On the transient behaviour of a continuous review (s,S) inventory policy

The transient behaviour of a continuous review (s,S) inventory without backlogging is analysed under the assumption that both the demand and the lead times follow an arbitrary distribution. Systems of integral equations satisfied by various state probabilities corresponding to different initial conditions are obtained using state-space method and a supplementary variable technique. An iterative numerical method is used to solve the system of integral equations obtained.