Approximate evaluation of continuous review $(R,Q)$ policies in two-echelon inventory systems with stochastic transportation times

summary:This paper considers a distribution inventory system that consists of a single warehouse and several retailers. Customer demand arrives at the retailers according to a continuous-time renewal process. Material flow between echelons is driven by reorder point/order quantity inventory control policies. Our objective in this setting is to calculate the long-run inventory, backorder and customer service levels. The challenge in this system is to characterize the demand arrival process at the warehouse. We present a Markovian methodology to elucidate and approximate this process. We illustrate the use of this methodology in the distribution inventory system under stochastic transportation times with identical and non-identical retailers