Quite a few years ago we had a system creating automatic schedules for film festival enthusiasts, enabling everyone to quickly order tickets before they run out. When the festival program arrives, all films are quickly entered. Individuals can then indicate desired films with a priority and the system automatically creates an entire schedule for the week. The challenge is that it is usually impossible to see all films since many are shown at the same time, and each film is often shown several times during the week.

For the above question, how it can be modeled, and what are the possible ways to solve the question.