We consider the lot-sizing and scheduling problem under uncertainties. It is assumed that all machines at the production line are imperfect, notably we concede that a deal of processed parts can be defective and each machine can breakdown. Thus we deal with random yields and random lead time uncertainties. The planning horizon and demand for parts of all products are given. We assume that a set-up time is necessary to change the type of manufacturing product. The goal is to optimize the order of lots and number of items of each product for a given planning horizon.