Schedules

This project is the first attempt to solve a common problem on any organization that wants to optimize the schedule between teachers and students taking into account

1. Teacher's availability and knowledge (subjects that can teach)
2. Students' needs (subjects that need to enroll)
3. Classrooms availability (hours and capacity)

based on the profit defined as

PROFIT = INCOME - COST

Where:

INCOME = SUM(students_payment)
COST = SUM(teacher_subject_cost) + SUM(classroom_total_hours_cost)

This can be used not only for money but also for teachers acceptance by students changing the income that every teacher creates on a given subject. See more in Example

Assumptions

1. All students take the schedule purposed.
2. Quality on every teacher is the same, so students' preferences don't apply.

Example

You can see the same example in Google Sheets here: Schedules | Example tables

Students' needs

student	subject 1	subject 2	subject 3	subject 4
1	x		x
2	x		x	x
3	x	x	x

Where:

• student 1 need to find a course for subject 1 and subject 3
• student 2 need to find a course for subject 1 and subject 3
• student 3 needs to find a course for subject 1, subject 2 and subject 3

Teachers' knowledge

teacher	subject 1	subject 2	subject 3	subject 4
1	x	x	x	x
2	x		x	x
3	x	x	x

Where:

• teacher 1 can teach subject 1, subject 2, subject 3, subject 4
• teacher 2 can teach subject 1, subject 3, subject 4
• teacher 3 can teach subject 1, subject 2, subject 3

Subject hours per week

subject	hours
1	6
2	8
3	4
4	6

Where:

• subject 1 need 6 hours a week and cost 1 to the students
• subject 2 need 8 hours a week and cost 1 to the students
• subject 3 need 4 hours a week and cost 1 to the students
• subject 4 need 6 hours a week and cost 1 to the students

Teacher cost per week

teacher	subject	cost	income
1	1	6	3
2	1	8	4
3	1	4	2
4	1	6	3

Income means the payment per student. That also is usefull to measure students' happiness in case the preference for some teachers is known.

Classroom availability (weekly)

classroom	cost	capacity	h2	h3	h4	h5	h6	h7	h8
1	5	10	x	x	x		x	x	x
2	7.5	15		x	x	x		x	x
3	6	12	x	x		x	x

Where:

• classroom 1 can be used on hours 1,2,3,4,6,7,8 by a single teacher for a single subject and has capacity for 10 persons
• classroom 2 can be used on hours 2,3,4,5,7,8 by a single teacher for a single subject and has capacity for 15 persons
• classroom 3 can be used on hours 1,2,4,5 by a single teacher for a single subject and has capacity for 12 persons

Teachers' availability

teacher	schedule	h1	h2	h3	h4	h5	h6	h7	h8
1	1		x	x	x	x	x	x	x
2	1	x	x
2	2						x	x	x
3	1	x	x		x	x		x

Teacher's can give multiple options for their own schedule. Example Teacher 2 can give 2 hours in the morning or 2 hours at night but 2 in the morning and 2 in the night.

Where:

• teacher 1, on schedule 1 can give class on hours 2,3,4,5,6,7,8 for a single subject
• teacher 2, on schedule 1 can give class on hours 1,2 for a single subject
• teacher 2, on schedule 2 can give class on hours 6,7,8 for a single subject
• teacher 3, on schedule 1 can give class on hours 1,2,4,5,7 for a single subject

UNAM Scenario

• Column "income" in "Teacher cost per week" table is 1
• Column "cost" in "Teacher cost per week" table is 0
• Column "cost" in "Classroom availability (weekly)" table is 0

TO DO:

Teachers' restrictions

• Classrooms: For infraestructure a teacher may not be able to use some specific classrooms.
• Capacity: A teacher will only accept a limited amount of students.

Students' restrictions

• Classrooms: For infraestructure a student may not be able to use some specific classrooms.
• Schedule: Student availability taking into account.
• Preference: Students with 100% credits can have preference over students with 90% credits and create an impact in the final schedule purposed. This would affect the main metric.

Subjects' restrictions

• Preference: Some subjects could be more "important" than others, so that can impact the final schedule purposed. This would affect the main metric.