Analysis of a multi-item queueing inventory system operating with an exchange facility

This paper explores a stochastic queuing-inventory system designed to efficiently manage both new and returned items, offering practical solutions for diverse customer needs. The system differentiates services for various customer classes through dedicated channels, encompassing the sale of new and returned items, as well as the purchase of used items from customers. This model incorporates four parallel queues for distinct customer classes, each serviced by a dedicated server. Customer arrivals are modeled using a Markovian Arrival Process (MMAP), with service times being exponentially distributed and independent. An $(s, S)$ policy is implemented for replenishing fresh items. The primary objective is to enhance service accessibility for various customer types within a single facility, promoting operational efficiency and customer satisfaction. Additionally, the system's ability to purchase used items underscores its role in fostering sustainability in an evolving society. By applying the Neuts matrix geometric technique, the paper analyzes the system to derive the long-term probability distribution and significant performance metrics. Numerical methods are utilized to investigate key system parameters and performance measures, and a cost function is introduced and optimized concerning the reorder level. This comprehensive analysis offers valuable insights for optimizing inventory and queuing systems in practical, real-world applications.