Golf league scheduling

[teetimejunky]

I have 20 players in groups of four.  I want the foursomes to be 4 different players each week.  I have the ability to set up 16 players, but I guess I don't have the brain power to add in another group of four.  It seems that I can't get the first and last player in the same group at any one time.  Any help would be appreciated.  The league spans from April through September, so I know that every six weeks, the cycle should repeat itself.  I just want everyone to have the opportunity to play with different players each week.

Thank you,

Rich

[Ian Wakeling]

Rich,

Mathematically speaking, 16 is a much nicer number of players to work with than 20.  In fact I believe that a six week schedule of foursomes where players play together at most once is impossible, so it's no wonder you are finding the problem hard.  A five week schedule with the same property is possible, for example use the first five weeks in the table below.

Week 1: (A B C D)  (E F G H)  (I J K L)  (M N O P)  (Q R S T)
Week 2: (A F K P)  (E J O T)  (I N S D)  (M R C H)  (Q B G L)
Week 3: (A J S H)  (E N C L)  (I R G P)  (M B K T)  (Q F O D)
Week 4: (A N G T)  (E R K D)  (I B O H)  (M F S L)  (Q J C P)
Week 5: (A R O L)  (E B S P)  (I F C T)  (M J G D)  (Q N K H)
Week 6: (A E I M Q)  (B F J N R)  (C G K O S)  (D H L P T)

I realise that many golf courses would not allow it, but if it were possible to play 4 fivesomes in week 6 as shown above, then everyone would have played with everyone else exactly once. If fivesomes are out of the question then let us know for how many weeks you will be playing? For foursomes the perfect number would be 19 weeks, as then it can be arranged that all players play with each other exactly 3 times.

Ian.

[teetimejunky]

Ian,

I had no problem with the 16 player roster.  This year we are expanding to a 20 player roster, thus my dilema.  Fivesomes are a big no-no, that is why I had to expand to the 20.  I appreciate you assistance.  I will just manually adjust the roster so that the players, who were not scheduled per the formula, will then play together.  Others may have to repeat a foursome.  We play from April 6, until players drop out, which usually is around the end of September.  We play once a week.

Thank you,

Rich Moss

[Ian Wakeling]

Rich,

From now to the end of September would be around 26 rounds of play, I have software that would generate a schedule for this, but my worry is that while the whole would be balanced, it would no longer look balanced if you split it into 4 parts of 6 or 7 weeks.  For example it is quite likely that in the first 7 weeks a few pairs would play together 3 or 4 times while a few other pairs not at all; I think your colleagues might notice this. So if it's the social mix that is important, then you may well be better off making adjustments to the 5 week schedule above.

There is an important property of this 5 week schedule that I did not mention earlier.  Within each week above, rotate the order of the foursomes so that they look like this:

        Tee-off Order
        first      second     third      fourth     fifth
Week 1: (A B C D)  (E F G H)  (I J K L)  (M N O P)  (Q R S T)
Week 2: (E J O T)  (I N S D)  (M R C H)  (Q B G L)  (A F K P)
Week 3: (I R G P)  (M B K T)  (Q F O D)  (A J S H)  (E N C L)
Week 4: (M F S L)  (Q J C P)  (A N G T)  (E R K D)  (I B O H)
Week 5: (Q N K H)  (A R O L)  (E B S P)  (I F C T)  (M J G D)

Now players get to tee-off once each at the five tee-off times.

Ian.

[teetimejunky]

Thanks, Ian.  I will try the rotation as you have suggested.  I believe that I will still try a few manual adjustments to tweak some of the players to be able to play together.


Rich