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12.8. Meeting scheduling

Assign each meeting to a starting time and a room. Meetings have different durations.

Hard constraints:

  • Room conflict: two meetings must not use the same room at the same time.
  • Required attendance: A person cannot have two required meetings at the same time.
  • Required room capacity: A meeting must not be in a room that doesn’t fit all of the meeting’s attendees.
  • Start and end on same day: A meeting shouldn’t be scheduled over multiple days.

Medium constraints:

  • Preferred attendance: A person cannot have two preferred meetings at the same time, nor a preferred and a required meeting at the same time.

Soft constraints:

  • Sooner rather than later: Schedule all meetings as soon as possible.
  • A break between meetings: Any two meetings should have at least one time grain break between them.
  • Overlapping meetings: To minimize the number of meetings in parallel so people don’t have to choose one meeting over the other.
  • Assign larger rooms first: If a larger room is available any meeting should be assigned to that room in order to accommodate as many people as possible even if they haven’t signed up to that meeting.
  • Room stability: If a person has two consecutive meetings with two or less time grains break between them they better be in the same room.

Problem size

50meetings-160timegrains-5rooms  has  50 meetings, 160 timeGrains and 5 rooms with a search space of 10^145.
100meetings-320timegrains-5rooms has 100 meetings, 320 timeGrains and 5 rooms with a search space of 10^320.
200meetings-640timegrains-5rooms has 200 meetings, 640 timeGrains and 5 rooms with a search space of 10^701.
400meetings-1280timegrains-5rooms has 400 meetings, 1280 timeGrains and 5 rooms with a search space of 10^1522.
800meetings-2560timegrains-5rooms has 800 meetings, 2560 timeGrains and 5 rooms with a search space of 10^3285.

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