IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v331y2023i2d10.1007_s10479-022-04901-2.html
   My bibliography  Save this article

Optimal service rates of a queueing inventory system with finite waiting hall, arbitrary service times and positive lead times

Author

Listed:
  • M. Keerthana

    (Madurai Kamaraj University)

  • N. Sangeetha

    (Manonmaniam Sundaranar University College)

  • B. Sivakumar

    (Madurai Kamaraj University)

Abstract

In this article, we consider a finite capacity queueing-inventory system in which the service rate is subject to control. We assume that the customers arrive according to a Poisson process. The customer who arrives to the service station, when the waiting hall is full, is considered to be lost. The inventory attached with the service facility is replenished according to a (s, Q) policy and the lead times are exponentially distributed. We calculate the optimal service rates to be employed at each service completion epoch so that the long-run expected cost rate is minimized for fixed maximum inventory level, reorder point and capacity of the waiting hall. This problem is modelled as a semi-Markov decision problem. The stationary optimal policy is obtained using linear programming algorithm and the results are illustrated numerically.

Suggested Citation

  • M. Keerthana & N. Sangeetha & B. Sivakumar, 2023. "Optimal service rates of a queueing inventory system with finite waiting hall, arbitrary service times and positive lead times," Annals of Operations Research, Springer, vol. 331(2), pages 739-762, December.
    • Handle: RePEc:spr:annopr:v:331:y:2023:i:2:d:10.1007_s10479-022-04901-2
    DOI: 10.1007/s10479-022-04901-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-022-04901-2
    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/s10479-022-04901-2?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. O. Berman & K.P. Sapna, 2002. "Optimal service rates of a service facility with perishable inventory items," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(5), pages 464-482, August.
    2. Hilal Al Hamadi & N. Sangeetha & B. Sivakumar, 2015. "Optimal control of service parameter for a perishable inventory system maintained at service facility with impatient customers," Annals of Operations Research, Springer, vol. 233(1), pages 3-23, October.
    3. Oded Berman & Eungab Kim, 2004. "Dynamic inventory strategies for profit maximization in a service facility with stochastic service, demand and lead time," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(3), pages 497-521, December.
    4. Philip Wolfe & G. B. Dantzig, 1962. "Linear Programming in a Markov Chain," Operations Research, INFORMS, vol. 10(5), pages 702-710, October.
    5. Kim, Eungab, 2005. "Optimal inventory replenishment policy for a queueing system with finite waiting room capacity," European Journal of Operational Research, Elsevier, vol. 161(1), pages 256-274, February.
    6. N. Sangeetha & B. Sivakumar, 2020. "Optimal service rates of a perishable inventory system with service facility," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 16(4), pages 515-550.
    Full references (including those not matched with items on IDEAS)

    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. S. K. Samanta & K. P. Sapna Isotupa & A. Verma, 2023. "Continuous review (s, Q) inventory system at a service facility with positive order lead times," Annals of Operations Research, Springer, vol. 331(2), pages 1007-1028, December.
    2. A. Krishnamoorthy & R. Manikandan & B. Lakshmy, 2015. "A revisit to queueing-inventory system with positive service time," Annals of Operations Research, Springer, vol. 233(1), pages 221-236, October.
    3. Song, Dong-Ping & Dong, Jing-Xin & Xu, Jingjing, 2014. "Integrated inventory management and supplier base reduction in a supply chain with multiple uncertainties," European Journal of Operational Research, Elsevier, vol. 232(3), pages 522-536.
    4. Jeganathan, K. & Abdul Reiyas, M. & Prasanna Lakshmi, K. & Saravanan, S., 2019. "Two server Markovian inventory systems with server interruptions: Heterogeneous vs. homogeneous servers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 177-200.
    5. V. Radhamani & B. Sivakumar & G. Arivarignan, 2022. "A Comparative Study on Replenishment Policies for Perishable Inventory System with Service Facility and Multiple Server Vacation," OPSEARCH, Springer;Operational Research Society of India, vol. 59(1), pages 229-265, March.
    6. Dhanya Shajin & A. Krishnamoorthy & R. Manikandan, 2022. "On a queueing-inventory system with common life time and Markovian lead time process," Operational Research, Springer, vol. 22(1), pages 651-684, March.
    7. Kangzhou Wang & Shouchang Chen & Zhibin Jiang & Weihua Zhou & Na Geng, 2021. "Capacity Allocation of an Integrated Production and Service System," Production and Operations Management, Production and Operations Management Society, vol. 30(8), pages 2765-2781, August.
    8. Dhanya Shajin & Jaison Jacob & A. Krishnamoorthy, 2022. "On a queueing inventory problem with necessary and optional inventories," Annals of Operations Research, Springer, vol. 315(2), pages 2089-2114, August.
    9. Dhanya Shajin & A. Krishnamoorthy, 2021. "On a queueing-inventory system with impatient customers, advanced reservation, cancellation, overbooking and common life time," Operational Research, Springer, vol. 21(2), pages 1229-1253, June.
    10. Hanukov, Gabi & Avinadav, Tal & Chernonog, Tatyana & Yechiali, Uri, 2020. "A service system with perishable products where customers are either fastidious or strategic," International Journal of Production Economics, Elsevier, vol. 228(C).
    11. Klaus Werner Schmidt & Öncü Hazır, 2019. "Formulation and solution of an optimal control problem for industrial project control," Annals of Operations Research, Springer, vol. 280(1), pages 337-350, September.
    12. Maike Schwarz & Hans Daduna, 2006. "Queueing systems with inventory management with random lead times and with backordering," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(3), pages 383-414, December.
    13. Umay Uzunoglu Kocer & Serife Ozkar, 2023. "A production queueing-inventory system with two-customer and a server subject to breakdown," Annals of Operations Research, Springer, vol. 331(2), pages 1089-1117, December.
    14. Jalili Marand, Ata & Li, Hongyan & Thorstenson, Anders, 2019. "Joint inventory control and pricing in a service-inventory system," International Journal of Production Economics, Elsevier, vol. 209(C), pages 78-91.
    15. Sha, Yue & Zhang, Junlong & Cao, Hui, 2021. "Multistage stochastic programming approach for joint optimization of job scheduling and material ordering under endogenous uncertainties," European Journal of Operational Research, Elsevier, vol. 290(3), pages 886-900.
    16. K. Helmes & R. H. Stockbridge, 2000. "Numerical Comparison of Controls and Verification of Optimality for Stochastic Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 106(1), pages 107-127, July.
    17. N. Nithya & N. Anbazhagan & S. Amutha & K. Jeganathan & Gi-Cheon Park & Gyanendra Prasad Joshi & Woong Cho, 2023. "Controlled Arrivals on the Retrial Queueing–Inventory System with an Essential Interruption and Emergency Vacationing Server," Mathematics, MDPI, vol. 11(16), pages 1-24, August.
    18. R. Suganya & Lewis Nkenyereye & N. Anbazhagan & S. Amutha & M. Kameswari & Srijana Acharya & Gyanendra Prasad Joshi, 2021. "Perishable Inventory System with N-Policy, MAP Arrivals, and Impatient Customers," Mathematics, MDPI, vol. 9(13), pages 1-15, June.
    19. Subrata Golui & Chandan Pal & R. Manikandan & Abhay Sobhanan, 2024. "Optimal control of a dynamic production-inventory system with various cost criteria," Annals of Operations Research, Springer, vol. 337(1), pages 75-103, June.
    20. Agassi Melikov & Ramil Mirzayev & Sajeev S. Nair, 2022. "Double Sources Queuing-Inventory System with Hybrid Replenishment Policy," Mathematics, MDPI, vol. 10(14), pages 1-16, July.

    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:annopr:v:331:y:2023:i:2:d:10.1007_s10479-022-04901-2. 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.