This paper considers a genetic algorithm (GA) for a machine-job assignment with controllable processing times (MJACPT). Integer representation with standard genetic operators is used. In an objective function, a job assignment is obtained from genetic code and for this, fixed assignment processing times are calculated by solving a constrained nonlinear convex optimization problem. Additionally, the job assignment of each individual is improved by local search. Computational results are presented for the instances from literature and modified large-scale instances for the generalized assignment problem (GAP). It can be seen that the proposed GA approach reaches almost all optimal solutions, which are known in advance, except in one case. For large-scale instances, GA obtained reasonably good solutions in relatively short computational time.