A Network Decomposition Approach for Approximating the Steady-State Behavior of Markovian Multi-Echelon Reparable Item Inventory Systems

We develop a method for obtaining approximate steady-state probabilities for large multi-echelon reparable item inventory systems modeled as non-Jacksonian Markovian networks with finite state space. The approximation involves decomposing the network model into smaller overlapping local subnetwork models, solving them in "isolation" and iterating back and forth among the subnetwork models until convergence is obtained. Numerical results show that the method is quite accurate and efficient for this application.