Stochastic Analysis of a Perishable Inventory System with Production, Retrial and Varying Service Rates

This study investigates a production (s, S) inventory structure where clients arrive based on Poisson process and the commodities are perishable. The length of time between each item’s manufacture is exponentially distributed. The service time in this single server system is also exponentially distributed. If the inventory is not empty and the server is available, a customer is served upon arrival. When a newly arriving customer discovers that the only server of the system is busy, they have two options: either leave the system or go to a waiting area known as the orbit with unlimited capacity. Each customer in the orbit uses an exponentially distributed time interval to attempt a second visit to the service facility. When the stock level is above or equal to ‘s’, the service rate is increased, to prevent loss due to deterioration. Using the Matrix Analytic Method, a solution to the problem is obtained using an algorithmic approach. Various performance indicators of the system modelled are derived. The effects of various characteristics on these measures are investigated quantitatively. The optimal profit is determined by constructing a suitable profit function.