A problem of lot-sizing and sequencing of manufacturing items for a production line with random machine breakdowns and random rejects is considered. Set-up times are taken into account. The goal is to maximize the probability of a desired output for a given period. The approach is based on the decomposition of the initial problem in two sub-problems: a travelling salesman problem and a knapsack problem. An iterative optimization procedure is proposed. Some tests are given and comparisons with heuristics and simulation are reported.