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.