In this paper, we considered solving approaches to flexible job shop problems. Makespan is not a good evaluation criterion with overlapping in operations assumption. Accordingly, in addition to makespan, we used total machine work loading time and critical machine work loading time as evaluation criteria. As overlapping in operations is a practical assumption in chemical, petrochemical, and glass industries, we used simulated annealing algorithm for multi-objective flexible job shop scheduling problem with overlapping in operations to find a suitable solution. To evaluate performance of the algorithm, we developed a mixed integer linear programming model, and solved it with the classical method (branch and bound). The results showed that in small size problems, the solutions of the proposed algorithm and the mathematical model were so close, and in medium size problems, they only had lower and upper bounds of solution and our proposed algorithm had a suitable solution. We used an experimental design for improving the proposed algorithm.