Evaluation of ( R,Q)-policies for two-level inventory systems with generally distributed customer inter-arrival times

Abstract

In this paper we consider a two-level inventory system with a central warehouse and a number of retailers. All facilities apply continuous review ( R,Q)-policies. We first extend Forsberg's exact Poisson model to the case with unit demand and customer inter-arrival times that are Erlang distributed. In the case with generally distributed customer inter-arrival times we approximate by Erlang distributions. We use two different methods to choose the approximate Erlang distribution. The first method means that we, for each retailer, choose the Erlang distribution that has the exact mean and minimum difference in standard deviation. Our second method means that we, for each retailer, choose the Erlang distribution of customer inter-arrival times that gives the exact mean and minimum difference in the standard deviation of the demand per unit of time instead of the inter-arrival time. Both methods are tested on 38 simulated cases. In all cases both methods give the same approximation.