In this paper, we consider an extended class of flexible shop scheduling problems. First, we translate the problem into a mathematical programming formula, i.e., a mixed-integer programming problem. This makes it possible to apply standard packages of mixed integer programming solvers and, while lots of computational time is required in general, to obtain the optimal schedule. Then, in order to seek the schedules close to the optimal, we newly compose a solution method by adopting genetic algorithms based on the formula, and also we design a hybrid method in which integer programming methods and genetic algorithms are combined. Through some computational experiments, the effectiveness and the potential of the proposed approach are examined.