Load balancing in a network of queueing-inventory systems

Sonja Otten ()
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Sonja Otten: Hamburg University of Technology

Annals of Operations Research, 2023, vol. 331, issue 2, No 9, 807-837

Abstract: 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.

Keywords: Queueing networks; Inventory control; Base stock policy; Product-form steady state; 60K25; 68M20; 90B22; 90B05; 90B06 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10479-022-05017-3

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