Book Description

This dissertation presents an analysis of continuous review models of a two-echelon inventory system for recoverable items. The system consists of a depot and a set of bases. Primary demands occur at the bases for one or several units at a time. It is assumed that demands arrive in a Poisson manner. Upon arrival of a demand for certain units, a like number of failed units are turned in at the base. An inspection of the failed units is carried out to decide whether the units will be repaired at the base or at the depot or will be removed from the system in case repair is not economical. The bases use an (s-1, s) policy for procurement of serviceable units from the depot, and the depot uses an (s, S) policy to procure from the external supplier. Demands in an out-of-stock situation are backlogged. It is assumed that all the locations have infinite repair capacities and repair and procurement lead times are constant. A common problem in inventory management is to specify the policy parameters that will minimize expected cost per unit time for operating the system subject to constraints of certain performance measures. To formulate such a problem we must find the stationary distributions for inventory position, on-hand inventory, backorders and in-repair inventory. Our main objective is to find exact expressions for these distributions.