A Queuing Inventory Model with Production and Reuse of Perishable Goods

This paper addresses a queuing inventory system involving two commodities with interconnected production processes, incorporating the notion of reusability in the context of perishable goods. Commodity 1 is perishable and utilizes instantaneous inventory replenishment while commodity 2 is non perishable and is a value added product manufactured from commodity 1 through production. An arriving customer can demand for either commodity 1 or both the commodities at the time of service but with suitable probabilities. If commodity 2 is unavailable, customers have the option to place orders. The stability of the system is analyzed by matrix geometric method and some important performance measures are discussed. Numerical illustrations are provided to give a glance of some system performances. Also a suitable cost function is constructed and an optimum is obtained.