We consider the problem of stochastic optimization, where the objective function values are not available and need to be simulated to get their estimates. When the function values are available one can use the simulated annealing algorithm. In this paper, we modify an algorithm that uses the hill climbing feature of simulated annealing with fixed temperature to search the feasible solution set. The proposed algorithm uses indifference zone approach of ranking and selection method to compare the current optimal solution and the potential solution that guarantee the optimal solution with a pre specified level of confidence. The algorithm is tested on a (s, S) inventory problem and compared to other competing algorithm. The numerical results show that the proposed method outperforms the competing method and indeed locate the optimal solution quickly.