Optimal policy for a production-inventory system with price shift and setup cost

We consider a continuous review production-inventory system with price shift and setup cost, which is controlled by a (s,s',S) policy. Unsatisfied demand is lost. When the machine is on, the inventory can be sold at two different prices. While the machine is off, the inventory only can be sold at the high price. We show the method to find the optimal (s,s',S) control policy for this system and develop an efficient algorithm to compute the optimal control parameters.