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Queueing systems with inventory management with random lead times and with backordering

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  • Maike Schwarz
  • Hans Daduna

Abstract

We investigate M/M/1/∞-systems with inventory management, continuous review, exponentially distributed lead times and backordering. We compute performance measures and derive optimality conditions under different order policies. For performance measures, which are not explicitly at hand, we present an approximation scheme for all possible parameter combinations. Although we cannot completely determine analytically the steady state probabilities for the system we are able to derive functional relations between interesting probabilities and show surprising insensitivity properties of several performance measures. For the approximations we develop an algorithm adapted to the system structure which suggests easy adaption to other systems. Copyright Springer-Verlag 2006

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:64:y:2006:i:3:p:383-414
    DOI: 10.1007/s00186-006-0085-1
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    References listed on IDEAS

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    1. 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.
    2. Oded Berman & Eungab Kim, 2001. "Dynamic order replenishment policy in internet-based supply chains," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 53(3), pages 371-390, July.
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    Cited by:

    1. Youseef Alotaibi, 2016. "Business process modelling challenges and solutions: a literature review," Journal of Intelligent Manufacturing, Springer, vol. 27(4), pages 701-723, August.
    2. 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.
    3. A. Krishnamoorthy & Dhanya Shajin & B. Lakshmy, 2016. "On a queueing-inventory with reservation, cancellation, common life time and retrial," Annals of Operations Research, Springer, vol. 247(1), pages 365-389, December.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Baek, Jung Woo & Bae, Yun Han, 2022. "A queuing-inventory model for manufacturing systems with fluid-type inventory," Omega, Elsevier, vol. 111(C).
    10. 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.
    11. 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.
    12. 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.
    13. 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.

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