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Load balancing in a network of queueing-inventory systems

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  • Sonja Otten

    (Hamburg University of Technology)

Abstract

We study a supply chain consisting of production-inventory systems at several locations which are coupled by a common supplier. Demand of customers arrives at each production system according to a Poisson process and is lost if the local inventory is depleted (“lost sales”). To satisfy a customer’s demand a server at the production system needs raw material from the associated local inventory. The supplier manufactures raw material to replenish the local inventories, which are controlled by a continuous review base stock policy. The routing of items depends on the on-hand inventory at the locations with the aim to obtain “load balancing”. We show that the stationary distribution has a product form of the marginal distributions of the production subsystem and the inventory-replenishment subsystem. For the marginal distribution of the production subsystem we derive an explicit solution and for the marginal distribution of the inventory-replenishment subsystem we deduce an explicit solution or a recursive algorithm for some special cases.

Suggested Citation

  • Sonja Otten, 2023. "Load balancing in a network of queueing-inventory systems," Annals of Operations Research, Springer, vol. 331(2), pages 807-837, December.
    • Handle: RePEc:spr:annopr:v:331:y:2023:i:2:d:10.1007_s10479-022-05017-3
    DOI: 10.1007/s10479-022-05017-3
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