Load balancing in a network of queueing-inventory systems

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.

Automated summary

We analyze a supply chain with multiple production-inventory systems connected by a common supplier. The customer demand follows a Poisson process and is lost if local inventory is depleted. We propose a continuous review base stock policy to control the local inventories and achieve load balancing. Our findings demonstrate that the stationary distribution has a product form, allowing for explicit solutions or recursive algorithms for the marginal distributions of the production and inventory-replenishment subsystems.