Multi-echelon service models for inventory systems under different rationing policies

In this paper we model the service performance of two-echelon divergent production networks consisting of one central stock-point feeding a number of end stock-points where the external demand is realized. The systems we consider allow all stock-points to hold inventory and use periodic review ordering policies at all levels. Whenever the lower echelon has insufficient inventory to cover all upper echelon requisitions some policy to ration the available material is needed. Concentrating on one push and one pull rationing policy, we explore the system dynamics and develop models for three popular measures of the system service performance. All models make use of non-dimensional ratios which drastically reduce the number of parameters involved. Although these models are only approximate, numerical and simulation results demonstrate the adequacy of the approximations involved.