This paper presents a Monte Carlo simulation-based approach for solving stochastic discrete optimization problems. The method involves generating a random sample of the random vector W, approximating the expected value function by the sample average function, and solving the resulting sample average approximation (SAA) problem. The procedure is repeated until a stopping criterion is met. The paper discusses the convergence of the SAA method, showing that with probability approaching one exponentially fast as the sample size increases, an optimal solution of the SAA problem provides an exact optimal solution of the true problem. It also outlines an algorithm design for the SAA approach, including stopping rules and performance bounds. The paper presents a numerical example of the SAA method applied to a stochastic knapsack problem, demonstrating the effectiveness of the method in solving such problems. The results show that the SAA method converges exponentially fast and that the convergence rate depends on the well-conditioning measure of the problem. The paper also discusses the impact of the number of decision variables and the well-conditioning measure on the performance of the SAA method. The numerical results show that the SAA method is effective in solving stochastic discrete optimization problems, with the convergence rate and performance depending on the problem's characteristics.This paper presents a Monte Carlo simulation-based approach for solving stochastic discrete optimization problems. The method involves generating a random sample of the random vector W, approximating the expected value function by the sample average function, and solving the resulting sample average approximation (SAA) problem. The procedure is repeated until a stopping criterion is met. The paper discusses the convergence of the SAA method, showing that with probability approaching one exponentially fast as the sample size increases, an optimal solution of the SAA problem provides an exact optimal solution of the true problem. It also outlines an algorithm design for the SAA approach, including stopping rules and performance bounds. The paper presents a numerical example of the SAA method applied to a stochastic knapsack problem, demonstrating the effectiveness of the method in solving such problems. The results show that the SAA method converges exponentially fast and that the convergence rate depends on the well-conditioning measure of the problem. The paper also discusses the impact of the number of decision variables and the well-conditioning measure on the performance of the SAA method. The numerical results show that the SAA method is effective in solving stochastic discrete optimization problems, with the convergence rate and performance depending on the problem's characteristics.