Two commodity perishable queueing inventory system with random common lifetime of commodities and positive lead time

In this paper, we consider a two commodity queueing inventory system with random common lifetimes for each commodity, positive service time, positive lead time, and individual ordering policy. Inventory is managed by the continuous review $$(s_{i}, S_{i})$$ ( s i , S i ) policy for the commodity $$i, i=1, 2$$ i , i = 1 , 2 . On realization of the common lifetime or inventory level less than or equal to $$s_{i}, i=1,2$$ s i , i = 1 , 2 by service completions, a replenishment order is placed for $$S_{i}, i=1,2$$ S i , i = 1 , 2 items to bring the inventory level back to $$S_{i}, i=1,2$$ S i , i = 1 , 2 . There are two types of customers called priority and non-priority. Customers arrive according to two independent Poisson processes. A single server processes the inventory before delivery. Lifetimes and lead times of each commodity and service time for each customer category follow an independent exponential distribution with different rates. No customer will be allowed to join when the inventory levels become zero. System performance measures are derived. We also examine the effect of the lead time parameters and common lifetime parameters on the system performance measures. The model was examined in the steady state by using the matrix geometric approach. Further, we analyzed an associated optimization problem and carried out numerical illustrations.