Algorithmic Model

The mathematical problem that the best 15 optimisation solves is a MIP problem of maximizing the objective value selected by the user (selection between: Value, Form, Total Point, ICT Index), while also respecting the following constraints:

  1. Maximum of 3 players can be selected by each team.

  2. Exactly 2 Goalkeepers, 5 Defenders, 5 Midfielders and 3 Forwards should be selected.

  3. Cost of players selected has a maximum of 100 units.

Mathematical modelling

  • Pi: player of team i

  • G: goalkeeper - binary

  • D: defender - binary

  • M: midfielder - binary

  • F: forward - binary

  • T: set of teams

  • Cp: cost of player

  • Vp: objective value of player

  • Pi ε {G, D, M, F}

  • Σ(Pi) = 2G + 5D + 5M + 3F

  • Σ(Pi * Cp) <= 100

  • Σ(Pi) <= 3 for every i ε T

  • max(Σ(Pi * Vp))