Round Robin Tournament Scheduling

Bridge scheduling

Ropa · 2 · 4455

Ropa

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on: February 25, 2016, 02:23:46 PM
Hello,
Looking for an eight (8) couples bridge club schedule(s) playing 4 couples at two locations for 10 rounds and another for 12 rounds. Understand hosting and playing couples would be unbalanced but hoping for as balanced as possible.

Ropa  


Ian Wakeling

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Reply #1 on: February 28, 2016, 08:55:43 AM
This is not an easy problem because of the unbalance that you mention and the low number of couples.  I think any schedule will have issues that the players might notice.  Consider this one for 12 rounds where the two players who host are the pair at the end of each row (round).

  (4  2  5  3)  (8  6  1  7)     (3  1)
  (5  3  2  8)  (4  6  1  7)     (5  4)
  (2  8  4  6)  (7  3  5  1)     (2  7)
  (5  7  6  2)  (8  4  3  1)     (6  8)

  (5  7  6  2)  (3  1  4  8)     (5  3)
  (8  6  7  3)  (2  4  1  5)     (7  1)
  (7  5  8  4)  (3  1  2  6)     (4  2)
  (1  7  2  8)  (6  5  3  4)     (8  6)

  (3  2  8  6)  (4  1  7  5)     (3  5)
  (7  8  4  2)  (1  3  6  5)     (7  1)
  (6  5  8  1)  (2  4  3  7)     (6  4)
  (1  2  7  3)  (6  8  5  4)     (2  8)


So the schedule is arranged so that after each block of 4 rounds, each couple has hosted once.  The schedule has issues.  The number of times pairs of couples meet varies from 4 to 6 times (this is unavoidable). There are also two missing combinations.  Couple 2 never hosts couple 5, and couple 3 never hosts couple 7.  Also 4 hosts 7 3 times, and 6 hosts 5 3 times.

If you wanted only 10 rounds just cut the schedule back.