Round Robin Tournament Scheduling

create an objective function for minimizing breaks

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magnhau

  • Guest
on: October 14, 2009, 08:52:02 AM
Problem: :-/
6 teams
double round robin tournament
not mirrored

How do I formulate the objective function when my objective is to minimize the total number of breaks?

My model has binary decision variables Xijt, taking the value 1 if team i plays team j at home in round t.

So far I have tried to multipy two decision variables (t with t+1) and minimize the total.
But Xpress-IVE does not like non-linear functions.

someone help me?


wbport

  • Senior Member
  • ****
    • Posts: 129
Reply #1 on: October 15, 2009, 07:57:11 AM
I'm not sure if you are asking for a schedule or homework help.

We've looked at how to avoid three-in-a-row at the end of the first half and start of the second.  The only thing that seems to work is play the 2nd half in reverse order from the first with colors (i.e., home-away status) reversed.
5 or 6 players

Rd         Pairings
 1:   1-6    4-3    5-2  
 2:   6-4    2-1    3-5  
 3:   2-6    5-4    1-3  
 4:   6-5    3-2    4-1  
 5:   3-6    1-5    2-4
 6:   6-3    5-1    4-2
 7:   5-6    2-3    1-4
 8:   6-2    4-5    3-1
 9:   4-6    1-2    5-3
10:   6-1    3-4    2-5