$title teacher assignment problem
*some teachers are will to take overtime sessions
SETS I teachers /1, 2, 3, 4, 5, 6, 7, 8, 9, 10/
J schools /1, 2, 3, 4, 5, 6, 7, 8, 9, 10/
MW(J) Schools with classes on Mon and Wed /1, 2, 3, 4, 5, 6, 7, 8/
TT(J) Schools with classes on Tue and Thr /9, 10/
K sessions /am, pm/;
SCALAR
Overtime The max classes that an overtime teacher is willing to teach /3/
Regular The max classes that a regular teacher is willing to teach /2/;
PARAMETER Y(I) indicates whether teacher i is willing to teach overtime classes
/1 1
2 0
3 1
4 0
5 0
6 1
7 1
8 0
9 1
10 0/;
TABLE S(I,K,J) the combined score of the teachers' and schools' preference
1 2 3 4 5 6 7 8 9 10
1.am 4 10 18 4 10 18 100 72 49 90
2.am 7 36 28 12 21 40 90 42 64 3
3.am 21 54 50 18 80 30 40 56 4 8
4.am 70 80 6 16 8 28 23 10 12 2
5.am 16 50 24 20 35 60 54 2 10 54
6.am 35 6 90 24 24 45 10 3 90 16
7.am 64 27 54 15 4 28 16 12 10 70
8.am 6 2 12 16 81 16 15 50 6 35
9.am 12 70 21 50 48 3 2 60 24 54
10.am 9 18 3 28 5 60 7 48 27 80
1.pm 4 10 18 4 10 18 100 72 49 90
2.pm 7 36 28 12 21 40 90 42 64 3
3.pm 21 54 50 18 80 30 40 56 4 8
4.pm 70 80 6 16 8 28 23 10 12 2
5.pm 16 50 24 20 35 60 54 2 10 54
6.pm 35 6 90 24 24 45 10 3 90 16
7.pm 64 27 54 15 4 28 16 12 10 70
8.pm 6 2 12 16 81 16 15 50 6 35
9.pm 12 70 21 50 48 3 2 60 24 54
10.pm 9 18 3 28 5 60 7 48 27 80
VARIABLES
X(I,K,J) the assignment of teacher i to school j where X is either 0 or 1
Z the total score over the 10 schools;
POSITIVE VARIABLE X;
EQUATIONS
SCORE define the total score which is the objective function
SCHOOLAM(K,J) restriction that only one teacher is assigned to one am session
SCHOOLPM(K,J) restriction that only one teacher is assigned to one pm session
MAXCLASS(I) restriction that each teacher's maximum classes willing to teach
TamMW(I,K) restriction that only one MW am session is assigned to one teacher
TpmMW(I,K) restriction that only one MW pm session is assigned to one teacher
TamTT(I,K) restriction that only one TT am session is assigned to one teacher
TpmTT(I,K) restriction that only one TT am session is assigned to one teacher
DIFFSCH(I,J) restriction that each teachers are assigned to two different school;
SCORE.. Z =E= SUM(I,(SUM(K,(SUM(J,S(I,K,J)*X(I,K,J))))));
MAXCLASS(I).. SUM((K,J), X(I,K,J)) =L= ((Y(I)*Overtime)+((1-Y(I))*Regular));
SCHOOLAM("am",J).. SUM(I, X(I,"am",J)) =E= 1;
SCHOOLPM("pm",J).. SUM(I, X(I,"pm",J)) =E= 1;
TamMW(I,"am").. SUM(MW, X(I,"am",MW)) =L= 1;
TpmMW(I,"pm").. SUM(MW, X(I,"pm",MW)) =L= 1;
TamTT(I,"am").. SUM(TT, X(I,"am",TT)) =L= 1;
TpmTT(I,"pm").. SUM(TT, X(I,"pm",TT)) =L= 1;
DIFFSCH(I,J).. X(I,"pm",J)-(1- X(I,"am",J)) =L= 0;
MODEL ASSIGN/ALL/;
SOLVE ASSIGN USING LP MAXIMIZING Z;