The paper deals with a stochastic multi-product sequencing and lot-sizing problem for a line that produces items in lots. Two types of uncertainties are considered: random lead time induced by machine breakdowns and random yield to take into account part rejects. In addition, sequence dependent setup times are also included. This study focuses on maximizing the probability of producing a required quantity of items of each type for a given finite planning horizon. A decomposition approach is used to separate sequencing and lot-sizing algorithms. Previous works have shown that the sequencing sub-problem can be solved efficiently, but the lot-sizing sub-problem remains difficult. In this paper, a memetic algorithm is proposed for this second sub-problem. Computational results show that the algorithms developed can be efficiently used for large scale industrial instances.