Bowling club leagues

[bowlertrebor]

I am try to create a computer program that will allow me to do the following
The bowls club has  6 rinks and teams play 2 rinks per game and has 2 sessions
ie 3 games can be played on any one session

teams play on rinks 1,3,5 and on an early and late session teams that play on a rink on one week have to rotate through the other rinks on subsequent weeks and also have to play alternate early and late sessions any advice please

[Ian Wakeling]

I don't think I fully understand the problem. Are the rinks in fixed pairs, so there are always the same three slots for a game in any one session?  How many teams are there?  At the moment I am thinking that if there are 12 teams,  each with one game per week, then something balanced might be possible, otherwise it becomes a hard problem, with byes, or some teams playing both early and late.

If teams were to strictly alternate early and late, then the same two subsets of teams would always be playing at the same time, and scheduling games between subsets would not be possible, so you must allow teams to have two consecutive weeks scheduled at the same time.

[bowlertrebor]

yes the rinks are in pairs ie 1/2 3/4 4/5 so a team plays 2 rinks at a time
we currently have 12 teams per league but in previuos years we hav had 10 o r 11or 13 so provision has to be made for these eventualties

it is possible for teams to play some early or late sessions concurrently

[Ian Wakeling]

Here is the balanced schedule for 12 teams.

(K H) (B J) (G D)
(L F) (A I) (E C)
------------------
(J L) (F H) (C I)
(A G) (B E) (D K)
------------------
(A B) (H I) (F K)
(D E) (J G) (C L)
------------------
(D H) (C F) (A E)
(B K) (G L) (J I)
------------------
(D C) (A L) (J F)
(G I) (E K) (B H)
------------------
(C G) (I K) (H L)
(A J) (D B) (F E)
------------------
(L E) (A C) (K G)
(H J) (F D) (I B)
------------------
(K J) (E G) (L B)
(I D) (H C) (A F)
------------------
(I E) (K L) (A D)
(F B) (C J) (H G)
------------------
(G F) (J D) (B C)
(E H) (L I) (A K)
------------------
(I F) (G B) (E J)
(K C) (A H) (L D)

which has teams 3 or 4 times in each of the three columns and 5 or 6 times early and late.

In some ways 13 teams is better, as you can have all teams 4 times each in the columns and 6 times each early and late.

(I F) (C E) (H D)
(B A) (J L) (K G)
------------------
(C H) (A F) (L I)
(E B) (D K) (M J)
------------------
(K I) (M D) (C L)
(J G) (H A) (B F)
------------------
(F G) (H M) (J E)
(K L) (B D) (I A)
------------------
(M C) (G I) (A K)
(D J) (L B) (E H)
------------------
(A L) (B H) (K C)
(F E) (I M) (G D)
------------------
(J B) (D A) (E G)
(C I) (M F) (H K)
------------------
(B K) (E L) (M A)
(H F) (C G) (J I)
------------------
(H J) (L G) (D F)
(M K) (E I) (C B)
------------------
(G A) (J C) (B M)
(I D) (K E) (F L)
------------------
(D E) (I B) (F J)
(A C) (G H) (L M)
------------------
(E M) (F K) (G B)
(L H) (A J) (D C)
------------------
(L D) (K J) (I H)
(G M) (F C) (A E)

[Ian Wakeling]

Some more schedules for you to consider.  I have kept the schedule as short as possible by allowing some teams to play both sessions.

10 teams

(D I) (C F) (B H)
(E G) (A J) (---)
------------------
(A E) (G H) (C I)
(B F) (---) (D J)
------------------
(I J) (B E) (C H)
(---) (D F) (A G)
------------------
(E F) (G J) (A D)
(F H) (B I) (C E)
------------------
(H J) (A I) (F G)
(C D) (E H) (B G)
------------------
(A B) (C G) (D E)
(A H) (F I) (B J)
------------------
(G I) (E J) (A F)
(C J) (B D) (H I)
------------------
(B C) (D H) (F J)
(D G) (A C) (E I)


11 teams
(F G) (E I) (D H)
(B C) (A K) (---)
------------------
(A H) (I J) (B K)
(E F) (---) (D G)
------------------
(A D) (H I) (E K)
(---) (C F) (B J)
------------------
(B I) (A C) (F H)
(G J) (D K) (---)
------------------
(D J) (I K) (C G)
(E H) (---) (A B)
------------------
(A F) (B E) (C D)
(J K) (C H) (G I)
------------------
(G K) (B F) (C E)
(D E) (H J) (A I)
------------------
(C I) (E G) (A J)
(G H) (B D) (F K)
------------------
(C K) (D F) (E J)
(B H) (A G) (F I)
------------------
(F J) (B G) (H K)
(D I) (C J) (A E)

[bowlertrebor]

Sorry I Have not thanked you but I have been ill and in hospital the 11 and 10 sequences will not work as teams cannot play twice in one night.
the other consideration is that teams should play as far as possible equally on rinks 1/2 , 3/4 ,5/6 through the sequence

[Ian Wakeling]

I am sorry to hear that you have been ill.

I think all the schedules above have teams equally as possible in each column, so the rink balance is there.

How about this for 10 teams?

(H J) (F G) (C I)
(A B) (D E) (---)
------------------
(D G) (A H) (B C)
(E I) (---) (F J)
------------------
(C F) (I J) (B D)
(---) (G H) (A E)
------------------
(F H) (B I) (---)
(E G) (A D) (C J)
------------------
(A J) (---) (E H)
(C D) (F I) (B G)
------------------
(---) (E J) (G I)
(B F) (A C) (D H)
------------------
(D I) (B E) (A F)
(G J) (C H) (---)
------------------
(B H) (---) (D J)
(A I) (C G) (E F)
------------------
(C E) (D F) (A G)
(---) (B J) (H I)

and this for 11?

(B E) (F H) (G K)
(A C) (D I) (---)
------------------
(H J) (A D) (C E)
(F G) (---) (B I)
------------------
(I K) (B C) (A H)
(---) (E G) (D J)
------------------
(E I) (B J) (---)
(G H) (D K) (C F)
------------------
(A E) (---) (F J)
(C D) (B K) (H I)
------------------
(---) (F I) (B G)
(A K) (E J) (C H)
------------------
(C G) (A F) (D E)
(J K) (B H) (---)
------------------
(D H) (A G) (I J)
(B F) (---) (E K)
------------------
(F K) (C I) (D G)
(---) (E H) (A J)
------------------
(B D) (C K) (---)
(A I) (G J) (E F)
------------------
(C J) (---) (H K)
(D F) (G I) (A B)