safety stock placement for serial systems under supply process uncertainty

In this study, we address safety stock positioning when demand per period is a known constant but supply is uncertain. the supply is either available or not available, while the setting is that of a periodically reviewed, serial system following a base stock policy. each stage is allowed to operate according to the guaranteed or stochastic service model. we use a discrete time markov chain model for expressing the expected on-hand inventories for each stage, along with other terms of interest, as a function of policy parameters determined by a given service level requirement for the end product. exact models are constructed for single-stage and two-stage systems. as the number of states for a two-stage system grows exponentially, we propose an approximation for expressing the effect of the input stage using a single parameter. a generalization for the approximation is provided for a multi-stage problem. computational evaluations of the approximation, as well as numerical comparisons of different cases, are presented.