This paper addresses the robust flexible job-shop scheduling problem considering uncertain operation processing times associated with an uncertainty budget. Exact solution methods based on mixed integer linear programming and constraint programming are proposed to solve the problem. Such solutions are hybridized in the framework of a two-stage robust optimization, and a column and constraint generation algorithm is used to solve representative instances. The experimental results show the advantages of a two-stage approach where constraint programming and integer programming are mixed to solve a master problem and a subproblem, respectively.