A Two-Commodity Queuing Inventory Model with Reuse of Perishable Goods and Production

This paper presents a two-commodity queuing inventory system with a single server and a production unit. The system consists of a perishable commodity C1, controlled under an (s,S) inventory policy and a non-perishable value-added commodity C2 obtained from C1 through production. Customer demands arrive according to a Poisson process and may request either one or both commodities with suitable probabilities. Customers are allowed to enter the system even when the server is busy and inventory is temporarily unavailable, with the hope that inventory becomes available before the the commencement of service. Service times, lead time, production rate, perishability rate are all assumed to follow exponential distributions. Production is initiated based on deterioration and inventory-threshold conditions, enabling the reuse of perishable goods to generate a non-perishable product. The system is formulated as a continuous- time Markov chain (CTMC) and its steady-state behavior and performance measures are analyzed. The proposed model highlights the role of production in reducing wastage of perishable items while improving inventory utilization and service efficiency.