9.2 Sports Scheduling: An Introduction to Integer Optimization

9.2 Sports Scheduling: An Introduction to Integer Optimization

Quick Question

Suppose that you are trying to schedule 3 games between 6 teams (A, B, C, D, E, and F) that will occur simultaneously. Which of the following are feasible schedules? Select all that apply.

 A plays B, C plays D, and E plays F  check
 A plays C, B plays D, and C plays F  close
 A plays F, B plays E, and C plays D  check
 A plays B, B plays C, and C plays D  close
 A plays D, B plays E, and C plays F  check
Check Show Solution

Explanation Each of the teams has to play exactly one of the other teams for the games to occur simultaneously. In the second option, C is playing twice, which is impossible. In the fourth option, B and C are both playing twice.

How many different feasible schedules are there?

 5  close
 10  close
 15  check
 20  close
 25  close
Check Show Solution

Explanation There are 15 different feasible schedules. We can count them by observing that A can play any of the 5 teams. Once this is fixed, we have 4 teams left. There are 3 ways to make two pairs out of 4 teams. So in total, there are 5\*3 = 15 different schedules. Here is a list of all of them: A plays B, C plays D, E plays F A plays B, C plays E, D plays F A plays B, C plays F, D plays E A plays C, B plays D, E plays F A plays C, B plays E, D plays F A plays C, B plays F, D plays E A plays D, B plays C, E plays F A plays D, B plays E, C plays F A plays D, B plays F, C plays E A plays E, B plays C, D plays F A plays E, B plays D, C plays F A plays E, B plays F, C plays D A plays F, B plays C, D plays E A plays F, B plays D, C plays E A plays F, B plays E, C plays D

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