Within the evolving landscape of Industry 4.0, the significance of flexible job shop scheduling problems is on the rise. This study addresses a novel category of NP- hard scheduling problems: the flexible job shop scheduling problems that incorporate site routing and operation sequenc- ing flexibility. These problems are crucial and applicable in various contexts, including carrier-based aircraft scheduling, shipbuilding assembly scheduling, and cutting tool operation scheduling. For these problems, we present two new MILP models: Model-1 is a time-indexed model, and Model-2 is a precedence variable-based model. These models are evaluated under ten cases of the problems. Our findings indicate that the two models exhibit varying solution efficiencies when deal- ing with problems of diverse magnitudes. Model-2 performs better than Model-1 on small-scale problems, while Model-1 outperforms Model-2 on medium-scale problems.