For an assignment I have to program an application to schedule conversations. There is an event where representatives of the elementary schools talks with the representatives of high schools. They will talk about the students that will be transferred to the highschool. There are approximately 200 elementary schools and 40 high schools that will be participating in this event. The schools already know which student is transferring to which high school. The conversations will only be between representatives of E and H from student that will be transferring to H.
The rules are:
- The duration of each conversation is based on the amount of students per representatives.Each conversation last 5 minutes per student. If a group consist of 1 student, this conversation last 10 minutes.
- No timeclashes
- All the students of the same group will be scheduled together, so, a representatives will only face the same representative once.
- Timespan is 13.00-19.00
- The waiting time of a representative is at most 20% of his time. A waiting time is an empty timeslot between the 1st and last conversation.
- Schedules for 2 days
- Each representatives participate for 1 day.
The problem is that I know that this is hard to solve, but I dont know if it's NP-hard. Right now I only know this problem is similar to a Job Shop Problem. What can I do to proof that my problem is NP-hard? I read that I need to reduce a known problem to my problem. But how do I do this? I have read different articles and books, but I still don't understand the steps to do it.