IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i2p194-d1314561.html
   My bibliography  Save this article

On the Control Policy of a Queuing–Inventory System with Variable Inventory Replenishment Speed

Author

Listed:
  • Jung Woo Baek

    (Department of Industrial and Systems Engineering, Dongguk University, Seoul 04620, Republic of Korea)

Abstract

This paper considers a make-to-order production–inventory system that comprises a production facility and an inventory warehouse. Customers arrive at the facility to place an order, and the orders are processed using the first-come-first-served (FCFS) discipline. The warehouse supplies inventory items (raw materials) for the production process, and the warehouse inventory is replenished by internal production. The speed of internal production can be controlled through additional costs. If the inventory level drops to zero, the unmet demand waits in the facility until the inventory is replenished. During the stockout period, newly arriving demand is lost. The stationary joint probability of unmet demands and inventory items is derived, and a cost model is constructed. The optimal control policy for internal production is investigated to minimize the cost per unit time of the system. The experimental results show that such a production speed adjustment could reduce costs by up to 42% compared to the cases without the adjustment.

Suggested Citation

  • Jung Woo Baek, 2024. "On the Control Policy of a Queuing–Inventory System with Variable Inventory Replenishment Speed," Mathematics, MDPI, vol. 12(2), pages 1-19, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:194-:d:1314561
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/2/194/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/2/194/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Agassi Melikov & Laman Poladova & Sandhya Edayapurath & Janos Sztrik, 2023. "Single-Server Queuing-Inventory Systems with Negative Customers and Catastrophes in the Warehouse," Mathematics, MDPI, vol. 11(10), pages 1-16, May.
    2. Brynzer, H. & Johansson, M. I., 1995. "Design and performance of kitting and order picking systems," International Journal of Production Economics, Elsevier, vol. 41(1-3), pages 115-125, October.
    3. A. Krishnamoorthy & Binitha Benny & Dhanya Shajin, 2017. "A revisit to queueing-inventory system with reservation, cancellation and common life time," OPSEARCH, Springer;Operational Research Society of India, vol. 54(2), pages 336-350, June.
    4. He, Q. -M. & Jewkes, E. M. & Buzacott, J., 2002. "Optimal and near-optimal inventory control policies for a make-to-order inventory-production system," European Journal of Operational Research, Elsevier, vol. 141(1), pages 113-132, August.
    5. Bozer, Yavuz A. & McGinnis, Leon F., 1992. "Kitting versus line stocking: A conceptual framework and a descriptive model," International Journal of Production Economics, Elsevier, vol. 28(1), pages 1-19, November.
    6. Zhao, Ning & Lian, Zhaotong, 2011. "A queueing-inventory system with two classes of customers," International Journal of Production Economics, Elsevier, vol. 129(1), pages 225-231, January.
    7. Zaiming Liu & Xuxiang Luo & Jinbiao Wu, 2020. "Analysis of an M/PH/1 Retrial Queueing-Inventory System with Level Dependent Retrial Rate," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-10, August.
    8. 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.
    9. Krishnamoorthy, A. & Viswanath, Narayanan C., 2013. "Stochastic decomposition in production inventory with service time," European Journal of Operational Research, Elsevier, vol. 228(2), pages 358-366.
    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. Baek, Jung Woo & Bae, Yun Han, 2022. "A queuing-inventory model for manufacturing systems with fluid-type inventory," Omega, Elsevier, vol. 111(C).
    2. Schmid, Nico André & Limère, Veronique & Raa, Birger, 2021. "Mixed model assembly line feeding with discrete location assignments and variable station space," Omega, Elsevier, vol. 102(C).
    3. Youseef Alotaibi, 2016. "Business process modelling challenges and solutions: a literature review," Journal of Intelligent Manufacturing, Springer, vol. 27(4), pages 701-723, August.
    4. Zhao, Ning & Lian, Zhaotong, 2011. "A queueing-inventory system with two classes of customers," International Journal of Production Economics, Elsevier, vol. 129(1), pages 225-231, January.
    5. Sternatz, Johannes, 2015. "The joint line balancing and material supply problem," International Journal of Production Economics, Elsevier, vol. 159(C), pages 304-318.
    6. 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.
    7. Manafzadeh Dizbin, Nima & Tan, Barış, 2020. "Optimal control of production-inventory systems with correlated demand inter-arrival and processing times," International Journal of Production Economics, Elsevier, vol. 228(C).
    8. 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.
    9. S. R. Chakravarthy & Arunava Maity & U. C. Gupta, 2017. "An ‘(s, S)’ inventory in a queueing system with batch service facility," Annals of Operations Research, Springer, vol. 258(2), pages 263-283, November.
    10. Boysen, Nils & Emde, Simon, 2014. "Scheduling the part supply of mixed-model assembly lines in line-integrated supermarkets," European Journal of Operational Research, Elsevier, vol. 239(3), pages 820-829.
    11. 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.
    12. Dhanya Shajin & A. Krishnamoorthy & A. N. Dudin & Varghese C. Joshua & Varghese Jacob, 2020. "On a queueing-inventory system with advanced reservation and cancellation for the next K time frames ahead: the case of overbooking," Queueing Systems: Theory and Applications, Springer, vol. 94(1), pages 3-37, February.
    13. A. Krishnamoorthy & Dhanya Shajin & B. Lakshmy, 2016. "GI/M/1 type queueing-inventory systems with postponed work, reservation, cancellation and common life time," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(2), pages 357-388, June.
    14. 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.
    15. Agassi Melikov & Laman Poladova & Janos Sztrik, 2024. "Queuing-Inventory System with Catastrophes in the Warehouse: Case of Rare Catastrophes," Mathematics, MDPI, vol. 12(6), pages 1-19, March.
    16. Yuying Zhang & Dequan Yue & Wuyi Yue, 2022. "A queueing-inventory system with random order size policy and server vacations," Annals of Operations Research, Springer, vol. 310(2), pages 595-620, March.
    17. Daria Battini & Nils Boysen & Simon Emde, 2013. "Just-in-Time supermarkets for part supply in the automobile industry," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 24(2), pages 209-217, July.
    18. Agassi Melikov & Ramil Mirzayev & Janos Sztrik, 2023. "Double-Sources Queuing-Inventory Systems with Finite Waiting Room and Destructible Stocks," Mathematics, MDPI, vol. 11(1), pages 1-16, January.
    19. Grzegorz Tarczyński, 2023. "Linear programming models for optimal workload and batching in pick-and-pass warehousing systems," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 33(3), pages 141-158.
    20. 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.

    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:gam:jmathe:v:12:y:2024:i:2:p:194-:d:1314561. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.