A procedure for the approximation of the waiting time distribution in a discrete-time (r, S) inventory system

We study a single-item periodic review inventory policy. Demands arrive on a discrete (e.g. daily) time axis. This is the time model underlying the Advanced Planning Software systems used for supply chain management in industrial practice. We present a procedure for the calculation of the probability distribution of the customer waiting time. We discuss optimisation problems which can be solved on the basis of the probability distribution of the waiting time.