Stochastic Analysis of a Discrete-Time Production Inventory Model Incorporating Perishable Items and Positive Service Time

In this article, we examine a discrete time (s, S) production inventory system with positive service time and perishable products. We define a reasonable cost function for the model by assuming that the demand process is a Bernoulli process and that production and service time are geometric. This model is examined as a level independent quasi-birth-death process.We investigate the model using the Matrix Analytic Method. Furthermore, we use numerical experiments to determine the optimal (s, S) pair for the model across a range of parameter values.