Safety stock planning with dynamic programming

An approach for safety stock optimization in general serial and divergent multi-stage production systems with stochastic end-item demands is presented minimizing expected inventory holding costs at desired service levels. The specific problem structure allows the application of a DP algorithm which can be used in two ways. On the one hand it leads to a quite simple numerical solution procedure for determining optimal distribution and size of safety stocks even in complex systems. On the other hand it gives an opportunity for analyzing the properties of optimal safety stock policies and their dependence on problem parameters. Particularly, it is possible to develop simple criteria to check the optimality of simple safety stock rules, often met in practice, for any given multi-stage production process.