4-player team scheduling

[joker]

Trying to schedule a social volleyball league of 24 individuals for 10-12 weeks, to be arranged in teams of 4 players.  The teams are not fixed, you get mostly new teammates and opponents for each game.  To be fair, I would like everyone to play with and against each other an equal number of times.  Not so bad, right?

Except that there are only 2 courts available in 3 time slots (6,7,8 pm), so each person is to play 2 games each week.  Since one court is 'better' than the other, I'd like to equalize the courts also.  Finally, I hope not too many people are forced to play 6 and 8 pm with an hour of down time, but maybe this can't be avoided.

Thanks in advance for any help!

[joker]

Ok, so I figured out that it won't be possible to schedule consecutive time slots for everyone.  Everyone will have to play 6 pm and 8 pm about 1/3 of the time.  Still having a hard time with this.  Any help appreciated.

[Ian Wakeling]

This is a really hard problem and the 12 week schedule below is probably far from optimal.  I have tried to concentrate on balancing the pairs 'with' and 'against', but they still vary from between three to fives times each.  In doing this I have had to ignore the equalization of the courts.  As you have realised, there is of course no way of avoiding the down time issue,  If you want to give everyone two games per week, then the 8 players who don't play at 7pm, must play both at 6 and 8 pm.   Hope that helps.

(24 14 6 17 v 4 16 5 9)   (13 19 1 3 v 23 10 7 8)
(12 2 18 5 v 16 4 17 21)   (1 7 13 15 v 11 22 19 20)
(15 11 18 20 v 12 22 21 2)   (3 23 6 8 v 24 10 9 14)
  
(1 15 7 18 v 5 17 6 10)   (14 20 2 4 v 24 11 8 9)
(13 3 19 6 v 17 5 18 22)   (2 8 14 16 v 12 23 20 21)
(16 12 19 21 v 13 23 22 3)   (4 24 7 9 v 1 11 10 15)
  
(2 16 8 19 v 6 18 7 11)   (15 21 3 5 v 1 12 9 10)
(14 4 20 7 v 18 6 19 23)   (3 9 15 17 v 13 24 21 22)
(17 13 20 22 v 14 24 23 4)   (5 1 8 10 v 2 12 11 16)
  
(3 17 9 20 v 7 19 8 12)   (16 22 4 6 v 2 13 10 11)
(15 5 21 8 v 19 7 20 24)   (4 10 16 18 v 14 1 22 23)
(18 14 21 23 v 15 1 24 5)   (6 2 9 11 v 3 13 12 17)
  
(4 18 10 21 v 8 20 9 13)   (17 23 5 7 v 3 14 11 12)
(16 6 22 9 v 20 8 21 1)   (5 11 17 19 v 15 2 23 24)
(19 15 22 24 v 16 2 1 6)   (7 3 10 12 v 4 14 13 18)
  
(5 19 11 22 v 9 21 10 14)   (18 24 6 8 v 4 15 12 13)
(17 7 23 10 v 21 9 22 2)   (6 12 18 20 v 16 3 24 1)
(20 16 23 1 v 17 3 2 7)   (8 4 11 13 v 5 15 14 19)
  
(6 20 12 23 v 10 22 11 15)   (19 1 7 9 v 5 16 13 14)
(18 8 24 11 v 22 10 23 3)   (7 13 19 21 v 17 4 1 2)
(21 17 24 2 v 18 4 3 8)   (9 5 12 14 v 6 16 15 20)
  
(7 21 13 24 v 11 23 12 16)   (20 2 8 10 v 6 17 14 15)
(19 9 1 12 v 23 11 24 4)   (8 14 20 22 v 18 5 2 3)
(22 18 1 3 v 19 5 4 9)   (10 6 13 15 v 7 17 16 21)
  
(8 22 14 1 v 12 24 13 17)   (21 3 9 11 v 7 18 15 16)
(20 10 2 13 v 24 12 1 5)   (9 15 21 23 v 19 6 3 4)
(23 19 2 4 v 20 6 5 10)   (11 7 14 16 v 8 18 17 22)
  
(9 23 15 2 v 13 1 14 18)   (22 4 10 12 v 8 19 16 17)
(21 11 3 14 v 1 13 2 6)   (10 16 22 24 v 20 7 4 5)
(24 20 3 5 v 21 7 6 11)   (12 8 15 17 v 9 19 18 23)
  
(10 24 16 3 v 14 2 15 19)   (23 5 11 13 v 9 20 17 18)
(22 12 4 15 v 2 14 3 7)   (11 17 23 1 v 21 8 5 6)
(1 21 4 6 v 22 8 7 12)   (13 9 16 18 v 10 20 19 24)
  
(11 1 17 4 v 15 3 16 20)   (24 6 12 14 v 10 21 18 19)
(23 13 5 16 v 3 15 4 8)   (12 18 24 2 v 22 9 6 7)
(2 22 5 7 v 23 9 8 13)   (14 10 17 19 v 11 21 20 1)

[joker]

Wow, thank you so much.  This is far better than anything I tried.  This will work great!

I'm curious what your method was.  I see some patterns in spots but not completely.  I assume you started out with a pattern and tweaked it at some point to satisfy the requirements?

Thanks again!