This paper developed an on-going deteriorating inventory model for a single item. Stochastic fluctuating demand patterns is concerned which decreases with the price of items. Deteriorating rate is constant and replenishment rate is infinite. Replenishment lead time is a constant. Continuous review (s, S) inventory policy is adopted which means an order to replenish the inventory to S is placed when current inventory level drops to s. Demand in each replenishment cycle forms a regenerative process. Our objective is to find the joint optimal pricing and replenishment policies to maximize the expected total average profit of the system. This problem can be simplified as a deterministic problem which can be solved by genetic algorithms. The detailed procedure of algorithm is listed. Finally, a numerical example is given which is simulated by Matlab 7.0.