Bridge Scheduling 16 teams, 11 rounds, 4 sites

[gsutton45]

I have a similar problem to the one posted on 8/14.

I have 16 bridge teams (couples who always play together).  The teams will play once a month for 11 months.  The matches will be held at 4 sites each month.

 Can anyone help whip up a schedule?

Thanks,

George

[Ian Wakeling]

George,

The quick answer is to use the first 11 rounds from this schedule for golf foursomes.  But notice that when you have completed 10 rounds every pair of teams will have met at a site exactly twice, so this might be a good point to calculate a ranking for all the teams and then have some sort of championship playoff in the 11th month.  Here I am thinking that the 4 top ranked teams would meet at one site, the four next best at site another site, etc.

How important is it that the teams go to the 4 sites equally often?  As it stands, team A
would go to site 1 all the time, so at the very least it would prudent to randomize the
assigment of the foursomes to the 4 sites in each round.  However it may be possible to do
better than this if it is important to you.

Ian.

[gsutton45]

Ian,  

Thanks for the reply.  I looked at the schedule you linked to and then I discovered another requirement.  Each team (couple) must be the host site twice during the 8 rounds (yes, the numbers of rounds has dropped from 11 to 8).

Would it be possible to set a schedule that included the hosting requirement along with keeping the number of times teams face each other to a minimum?

Thanks,

George

[Ian Wakeling]

George,

The golf foursomes schedule is still looking like a good place to start.  Below I have rearranged 8 of the rounds and added the host sites in square brackets.

(ABCD)  (EFGH)  (IJKL)  (MNOP)    [A,E,I,M]
(AHJO)  (BGIP)  (CFLM)  (DEKN)    [D,H,L,P]
(AGLN)  (BHKM)  (CEJP)  (DFIO)    [C,G,K,O]
(AFKP)  (BELO)  (CHIN)  (DGJM)    [B,F,J,N]
(DJNP)  (AKLM)  (BGHO)  (CEFI)    [A,D,H,I]
(AEIM)  (BFJN)  (CGKO)  (DHLP)    [F,G,M,P]
(ILOP)  (BDFK)  (EHMN)  (ACGJ)    [E,J,K,O]
(ABEP)  (FHJL)  (CDMO)  (GIKN)    [B,C,L,N]

In terms of facing each other, each team will meet 6 out of the 15 possible opponents just once, and meet with the remaining 9 opponents twice. Above I have tried to maximize the length of time between the two rounds when a team hosts.  In fact Team F is the only one with their two hosting occasions two months apart, all the other teams have longer gaps.  This is at the expense of introducing more occasions in rounds 5 and 6 where the same two teams meet in consecutive months.  Rounds 5 and 6 could be interchanged to reduce this consecutive meeting of teams, however it would mean that Team F would now host twice in succession.

Hope that helps,

Ian.

[gsutton45]

Ian,

Many thanks.  This worked great.

George