On the performance of the base-stock inventory system under a compound Erlang demand distribution

In this paper, we propose a new method for determining the optimal base-stock level in a single echelon inventory system where the demand is a compound Erlang process and the lead-time is constant. The demand inter-arrival follows an Erlang distribution and the demand size follows a Gamma distribution. The stock is controlled according to a continuous review base-stock policy where unfilled demands are backordered. The optimal base-stock level is derived based on a minimization of the total expected inventory cost. A numerical investigation is conducted to analyze the performance of the inventory system with respect to the different system parameters and also to show the outperformance of the approach that is based on the compound Erlang demand assumption as compared to the classical Newsboy approach. This work allows insights to be gained on stock control related issues for both slow and fast moving stock keeping units.

• We are concerned with the base-stock system under a compound Erlang demand.
• We derive the optimal base-stock level under a cost minimization objective.
• We numerically analyze the performances of the inventory system with respect to its parameters.
• We compare the performance of the compound Erlang model to that of the Newsboy approximation model.