I'm trying to solve one interesting math task.
Let’s imagine we have a number of instructors with different timespans during the day in which they work or they are available. We need to display to students timeslots where they can book inside the available timespan of the instructor. Within this time period we need to optimize the appointments so that there is a minimum number of "idle" timeslots. Once an appointment has been set we cannot move the appointment. The negotiation of an appointment must happen without negotiating with other students. Appointments have variable and unknown lengths?
Any ideas people ?