Solution Summary

The optimal solution to extended problem #2:

school teacher	1	2	3	4	5	6	7	8	9	10
1	P		A
2	A	P
3		A	P
4					A	P
5						A	P
6				P					A
7							A			P
8					P			A
9				A				P
10									P	A

With the optimal objective value of 977.

Note that the optimal value of the utility for this problem is less than that of the core problem, this is due to the fact that this model has more stringent feasible region, as imposed by the additional constraint.

Mathematical Model

Assumptions

In additions to the assumptions of the core problem, we also assume that sessions from special schools must be assigned to the qualified teachers.

Index Sets and Variables

The additional subsets are:

SI(I) are the special teachers

SJ(J) are the special schools.

These two subsets have the effect of designated teachers 1, 2, and 3 to be special teachers, and schools 1, 2, and 3 are considered special schools.

The objective function and the variables are the same as defined for the core problem.

Data

The same set of data as defined in the core problem is used to demonstrate the effect of this additional requirement.

Program

The additional requirement gives the following constraints

S(j) xikj = 1 , j Í SJ, for each i Í SI

Each special teacher is assigned to a session in a special school

S(i) xikj = 1 , i Í SI, for each j Í SJ

Each session in a special school is assigned a special teacher