set STUDS;
set COURSES;
set GRADES within {STUDS, COURSES};

param grade {GRADES};

var aptitude {STUDS};
var difficulty {COURSES};
var dev {GRADES} >= 0;

minimize sum_dev: sum {(s,c) in GRADES} dev[s,c];

subject to def_pos_dev {(s,c) in GRADES}:
	aptitude[s] - difficulty[c] - grade[s,c] <= dev[s,c];

subject to def_neg_dev {(s,c) in GRADES}:
	-dev[s,c] <= aptitude[s] - difficulty[c] - grade[s,c];

subject to normalized_difficulty:
	sum {c in COURSES} difficulty[c] = 0;

data;
set STUDS := 
	John
	Paul
	George
	Ringo
;
set COURSES := 
	MAT
	CBE
	ANT
	REL
	POL
	ECO
;
param: GRADES: grade := 
	John      ANT   2.3
	John      REL   2.7
	John      POL   3
	John      ECO   3.3
	Paul      CBE   2.3
	Paul      ANT   2.7
	Paul      POL   3.3
	Paul      ECO   3.7
	George    MAT   2.3
	George    CBE   2.7
	George    REL   3.3
	George    POL   3.7
	Ringo     MAT   2.7
	Ringo     CBE   3
	Ringo     ANT   3.3
	Ringo     REL   3.7
;

solve;

display aptitude;
display difficulty;