Monotonicity of base stock policies

We analyze monotonicity of base stock levels in multi-product inventory-production systems where arriving demand triggers production of a new unit. In a paper from 1996, Rubio and Wein used open Jackson networks to describe such integrated models. They conjectured that the base stock level should increase with the utilization in the production system. We present a basic analytical proof of the general presumption for single- and multi-product systems.