Question

The Aguilucha University offers, within the Industrial Engineering degree, the certificate in Operations Research. To obtain it, you must cover at least two credits in the Mathematics area, at least two in the Operations Research area and at least two in the Computer area. Various courses are offered, each of which can satisfy a credit from one or more areas. The Calculus course covers only one credit in Mathematics; the Operations Research course covers one credit in Mathematics and one in Operations Research; the Data Structure course covers one credit in Computing and one in Mathematics; the Statistics course covers one credit in Mathematics and one in Operations Research; the Simulation course covers one credit in Operations Research and one in Computer Science; the Programming course covers only one credit in Computing; and the Forecasting course covers one credit in Operations Research and one in Mathematics. In addition, some courses are prerequisites for others: Calculus is a prerequisite for Statistics; Programming is a prerequisite for Simulation and Data Structure; and Statistics is a prerequisite for Forecasting. Let's consider the following variables 0-1 for each of the courses, where the value 1 means that the course is taken, 0 that it is not:
• x1: Calculation
• x2: Operations Research
• x3: Data Structure
• x4: Statistics
• x5: Simulation
• x6: Programming
• x7: Forecasts
Using these variables, formulate, without solving, an Integer Programming problem that minimizes the number of courses taken in such a way that all the requirements to obtain the certificate are met. Don't forget to model the prerequisites.

Answer 1

Answer:

The integer programming model is as below:

Objective function:

Minimize

$Z=x_1+x_2+x_3+x_4+x_5+x_6+x_7$

Subject to:

$x_1+x_2+x_3+x_4+x_7 \geq 2$

74r + $r + vr + or

C3 + 25 + 16 2

$x_1-x_4\geq 0$

$-x_3-x_5+2x_6\geq 0$

$x_4-x_7\geq 0$

$x_1,x_2,x_3,x_4,x_5,x_6, x_7 ={\left \{ 0,1 \right \}$ (All variables are binary)

EXPLANATION FOR THE MODEL

The given data for credits of all courses can be summarized as in the given table:

	Mathematics	Operations research	Computer Science
Calculus	1
Operations Research	1	1
Data Structure	1		1
Statistics	1	1
Simulation		1	1
Programming			1
Forecasting	1	1
Minimu requirement	2	2	2

Objective function:

The Objective is to minimize the total courses taken :

Minimize

$Z=x_1+x_2+x_3+x_4+x_5+x_6+x_7$

Subject to:

1) At least two credits in the Mathematics area,

From above table

$x_1+x_2+x_3+x_4+x_7 \geq 2$

2) At least two credits in the Operations Research area

74r + $r + vr + or

3) At least two credits in the Computer area.

C3 + 25 + 16 2

4) Calculus is a prerequisite for Statistics;

$x_1\geq x_4$

which can be rewritten as

$x_1-x_4\geq 0$

5) Programming is a prerequisite for Simulation and Data Structure;

$2x_6\geq x_5+ x_3$

which can be rewritten as

$-x_3-x_5+2x_6\geq 0$

6) Statistics is a prerequisite for Forecasting.

$x_4-x_7\geq 0$