Time Dependent Production Inventory Model with Random Switching Time

This paper analyzes a single product stochastic inventory model with two different rates of production, where demand follows Poisson distribution. It is assumed that products have infinite lifetimes that do not decay for the time under consideration. It is thought that when the system reaches a predetermined level, the system is converted to ON mode from OFF mode with a significant switching time with exponential parameter 𝜏. During switching time, no demand will be met. Hence, the demand during switching time is lost forever. Here, backlogs are allowed, and during backlogs, the Production rate is higher than that of normal production time. Some system characteristics are displayed with time variation, and total cost functions are derived. Finally, graphical representations are made.