Improve table allocation balance for 8.10,12 teams

[gmctt]

I have developed 8, 10 and 12 team mirrored double round robin fixtures using Ian's spreadsheet output as a starting point. [By the way, thankyou for the spreadsheet, Ian.]
The sport is table tennis. The fixtures are to be used at mutliple venues in which case home and away pairing of teams is required, as well at a single venue in which case balanced table allocation is the priority.

The attached spreadsheet in the zip file is only part way to being balanced.
The 8 team fixture has 4 occurances departing from table allocation balance in H and A matches for each team with 0 occurances departing from balance in the full fixture.
The 10 team fixture has 12 occurances departing from table allocation balance in H and A matches for each team with 6 occurances departing from balance in the full fixture.
The 12 team fixture has 32 occurances departing from table allocation balance in H and A matches for each team with 14 occurances departing from balance in the full fixture.

Can anyone improve on the fixtures attached to maximize the balancing of table allocation while keeping teams paired in terms of home and away sequences and keeping the runs of 3 home or 3 away games to a minimum?

[Ian Wakeling]

I am not sure that I can help you here, as I can't see any obvious way to improve the schedules that you have posted.  It might help a little if I describe what my spread sheet does for a double round robin in 'home/away' format.  It starts with two copies of the same schedule, then changes some games around to avoid the problems in the HA sequence that are introduced at the join of the two schedules.  This problem was studied mathematically, and it has been proven that the schedule generated has minimum departure from an alternating HAHA...  or AHAH... sequence.  But the assumption here is that schedule is for a league where each team has its own home venue, and not your situation with shared venues, where each team is designated to be either home or away.   I think there is probably a trade off between balance at a venue and a good overall home/away sequence, so you may need to look for some sort of computer optimisation to make any progress.  Sorry not to be of more help.

[wbport]

One way to not have three home/away (or Whites or Blacks, etc) for a double round robin is to play the first schedule backwards reversing Home status or color.

I developed this for chess, but it can be used for any one on one competition where partners are not assigned. rrpair.htm.