Performance Assessment of Production Inventory System With Catastrophes Including Negative Customers and Machine Breakdowns - Kanni, A. Abi Shunmuga; Amirthakodi, M. (Communications in Mathematics and Applications, 2025)
This study looks at a production inventory system that experiences breakdowns in machines, negative customers and catastrophes. If a customer arrives and raises their level in the waiting hall with a probability of \(r\), they are considered ordinary; if they drop their level without inventory with a probability of \(1-r=\bar{r}\), they are known as negative customers. Upon completion of service, a customer exits the system, causing the inventory level to decrease by one. Catastrophic events force the inventory level to drop to zero. The production policy is \((s, S)\), where \(S\) is the fixed maximum inventory level. A machine could break down during production, in which case it will be fixed at random. The steady-state joint probability distribution of the inventory level, the number of customers in orbit, and the machine status are derived using the matrix-geometric method. Several performance measures are calculated, and the results are used to develop a cost function. Finally, numerical results are presented to demonstrate the system's behavior.