Badminton 5 courts - 40 players

[jensnielsen]

Hi everyone,
need help with this project. Need to schedule a weekly round robin tournament for a badmintonclub with only 5 courts available, and up to 40 players competing. The actual number of players can vary, but usually lies around 25.
They play mixeddoubles and regular doubles (foursomes). Two players should not partner more than once, and each player should meet an opponent only up to twice. They play games of 30 mins length, and have up to 5 rounds per evening.
Obviously only 20 can play in the courts at any time, so the thing is to ensure that everyone gets playtime.

Also the club has a ranking system, where each player is ranked from 1-4, where 1 is best and 4 is beginner. They want to even out the games so that two 4+4 players don't meet two 1+1 players, since this would be unfair.

Is it possible to schedule a tournament that guarantees everyone playtime, and takes into account the fairness principle?

This has caused me quite a headache until now.

Cheers
Jens, Denmark

[Ian Wakeling]

Jens,

The problem that you have specified is very general and you will most likely need a computer program to evaluate many different schedules and pick out the best. Complications such as the variable number of players who turn up for the evenings play, the possible need for mixed doubles and forbidden matches based on player ability all mean that you are unlikely to find an off-the-shelf schedule.  However, you mention that the normal number of players is 25, it just so happens that 25 would be a good number if you were planning on 5 rounds of regular doubles.

     Court 1         Court 2         Court 3         Court 4         Court 5        Byes
[(H X) v (M W)] [(E O) v (I L)] [(B Q) v (J G)] [(D T) v (C Y)] [(N V) v (R S)] (A F K P U)
[(I Y) v (N X)] [(A K) v (J M)] [(C R) v (F H)] [(E P) v (D U)] [(O W) v (S T)] (B G L Q V)
[(J U) v (O Y)] [(B L) v (F N)] [(D S) v (G I)] [(A Q) v (E V)] [(K X) v (T P)] (C H M R W)
[(F V) v (K U)] [(C M) v (G O)] [(E T) v (H J)] [(B R) v (A W)] [(L Y) v (P Q)] (D I N S X)
[(G W) v (L V)] [(D N) v (H K)] [(A P) v (I F)] [(C S) v (B X)] [(M U) v (Q R)] (E J O T Y)

In the schedule above, each player plays in exactly four rounds, has four different partners and has eight different opponents.  A player's partners and opponents are all different.  Furthermore, if you were to divide the players into 5 ability ranking groups as follows:

rank 1: A B C D E
rank 2: F G H I J
rank 3: K L M N O
rank 4: P Q R S T
rank 5: U V W X Y

then the matches are arranged so that the ability differences are small.  In particular all matches on the same court are drawn from the same rank groups.  The table below gives the matches in terms of groups.

Court   Rank Groups
  1   [(2 5) vs (3 5)]
  2   [(1 3) vs (2 3)]
  3   [(1 4) vs (2 2)]
  4   [(1 4) vs (1 5)]
  5   [(3 5) vs (4 5)]

Hope that helps.

Ian.