On exhibiting inventory systems with Erlangian lifetimes under renewal demands

A continuous revies (s, S) inventory system with renewal demand in which one item is put into operation as an exhibiting piece is analyzed. The lifetime of any operating unit has Erlangian distribution, and on failure is replaced by another one from the stock and the failed item is disposed of. Replenishment of stock is instantaneous. The transient and stationary values of inventory level distribution and the mean reorder rate are obtained using the techniques of semi-regenerative processes. Decision rules for optimum s and S that minimize the long-run expected cost rate are derived. The solution for a dual model with the distribution of lifetimes and inter-demand times interchanged is also given. © 1989 The Institute of Statistical Mathematics.