Computational Issues in an Infinite-Horizon, Multiechelon Inventory Model

Clark and Scarf (Clark, A., H. Scarf. 1960. Optimal policies for a multi-echelon inventory problem. Mgmt. Sci.6 475–490.) characterize optimal policies in a two-echelon, two-location inventory model. We extend their result to the infinite-horizon case (for both discounted and average costs). The computations required are far easier than for the finite horizon problem. Further simplification is achieved for normal demands. We also consider the more interesting case of multiple locations at the lower echelon. We show that, under certain conditions, this problem can be closely approximated by a model with one such location. A rather simple computation thus yields both a near-optimal policy and a good approximation of the cost of the system.