Round Robin Golf Match Play - 12 Clubs, 12 Venues

[freeman]

Hi. Good day!

I was tasked to plot the schedule of a Golf Match Play. Been trying to figure out on how to schedule it but I keep on hitting dead ends.  

I have 12 Golf Country Clubs and 12 Venues (same as the 12 Golf Country Clubs). Currently, I have 13 Golf Clubs and 13 venues but for the next Match Play Tournament, 1 club is dropping out thus reducing the clubs and venues to 12.  The conditions of the schedule are:

1. Clubs must play on neutral grounds (meaning "Golf Country Club A" cannot play at "Country Club A")
2. Number of Legs/Rounds be stretched to 12 Legs/Rounds

Been scanning the site for a possible similar scenario, but cannot find any.

Thanks!

[Ian Wakeling]

Hi,

I am not sure or not if the 12 regular Clubs and 12 Country Clubs are to be kept separate?

My best guess is that you have a combined pool of 24 clubs, and you would like to play 12 rounds, where each team plays at 12 different neutral grounds.  Is that correct?

Thanks,

Ian.

[freeman]

Hi Ian,

Thank you very much for responding to my enquiry.

Just to give you an idea, I have attached the schedule I've done during the time that there were 13 clubs participating in the league. Please note that these 13 clubs play hosts as well. The club cannot host a round on its own turf though.

I would like to do a similar schedule now that the pool is reduced to 12 clubs and the criteria remain the same.

If it's still confusing or if you need more info/clarification, please do not hesitate to let me know and will try my best to explain/answer whatever detail you need.

Thanks again!

[Ian Wakeling]

Clearly it would be better to have 11 rounds rather than 12 as then every team plays each other exactly once.

I don't think you can do much better than the schedule below, where the 11 rows are the rounds and they are played in the order indicated by the numbers in the 1st column.  This order guarantees that the same ground never hosts a match in consecutive legs.  All teams have a neutral ground where they don't play, and one neutral ground where they play twice.

the notation (F D)a indicates that F play D at ground 'a'  (in round 3).

 3 (F D)a (J K)c (A G)e (E L)g (C H)i (I B)k 
 5 (E J)a (H F)c (B K)e (I C)g (L G)i (A D)k 
 7 (L I)a (G B)c (J H)e (K D)g (E A)i (C F)k 
 9 (G C)a (L A)c (I D)e (J B)g (F K)i (E H)k 
11 (H K)a (I E)c (L C)e (F A)g (D B)i (G J)k 
 1 (A B)c (C D)e (E F)g (G H)i (I J)k (K L)a 
 2 (D H)b (B L)d (C J)f (A I)h (K E)j (F G)l 
 4 (K G)b (F J)d (D L)f (B E)h (A C)j (H I)l 
 6 (C E)b (K I)d (H B)f (L F)h (G D)j (J A)l 
 8 (I F)b (E G)d (K A)f (D J)h (H L)j (B C)l 
10 (J L)b (A H)d (G I)f (C K)h (B F)j (D E)l 

[freeman]

OMG! I can't thank you enough for this!

I just hope that my boss and the tournament committee accepts and approve this schedule.

Again, thank you so much!

[freeman]

Hi Ian,

Good day! I hope this email finds you well.

Again, thank you for your assistance with the schedule I have request a few months back. Unfortunately, my organizing committee decided to adopt a new format for our Inter Club League and I would like to seek for your assistance once again.

We have 12 Clubs and 12 venues. They will now be split in to 2 groups. 1 Group will consist 6 Clubs to play at 6 venues while the other is group will consist of the remaining 6 clubs and 6 venues. The conditions remain the same.

I hope you could assist me with this.

Thank you very much!

Best Regards,
Freeman

[Ian Wakeling]

Hi Freeman,

There is a problem since the method I used to make the 12 club schedule does not work for less than 10 clubs.  Therefore I don't think any nice solutions will exist for smaller number of clubs.

All I can think of doing is taking the basic round-robin and then try to assign the venues by hand.  For example I have come up with:

(C F) e   (A E) c   (D B) a
(D F) b   (B E) d   (C A) f
(E D) c   (F A) e   (C B) a
(B A) f   (C D) b   (E F) d
(C E) a   (F B) c   (A D) e

but the distribution of teams playing at neutral venues will not be even.

[freeman]

Hi Ian,

Thank you again for your help. I really appreciate it!

Schedule was accepted by my committee and they will be presenting it to all clubs on Thursday. Hopefully, everybody will agree with the schedule.

Again, thank you!

Best Regards,
Freeman

[freeman]

HI Ian,

Good day to you! I hope you're doing well!

I would like to seek for your assistance again for our inter-club league. Technically, we have the same number of playing clubs and venue and the criteria remain the same. Now, the difference from the previous league are as follows:
- Venues are different from the Playing Clubs. Say Venues are V1, V2, V3, V4, V5 & V6
- Playing Clubs are PC1, PC2, PC3, PC4, PC5, PC6. These playing clubs must all play in a leg.

Hope you can come-up with a round robin schedule for this league again.

Thank you very much and have a great week ahead!

Best Regards,
Freeman

[Ian Wakeling]

Hi Freeman,

Would the following work, where the six playing clubs are the letters A to F?

  V1    V2    V3    V4    V5    V6
(A B) (C D) (E F) (---) (---) (---)
(---) (---) (---) (D E) (B F) (A C)
(C E) (A F) (---) (---) (---) (B D)
(D F) (---) (B C) (---) (A E) (---)
(---) (B E) (A D) (C F) (---) (---)
(---) (---) (---) (A B) (C D) (E F)

You could choose not to play the last leg (which has the same matches as the first leg), but if it is played it becomes a balanced schedule in the sense that all teams play exactly once at each venue.

Ian

[freeman]

Thank you Ian for your prompt reply. You're the best!  

My apologies. I forgot to include that the matches need to be squeezed into 5 legs.

So basically, there are 6 venues, 6 teams but the round robin needs to be finished in 5 legs.

Thank you and hope to hear from you soon!

[Ian Wakeling]

Just leave out the last leg, then all 15 matches from the round-robin will have been played.   Venues 4 to 6 will only have 2 matches each, but that can't be avoided.