Comparison of discrete time inventory systems with positive service time and lead time

Abstract

This paper investigates two discrete time queueing inventory models with positive service time and lead time. Customers arrive according to a Bernoulli process and service time and lead time follow geometric distributions. The first model under discussion based on replenishment of order upto $S$ policy where as the second model is based on order placement by a fixed quantity $Q$, where $Q=S-s$, whenever the inventory level falls to $s$. We analyse this queueing systems using the matrix geometric method and derive an explicit expression for the stability condition. We obtain the steady-state behaviour of these systems and several system performance measures. The influence of various parameters on the systems performance measures and comparison on the cost analysis are also discussed through numerical example.