This paper addresses the problem of scheduling in a flow shop manufacturing environment with non-traditional requirements, where some jobs must be scheduled earlier and others later depending on the priority established by the demand characteristics supplied. The problem is formulated mathematically, and given its nonlinearity, we propose a CSP (Constraint Satisfaction Problem) model, which is formulated using constraint programming with the software OPL Studio ®. A set of experiments was performed by varying the weighting of jobs. We also varied the deadlines and waiting times among the machines. Finally, different production schedules were attained according to the type of experiment, thus solving the problem of non-traditional scheduling.