laboratory-03/Exercise1.gms at main · modeling-simulation-and-optimization/laboratory-03 · GitHub

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Laboratorio 3 - MOS
Ejercicio 1

Realizado por:
Juan Andrés Romero C - 202013449
Juan Sebastián Alegría - 202011282
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Sets i               'Players'             /i1*i7/
     rolePerformance 'Role performance'    /BallControl, Shooting, Rebounds, Defense/
     position        'Available positions' /Attack, Center, Defense/;

Table Performance(i, rolePerformance)

     BallControl  Shooting  Rebounds  Defense
i1   3            3         1         3
i2   2            1         3         2
i3   2            3         2         2
i4   1            3         3         1
i5   3            3         3         3
i6   3            1         2         3
i7   3            2         2         1;

Parameter positions(i, position);

positions('i1', 'Attack') = 1;
positions('i2', 'Center') = 1;
positions('i3', 'Attack') = 1;
positions('i3', 'Defense') = 1;
positions('i4', 'Center') = 1;
positions('i4', 'Defense') = 1;
positions('i5', 'Attack') = 1;
positions('i5', 'Defense') = 1;
positions('i6', 'Center') = 1;
positions('i6', 'Defense') = 1;
positions('i7', 'Defense') = 1;
positions('i7', 'Attack') = 1;

Variables x(i) 'Indicates if said player is chosen'
          z    'Objective function';

Binary Variable x;

Equations targetFunc            'Target function'
          amountPlayers         'Amount of players'
          defenseConstraint     'Defense position constraint'
          attackingConstraint   'Attacking position constraint'
          centerConstraint      'Center position constraint'
          ballControlConstraint 'Ball control constraint'
          shootingConstraint    'Shooting constraint'
          reboundsConstraint    'Rebounds constraint'
          player2or3            'Player 2 or 3 chosen';

targetFunc..            z =e= sum(i, x(i)*Performance(i, 'Defense'));
amountPlayers..         sum(i, x(i)) =e= 5;
defenseConstraint..     sum(i, x(i)*positions(i, 'Defense')) =g= 4;
attackingConstraint..   sum(i, x(i)*positions(i, 'Attack')) =g= 2;
centerConstraint..      sum(i, x(i)*positions(i, 'Center')) =g= 1;
ballControlConstraint.. sum(i, x(i)*Performance(i, 'BallControl'))/5 =g= 2;
shootingConstraint..    sum(i, x(i)*Performance(i, 'Shooting'))/5 =g= 2;
reboundsConstraint..    sum(i, x(i)*Performance(i, 'Rebounds'))/5 =g= 2;
player2or3..            x('i2') + x('i3') =e= 1;

Model exercise1 /all/;
option mip=cplex
Solve exercise1 using mip maximizing z;
Display x.l, z.l;