In this research the model of multiple products lot sizing with random demand on a single facility with service level constraint has bee developed. The model considered with both static-dynamic strategy and static strategy. Also an efficient method has been used to solve it. The model of multiple products lot sizing is NP-Hard and as a result solving this model in big dimensions is not possible, so the SA (Simulated Annealing) method has been used to solve the model. Generally, maximizing the expected profit or minimizing the expected cost as objective function has been used in the lot sizing models, but there are other important objective functions. One of these objective functions is maximizing the probability of achieving a budgeted profit. In this dissertation this objective function has been surveyed in one product case and then has been developed to one product and multiple periods and multiple product and multiple periods. The SA method has been used for solving the model. The SA answers for some example problems have been compared with optimal answer or lower bound. The results show the efficiency of the SA.
