A Single-Unit Decomposition Approach to Multiechelon Inventory Systems

We show the optimality of state-dependent echelon base-stock policies in uncapacitated serial inventory systems with Markov-modulated demand and Markov-modulated stochastic lead times in the absence of order crossing. Our results cover finite-time horizon problems as well as infinite-time horizon formulations, with either a discounted or an average cost criterion. We employ a novel approach, based on a decomposition of the problem into a series of single-unit single customer problems that are essentially decoupled. Besides providing a simple proof technique, this approach also gives rise to efficient algorithms for the calculation of the base-stock levels.