The flexible job-shop scheduling problem (FJSP) is considered as an important problem in the modern manufacturing system. It is one of the most difficult problems in this area. In fact, this problem is a generalized and more complicated variant of the classical job-shop that introduces an additional decision level known as the assignment sub-problem in addition to the sequencing sub-problem. In this paper, we study the flexible job-shop scheduling problem under partial and total flexibility. The objective aims to minimize the total completion time. Nothing that mainly metaheuristic approaches have been considered for solving FJSP and only limited research actually makes use of their mathematical models to design exact approaches. We therefore propose two mathematical models, a mixed-integer linear programming model (MILP) and a constraint programming model (CP). Test experiments are performed on a large set of randomly generated instances using CPLEX software. The acquired results show the efficiency of the developed models for solving both partially and totally FJSP problems. Experimental results prove also the competitiveness of the CP model, compared to the MILP model, in solving large size FJSP problem with a reasonable processing time.