An (s; Q) Inventory System with Positive Lead Time and Service Time Under N-Policy

Abstract

Abtsrcat We consider an ( s, Q) inventory system of non-perishable items with exponential service time where N-policy is adopted during lead time. Ordering quantity is fixed, and is Q = S - s. We assume that arrival of demands is according to a Poisson process and lead time follows exponential distribution. N-policy is used in such a way that as and when the onhand inventory reaches the level s - N during a lead time, a local purchase of Q + N units is made by cancelling the replenishment order that is already placed. We obtain product-form solution for the state-probabilities. Several performance measures of the system are derived. Analysis of inventory cycle length is carried out. An explicit cost function is obtained and is analysed numerically. Numerical illustrations indicate that the cost function is strictly convex in N. Also it is numerically established that the total expected cost as a function of s, S and N is strictly convex.