Continuous-review inventory models using diffusion approximation for bulk queues

In this paper, two continuous-review inventory control models are developed using steady-state diffusion approximation method. Accuracy evaluations of the approximate optimal solutions for the inventory control models are reported for selected “Markovian-like” queues to approximate the steady-state queue size behavior of single-server queues with bulk-arrival and batch-service. The diffusion approximation method gives a remarkably good performance in approximating the base stock level one-to-one ordering policy inventory model. The approximation for the order-up to inventory model with replenishment lot size greater than one is also exceptionally good at selected values of heavy traffic intensity and when the service time replenishment process distributional characteristic does not differ greatly from the exponential inter - arr i val time of the demands.