$title teacher assignment problem

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/;

TABLE S(I,J) the combined score of the teachers' and schools' preference

	1	2	3	4	5	6	7	8	9	10
1       10      4       15      56      24      28      30      42      81      7
2       32      40      7       18      28      48      5       63      72      6
3       14      48      45      9       70      25      28      48      40      6
4       20      40      16      6       48      63      32      20      2       7
5       16      50      24      20      35      60      81      2       10      54
6       35      6       81      24      24      45      12      3       70      16
7       64      27      6       15      4       21      20      12      10      100
8       6       5       12      16      81      16      20      50      6       35
9       12      70      42      50      16      3       3       60      24      54
10      9       81      40      10      3       20      10      36      24      56;

VARIABLES
X(I,J) the assignment of teacher i to school j where X is either 0 or 1
Z	the total score over the 10 schools;

INTEGER VARIABLE X;

EQUATIONS

	SCORE define the total score which is the objective function
	SCHOOL(J) restriction that only one teacher is assigned to one school
	TEACHER(I) restriction that only one school is assigned to one teacher;

SCORE.. Z =E= SUM(I,(SUM(J,S(I,J)*X(I,J))));
SCHOOL(J).. SUM(I, X(I,J)) =E= 1;
TEACHER(I).. SUM(J, X(I,J)) =E= 1;

MODEL ASSIGN/ALL/;
SOLVE ASSIGN USING MIP MAXIMIZING Z;