countries: an innovation systems view of what it is and how to develop it," Journal of International Development, John Wiley & Sons, Ltd., vol. 17(5), pages 611-630.
    12. Athinoula A. Kosti & Simon Colreavy-Donnelly & Fabio Caraffini & Zacharias A. Anastassi, 2020. "Efficient Computation of the Nonlinear Schrödinger Equation with Time-Dependent Coefficients," Mathematics, MDPI, vol. 8(3), pages 1-12, March.
    13. Bruno Frey, 2005. "Problems with Publishing: Existing State and Solutions," European Journal of Law and Economics, Springer, vol. 19(2), pages 173-190, April.
    14. Lan, Heng-you, 2021. "Approximation-solvability of population biology systems based on p-Laplacian elliptic inequalities with demicontinuous strongly pseudo-contractive operators," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    15. Shelly Jeffcott & Nick Pidgeon & Andrew Weyman & John Walls, 2006. "Risk, Trust, and Safety Culture in U.K. Train Operating Companies," Risk Analysis, John Wiley & Sons, vol. 26(5), pages 1105-1121, October.
    16. Rainer Niemann, 2004. "Asymmetric Taxation and Cross-Border Investment Decisions," CESifo Working Paper Series 1219, CESifo.
    17. Zhenghua Gu & Xiaomeng Cao & Guoliang Liu & Weizhen Lu, 2014. "Optimizing Operation Rules of Sluices in River Networks Based on Knowledge-driven and Data-driven Mechanism," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(11), pages 3455-3469, September.
    18. Ian N. Gregory & Paul S. Ell, 2005. "Breaking the boundaries: geographical approaches to integrating 200 years of the census," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 168(2), pages 419-437, March.
    19. Alexis Comber & Paul Harris, 2018. "Geographically weighted elastic net logistic regression," Journal of Geographical Systems, Springer, vol. 20(4), pages 317-341, October.
    20. Fuamenya A. Francis, 2018. "Impact of Management Practices in Industries in the Industrial ¨C Free ¨C Trade Zones in Douala, Littoral Region of Cameroon: ¡°Challenges and Prospects¡±," Business and Management Research, Business and Management Research, Sciedu Press, vol. 7(3), pages 10-26, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:queues:v:86:y:2017:i:1:d:10.1007_s11134-017-9519-0. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.