Stochastic Optimization of Local Purchase Quantities in a Geo/Geo/1 Production Inventory System

Abstract

We consider an (s, S) production inventory system in which demand occurs according to a Bernoulli process and service time follows a geometric distribution. The maximum inventory that can be accommodated in the system is S. When the on-hand inventory is reduced to a preassigned level of s due to service completion (and consequent purchase of exactly one item by each customer), production is started. The production time for each item (inter-production time) follows a geometric distribution. When the inventory level becomes zero, an instantaneous local purchase of one/s/S units is made to meet the demand. These three types of local purchases are discussed as three separate models. Using the closed-form solution obtained for the steady-state probability vector and by constructing an appropriate cost function, we compare these models with the help of a few numerical work.