Optimal Structural Results for Assemble-to-Order Generalized M-Systmes

Cataloged from PDF version of article.We consider an assemble-to-order generalized M-system with multiple components and multiple products, batch ordering of components, random lead times, and lost sales. We model the system as an in nite-horizon Markov decision process and seek an optimal control policy, which speci es when a batch of components should be produced and whether an arriving demand for each product should be satis ed. To facilitate our analysis, we introduce new functional characterizations for convexity and submodularity with respect to certain non-unitary directions. These help us characterize optimal inventory replenishment and allocation policies under a mild condition on component batch sizes via a new type of policy: lattice-dependent base-stock and lattice-dependent rationing