Partial Court Balanced Schedule?

[OO7Ian]

Hello all,

I've been struggling with a scheduling issue for a bit now and took to Google to hopefully find a solution which eventually led me to this wonderful little corner of the Internet.  If anyone can help me figure this one out, I'd be very thankful.  Here's my struggle...

I have a 20 team, 14 round league I am scheduling for.  So every team only plays an opponent once but they do not play every other team.  The league consists of 5 teams from 4 neighboring cities.  Each city has a 3 venues (12 total) where the matches will be held.  With 14 matches per season, each team will have 7 home & 7 away.  When a team is scheduled to play at home, it would need to be scheduled to play at one of its home cities venues (i.e. Teams A1, A2, A3, A4, & A5 would all play their home games at venues A-bldg1, A-bldg2, or A-bldg3.  Teams B1, B2, B3, B4, & B5 would play home games at venues B-bldg1, B-bldg2, or B-bldg3. etc).  Essentially, 5 teams share 3 "home" venues.  What this means is that no city can host more than 3 home games per round and that 2 venues will go unused each round (only 10 matches scheduled per round).  The unused venues aren't an issue, but the issue is creating a schedule that would have every city only have a max of 3 home games each of the 14 rounds.

I was given the restriction to keep as much balance in the matchups as possible.  Where each team within a city should play every other team within that city as a priority, then balance the remaining schedule as much as possible over the other 3 city's teams (i.e. Team A1 plays 4 matches against the other City A teams - A2, A3, A4, A5 - then plays 4 games against random City B teams, 3 against random City C teams, and 3 against random City D teams).

The good news is that I have the matchups figured out and that they are nice and balanced.  My thought process was that if I could come up with the matchups first, then slotting the round by round schedule wouldn't be as difficult.  The bad news is that now that I have the matchups, I can't figure out how to slot them into a schedule so that every team plays every round and no city hosts more than 3 matches.  My question is does anyone know if this type of schedule is possible?  Am I making it impossible with the balanced matchup restrictions or by creating the matchups without taking slotting into account?

Any insight or directions would be greatly appreciated.

[Ian Wakeling]

The only easy solution I can see would be to ignore the priority on within city games.  Then the Excel generator will provide a solution.  Simply go for 20 teams in home/away format in 'do not randomize' mode and slice off rounds 15 to 19, finally divide the teams into 5 cities as show in the image.  This meets the no more than 3 home games per city per round (dark cells).

[OO7Ian]

Thanks for the quick response.  This might work for me league.  Now I just need to convince the teams that city games aren't that important

[OO7Ian]

Hello again.  So just as I thought I had this figured out, my league had to throw me a curve...

One of the cities will only be fielding 4 teams.  This gives us a total of 19 teams which means that Byes will be needed.  I figured that wouldn't be a problem and assigned Team A as the Bye.  I then knew that any team that had a Bye before Round 15 would need to play in round 15 to get their full 14 game schedule.  Simple enough and things were going well until I realized that some of the teams that had finished up their season of 14 games in Round 14 (no bye scheduled by that point) were needed to complete schedules for other teams in Round 15 (see attached schedule - red/blue highlighted matchups show the issue).

So my question is that if I have a 19 round schedule, and I introduce byes, is it still possible to truncate the schedule so that only 14 rounds are played?

[Ian Wakeling]

I think it will work if you go back to the generator and choose 19 teams.   The order of the last few rounds needs to be tweaked a little so that the opponents of the games for O P Q R & S in round 15 (was round 17) all come from the same city (these are the games you don't play).  See attached.