Queueing system with inventory for two-echelon supply chain

In this paper a two-echelon supply chain consisting of a supplier and a retailer is considered, Customers refer to retailer according to a Poisson process and retailer uses one for one inventory policy. Supplier follows continuous review (r, Q) policy. Satisfying each demand which arrives to the supplier needs an on hand-inventory and a process/service. Process/service and replenishment lead times are random variables which are exponentially distributed. During a period that supplier has non zero on-hand inventory, arriving demands from retailer join the queue. But when supplier has no on-hand inventory retailer buys product from the other source with zero lead time and additional cost. In this paper we calculate long-term performance measures of the systems that are used to minimize the supply chain costs.