Machine scheduling problems involving conflict jobs can be seen as a constrained version of the classical scheduling problem, in which jobs may not be proceeded simultaneously on different machines. This conflict constraint naturally arises in several practical applications and has recently received considerable attentions in the research community. In fact, the problem is typically NP-hard (even for approximation), and most of algorithmic results achieved so far have heavily relied on special structures of the underlying graph used to model the conflict-job relation. Our focus is on three objective functions: minimizing the makespan, minimizing the weighted summation of the jobs’ completion time, and maximizing the total weights of completed jobs; the first two of which have been intensively studied in the scheduling literature, but have been not considered for problems with conflict jobs. For each objective function, we present several mixed integer linear programming models and a constraint programming model, from which we can solve the problems to optimality using dedicated solvers. Binary search-based algorithms are also proposed to solve the makespan problem. The results of numerical experiments performed on randomly generated data sets with up to 90 jobs and 6 machines are reported and analyzed to verify the performance of the considered formulations.