I've been tasked with generating a schedule with 24 unique teams.
Rules:
- Over the 11 weeks each team plays 2 matchups
- In week 12 each team plays a single matchup
- The result is every team plays every other team exactly once
Problem setup
Constraints:
- a 24x24 matrix of cells are the input variables for the problem. Each value must be a week between 0 and 12. 0 is used to block out the cell to avoid scheduling a team against itself.
- Each row needs to add up to 144 (0+1+2+...12)
- On the far right 0 must be used in the correct cell, weeks 1-11 countif() needs to equal 2, and week 12 needs to equal 1 for every team/ream
The goal seeking objective is to target the sum of all the week numbers which should equal 144*24 = 3456
When I am running the solver (OpenSolver) It is returning errors with all the different linear and non-linear solvers. Any Ideas?
I don't know what is wrong with your model (difficult to tell without having a look at the spreadsheet or not being a mind reader).
This is a problem that really requires that we first develop a mathematical model before we start coding or typing. Here is my mathematical model for this problem:
I use the definition:
Not completely trivial, but this can be implemented with any MIP solver: all constraints are linear. When I tried this, my results look like:
Of course, the solution is not unique. The model solved in 0.2 seconds.