QF alike coordination mechanism in base stock controlled supply channel

We investigated a simple supply chain facing stationary stochastic demand with constant components replenishment lead-time. Holding costs are charged for final product inventory, demands are backordered when can´t be fulfilled in time and penalty costs are charged not only on the retailer but also on the supplier. Inventory decision of the retailer deviates from the system optimal due to double marginal effect and system performance is debased. Here, we try to design mechanism that is like quantity flexible in Newsboy model to coordinate the decentralized system. Such a mechanism is given to allocate cost arbitrarily.