Load balancing in a network of queueing-inventory systems

TL;DR

This paper analyzes a supply chain network with multiple production-inventory systems coupled by a common supplier, deriving explicit solutions for the stationary distribution and demonstrating load balancing through a product form solution.

Contribution

It introduces a novel analytical framework for load balancing in queueing-inventory networks with explicit stationary distribution solutions.

Findings

Stationary distribution has a product form.

Explicit solution for production subsystem distribution.

Recursive algorithm for inventory-replenishment subsystem.

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 derive an explicit solution resp. a recursive algorithm for some special cases.