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Models for integrated production-inventory systems: steady state and cost analysis

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  • S. Otten
  • R. Krenzler
  • H. Daduna

Abstract

We consider a two-echelon production-inventory system with a central supplier connected to production systems (servers) at several locations, each with a local inventory. Demand of customers arrives at each production system according to a Poisson process and is lost if the local inventory is depleted. To satisfy a customer’s demand, a server at the production system takes exactly one unit of raw material from the associated local inventory. The central supplier manufactures raw material to replenish the local inventories, which are controlled by a continuous review base stock policy. We derive stationary distributions of joint queue length and inventory processes in explicit product form. After performing a cost analysis, we find out that the global search for the vector of optimal base stock levels can be reduced to a set of independent optimisation problems. The explicit form of the stationary distribution enables us to get additional structural insights, e.g. about monotonicity properties and stability conditions. Obtaining the product form relies on some simplifying assumptions. The results are therefore compared with simulations of a more realistic system, which supports to use it as approximation.

Suggested Citation

  • S. Otten & R. Krenzler & H. Daduna, 2016. "Models for integrated production-inventory systems: steady state and cost analysis," International Journal of Production Research, Taylor & Francis Journals, vol. 54(20), pages 6174-6191, October.
    • Handle: RePEc:taf:tprsxx:v:54:y:2016:i:20:p:6174-6191
    DOI: 10.1080/00207543.2015.1082669
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    Cited by:

    1. Achyutha Krishnamoorthy & Srinivas R. Chakravarthy & Agassi Melikov & Viswanath C. Narayanan, 2024. "Queueing-inventory: analytical and simulation modeling and classical and retrial queues and inventory," Annals of Operations Research, Springer, vol. 340(2), pages 1221-1224, September.
    2. 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.
    3. Baek, Jung Woo & Bae, Yun Han, 2022. "A queuing-inventory model for manufacturing systems with fluid-type inventory," Omega, Elsevier, vol. 111(C).
    4. Sen Lin & Bo Li & Antonio Arreola-Risa & Yiwei Huang, 2023. "Optimizing a single-product production-inventory system under constant absolute risk aversion," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 510-537, October.

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