Developing a closed-form cost expression for an (R,s,nQ)(R,s,nQ) policy where the demand process is compound generalized Erlang

We derive a closed-form cost expression for an (R,s,nQ)(R,s,nQ) inventory control policy where all replenishment orders have a constant lead-time, unfilled demand is back-logged and inter-arrival times of order requests are generalized Erlang distributed. For given values of Q and R we show how to compute the optimal reorder level s.