I have developed an 8 team balanced round robin fixture using Ian's spreadsheet output as a starting point. [By the way, thankyou for the spreadsheet, Ian.]
The sport is table tennis, with multiple venues.
The fixture is to be used across multiple venues as well as for balanced table allocation in one grade at one venue so that there is only one fixture in use.
I am wondering if it is possible to improve on the 8 team fixture I have.
It is close to perfect; but I can't determine if it can be perfect.
The 7 rounds are repeated in rounds 8 to 14 with the home and away teams reversed.
The fixture has home and away pairing for teams 1/2; 3/4; 5/6; 7/8 with alternating 1/2.
There are no runs of 3 home or 3 away games. Such runs have to be minimised.
The table allocation is balanced overall; but not quite balanced for H and A matches for each team since team 4 and 8 both play 3 home or 3 away matches on a particular table.
The question is, is it possible to find such a fixture that satisfies all the constraints already satisfied, while obtaining the balance in the H and A table allocation.
In practice, this is not very significant, but it would be nice to have a perfect balance in table allocation.
| Round | Table1 | Table2 | Table3 | Table4 |
| 1 | 1 v 2 | 3 v 4 | 5 v 6 | 7 v 8 |
| 2 | 6 v 8 | 7 v 5 | 4 v 1 | 2 v 3 |
| 3 | 8 v 5 | 4 v 2 | 1 v 3 | 6 v 7 |
| 4 | 7 v 4 | 2 v 6 | 3 v 8 | 5 v 1 |
| 5 | 4 v 6 | 5 v 3 | 1 v 7 | 8 v 2 |
| 6 | 3 v 7 | 6 v 1 | 2 v 5 | 8 v 4 |
| 7 | 5 v 4 | 1 v 8 | 7 v 2 | 3 v 6 |
| 8 | 6 v 5 | 8 v 7 | 2 v 1 | 4 v 3 |
| 9 | 1 v 4 | 3 v 2 | 8 v 6 | 5 v 7 |
| 10 | 3 v 1 | 7 v 6 | 5 v 8 | 2 v 4 |
| 11 | 8 v 3 | 1 v 5 | 4 v 7 | 6 v 2 |
| 12 | 7 v 1 | 2 v 8 | 6 v 4 | 3 v 5 |
| 13 | 5 v 2 | 4 v 8 | 7 v 3 | 1 v 6 |
| 14 | 2 v 7 | 6 v 3 | 4 v 5 | 8 v 1 |
A screen shot showing the anaylsis of the fixture is attached.
