Matrix-Analytic Methods in Supply Chain Management: Recent Developments

Matrix-analytic methods are a popular modeling tool in a great number of fields, most notable in the analysis of telecommunication systems. Because of their ability to construct and analyze a wide class of stochastic models, they can also be applied in the analysis of complex supply chain problems where traditional analytical techniques or simulation analysis fall short. In this paper, we demonstrate the power of matrix-analytic methods in the analysis of four different supply chain problems: (1) to determine lead times in production/inventory models characterized by any arbitrary discrete (i.e., non-Poisson) demand distribution; (2) to gain insight in the upstream replenishment orders driven by (s,S) inventory policies; (3) to analyze waiting times and resource utilization in service systems that are driven by appointments (e.g., health care, legal services, administration); and (4) to determine the optimal maintenance policy/warranty in the aftermarket supply chain.