Integer Programming: Design Your Academic Curriculum

When designing an academic curriculum a lot of factors are taken into account. Based on the objectives defined for the career under consideration, experts have to propose the courses covering the fundamentals in each domain. Some explicit restrictions can also be imposed when developing a curriculum. For example, number of academic periods, maximum/minimum number of courses per period, and maximum/minimum academic load per period. Once this information is available, the assignment of courses to each academic period should be carried out to reach an adequate curriculum. Assuming that a balanced academic load favors academic habits and facilitates the success of students, we are interested in designing balanced academic curricula. The problem of designing balanced academic curricula consists in assigning courses to periods in such a way that the academic load of each period will be balanced, i.e., as similar as possible. In order to obtain such a balanced curriculum we think that a quantitative approach, instead of the traditional trial and error approach, can be very useful.

Regarding the curriculum design, let me give you some basic definitions about the curriculum.

Academic Curriculum: An academic curriculum is defined by a set of courses and a set of precedence relationships among them.

Number of periods: Courses must be assigned within a maximum number of academic periods.

Academic load: Each course has associated a number of credits or units that represent the academic effort required to successfully follow it.

Prerequisites: Some courses can have other courses as prerequisites.

Minimum academic load: A minimum amount of academic credits per period is required to consider a student as full time.

Maximum academic load: A maximum amount of academic credits per period is allowed in order to avoid overload.

Now, I want to design an integer model for the Bilkent Faculty of Business Administration. Given 18 courses, we need to assign these courses to first three semesters in an optimal way. Below I started forming a linear programming model. Please help me in completing my formulation.

Course	Prerequisite	Credits
ECON 101		3
ENG 101		3
GE 100		1
MAN 101		3
MATH 105		4
SOC 101		3
TURK 101		2
ECON 102	ECON 101	3
ENG 102	ENG 101	3
MAN 102	MAN 101	3
MATH 106	MATH 105	4
PSYC 100	SOC 101	3
TURK 102	TURK 101	2
ECON 221		3
GE 250		1
HUM 111		3
MAN 213	MAN 102	4
MATH 227	MATH 106	3

Parameters

Number of courses: 18

Number of academic periods : 3

i: Number of credits, of course, i; for all i = 1, , 18, which are listed above in the table.

Minimum academic load allowed per period: 9

Maximum academic load allowed per period: 24

Decision variables

..

Objective: Minimize the maximum semester load

.

Constraints

All courses i must be assigned to some period j:

.......

The academic load of period j must be greater than or equal to the minimum required:

........

The academic load of period j must be less than or equal to the maximum allowed:

...........

Course b has course a as prerequisite:

..

Provide your formulation and solve it in excel. Upload both the formulation and excel solution using the quiz template.