Round Robin Tournament Scheduling

Schedules - You must register to Post and Download => Requests => Topic started by: calgarytouchrugby on January 04, 2016, 10:31:20 PM

Title: 9 team, double round-robin with constraints
Post by: calgarytouchrugby on January 04, 2016, 10:31:20 PM

Hi everyone! I'm brand new to forum but from my research I don't think this request has been posted yet.
Here is my scheduling dilemma:
I have a league with 9 teams (1-9)
I have 9 weeks of field space, every Monday, with two side by side fields (Filed 1 & Field 2)
I have enough time to run four games per night PER field (So can have eight total games: Two simultaneous games x 4 time slots).
I would like to run the league as a DOUBLE round-robin, with each team getting Two BACK TO BACK games per night, with only ONE team on bye each week.
Ideally the first week would look like this:

Field 1 - Game 1: 1 v 2   Field 2 - Game 1: 3 v 4
Field 1 - Game 2: 1 v 3   Field 2 - Game 2: 2 v 4
Field 1 - Game 3: 5 v 6   Field 2 - Game 3: 7 v 8
Field 1 - Game 4: 5 v 7   Field 2 - Game 4: 6 v 8
Team 9 is on BYE.

The next week Team 8 would be on BYE and so on and so forth...
Is it possible to do this? I am able to do the schedule where four of the nine weeks have all teams playing back to back but the other five weeks the teams have at least a one game break.
Any help is much appreciated!!

Title: Re: 9 team, double round-robin with constraints
Post by: Ian Wakeling on January 05, 2016, 01:35:29 AM

I think this schedule will do what you want.  The team with the bye is the same as the week number.

          F1     F2
W1  G1  (9 7)  (3 8)
W1  G2  (9 3)  (7 8)
W1  G3  (6 4)  (2 5)
W1  G4  (4 5)  (6 2)

W2  G1  (1 8)  (4 9)
W2  G2  (1 4)  (8 9)
W2  G3  (7 5)  (3 6)
W2  G4  (5 6)  (7 3)

W3  G1  (2 9)  (5 1)
W3  G2  (2 5)  (9 1)
W3  G3  (8 6)  (4 7)
W3  G4  (6 7)  (8 4)

W4  G1  (3 1)  (6 2)
W4  G2  (3 6)  (1 2)
W4  G3  (9 7)  (5 8)
W4  G4  (7 8)  (9 5)

W5  G1  (4 2)  (7 3)
W5  G2  (4 7)  (2 3)
W5  G3  (1 8)  (6 9)
W5  G4  (8 9)  (1 6)

W6  G1  (5 3)  (8 4)
W6  G2  (5 8)  (3 4)
W6  G3  (2 9)  (7 1)
W6  G4  (9 1)  (2 7)

W7  G1  (6 4)  (9 5)
W7  G2  (6 9)  (4 5)
W7  G3  (3 1)  (8 2)
W7  G4  (1 2)  (3 8)

W8  G1  (7 5)  (1 6)
W8  G2  (7 1)  (5 6)
W8  G3  (4 2)  (9 3)
W8  G4  (2 3)  (4 9)

W9  G1  (8 6)  (2 7)
W9  G2  (8 2)  (6 7)
W9  G3  (5 3)  (1 4)
W9  G4  (3 4)  (5 1)

It's cyclic in the sense that Weeks 2 to 9 can all be generated from the first week, keep adding one to the team numbers to make the next week, and in the case of team 9 loop back 1.

The games from G1 and G2 combined are one complete round robin.  The games from G3 and G4 are the second round-robin.

Hope that helps.

Title: Re: 9 team, double round-robin with constraints
Post by: calgarytouchrugby on January 05, 2016, 08:46:48 AM

Well Ian, I'm thoroughly impressed, both in speed of delivery and result!
I had tried a cyclic method but didn't have a good starting point, which lead to repeats quite quickly.  I think I was majorly missing the bigger picture.

FYI - I stumbled upon this site after doing some searching regarding linear programming and the Google sheets linear optimization add-in. From that search I found your 5.1 spreadsheet, which led me to a spreadsheet Richard had put together which was posted on this site... and then lo and behold you are the moderator of this site!

Thank you so much for your help... I knew it was possible... All my friends who tried to help me figure this out will be thoroughly impressed as well :)
Take care,