Scheduler

Using integer linear programming (with gurobi via Pulp) to schedule interviews between students and firms.

Variables

Problem Variables

• F: Firms
• S: Students
• T: Number of timeslots
• M: Meetings needed (which firms need to meet with which students)

Linear Variables

• Possible Slots (FST): Boolean slot for each possible Firm-Student-Timeslot

Number of linear variables: M * T

Constraints

1. Students can only have one interview per timeslot and must have break after
2. Firms can only have one Student interview per timeslot
3. A firm-student interview must be in only one timeslot

Number of constraints:

1. ~ S * T
2. ~ F * T
3. M

Example Size

S = 25
F = 14
T = 20

Each firm wants to interview about half the students so:
M = 182

Variables: 3640

M * T = 182 * 20

Constraints: 572

(~ 25 * 20) + (~ 14 * 20) + 182
250 + 140 + 182

Program does not add a constraint on the ~ approximations if firm-student aren't to have a meeting
Thus ~ is about half as we determined firms would only want meetings with half the students
(and just assuming distribution of students among firms is even for ~14*20)

Optimization

Attempts to place all meetings in the morning, by weighting timeslots.
This also optimizes towards minimizing the length of time firms need to spend for interviews.