Approximation of the probability distribution of the customer waiting time under an (r,s, q) inventory policy in discrete time

We study a single-item periodic review (r, s, q) inventory policy. Customer demands arrive on a discrete (e.g. daily) time axis. The replenishment lead times are discrete random variables. This is the time model underlying the majority of the Advanced Planning Software systems used for supply chain management in industrial practice. We present an approximation of the probability distribution of the customer waiting time, which is a customer-oriented performance criterion that captures supplier–customer relationships of adjacent nodes in supply chains. The quality of the approximation is demonstrated with the help of a simulation experiment.