We introduce a modified delayed vacation strategy. We consider an inventory system with lost sales and $(s,S)$ strategy under the vacation strategy. When the inventory level is zero, the server goes to a random time to prepare for vacation in which if the replenishment is successful, the server still serves the customer normally. The random time is called a modified delayed vacation time. When the delayed vacation is over, the server immediately takes multiple vacations. We analyze the stationary distributions of the inventory system under the vacation strategy by using the Markov theory. On the basis, some performance measures and the average cost function are obtained. Finally, we get the optimal inventory policy by a genetic algorithms. On the basis, some performance measures and expected cost also are discussed by numerical examples.