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The problem definition is to define a 10 week schedule for our
volleyball league.

Games are always played on Wednesdays.

There are 48 teams in the league, divided into 8 6-team divisions.

Each team plays each of the other 5 teams twice, once as the home team
and once as the away team.

Each team in a division has an initial ranking.

Each team has a home gym.

Teams can share gyms.

Each gym has a normal set of times available for league play.

Gyms may (and do) have exclusions, i.e. A gym is not available on one
Wednesday in October.

The last division might only have 7 teams, in which case team 8 is a bye.

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The 'manual' algorithm currently used by the scheduler.

Set up all the constraints about gym usage, e.g. some gym isn't
available at some time.

Select an IDEAL  pairing set, i.e. an old schedule which has every
team playing over the ten week,
preferrably with teams 1 and 2 playing on the last week.

The week pairing should be reflective, i.e.  the home/away pairings on
Week 1 are the same as the away/home
pairings for Week 6, etc.

These home/away pairings will be refered to as I'n'-I'm':   e.g  I3-I5
means team 3 is home against team 5.

Start with Division 1, setting the team names as a list, assigning
them numbers B'n':  B1, B2, ... B6

Create for each home team a gym availability array of the gyms for
that division, if it doesn't already exist.

The array will consist of rows (Week 1, Week 2, ... Week 10) and with
columns representing the available
time slots.  The array will include all the gym usage constraints.

Check each team's home gym availablility array to see when the home
teams MUST be away.

Then map the team number of the away team to the number of the ideal
schedule, e.g. B3<=>I5.

Note that if a team is required to be home on a week that the gym is
not available, try reflecting the
ideal pairing set, e.g. have the Week 2 pairing switch with the Week 7
pairing.  This reflection is only
for the two pairs of home/away teams that are a problem.

Post to the gym availability array the name of the assigned home team
to the first available time slot.

Then create the division final mapping which consists of the replacing
the I'n' assignment with the B'n'
assignment, along with the time slot chosen from the gym availability array.

Then proceed to the next division and try the same methodology.

If all else fails, cry, cry, cry.

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Here is an example of the original IDEAL pairing set


Week 1                                          Week 6
1 vs 3                                          3 vs 1
6 vs 4                                          4 vs 6
2 vs 5                                          5 vs 2

Week 2                                          Week 7
4 vs 1                                          1 vs 4
6 vs 5                                          5 vs 6
3 vs 2                                          2 vs 3

Week 3                                          Week 8
5 vs 1                                          1 vs 5
2 vs 6                                          6 vs 2
4 vs 3                                          3 vs 4

Week 4                                          Week 9
6 vs 1                                          1 vs 6
2 vs 4                                          4 vs 2
3 vs 5                                          5 vs 3

Week 5                                          Week 10
1 vs 2                                          2 vs 1
6 vs 3                                          3 vs 6
5 vs 4                                          4 vs 5


Note that, for example, changing 2-6 in Week 3 with 6-2 in Week 8
doesn't change the pairings,
This is true for any pair set.

Note that Weeks 4-9 and Weeks 5-10 can be exchanged without changing
the pairings.

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What seems to make it fairly complicated is that gyms are shared by
teams within a division and with
teams in other divisions.  Additionally, the exclusion of some date
and/or time can effectively make
the schedule definition impossible.   This was actually the case this
year, so the scheduler had to go
to a gym and beg for additional time.

I hope this helps you.   I have code that manages the teams, defines
their home gyms and defines gym
exclusions.   There is also code for two other algorithms that I
pursued but couldn't generate final schedules
with.   I can let you see the interface if you would like.

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There are 19 gyms for the 48 teams.

The minimum time slot is 1 hour.   One hour is  the basic unit of
scheduling, by the way.

One gym as 4 times slots, noon, 1,2,3.  Others have 2 and 3 time
slots.  It all depends
on the gym.  In all cases, the number of available hours is constant
for each gym.  The
exclusions are used to removed something for the available pool.

Each team is assigned to only one gym, though.   I maintain a record
of all standard available times for each gym, then apply the exclusions.