Consider the last time you had to pick classes to fit a schedule. What were some things you had to consider in doing so? What sort of constraints did you consider necessary, and which were considered preferences? How does your answers compare to your classmates?
Yafa is an incoming freshman at Fantasi College and she is picking classes for her first semester. Fantasi College has classes either on Monday-Wednesday-Friday from 8:30-9:30, 10:00-11:00, 12:30-1:30 and 2:00-3:00, and on Tuesday-Thursday from 8:30-10:00, 10:30-12:00, and 1:00-2:30.
Yafa has put together a list of potential classes she could take this semester, and assigned to them a score from 1 - 10 depending on her interest in the class, the time of day, and her own “research” looking up professors on external rating sites. (Yafa has not yet taken her introductory statistics course, and so doesn’t yet know how unreliable and biased these sites, and reviews in general, are.)
Yafa wishes to get a head start on her general education, so she wants to take at least one of either Literature (Lit) or Art (Art). Similarly, she wishes to take at least one of Economics (Econ) or History (Hist).
Let’s call Yafa from Activity 9.3.2 student \(1\text{.}\) In a gross oversimplification suppose there were in total 5 students including Yafa registering, and that each class could sit at most 2 students.
Each student assigns their own score to each course, \(c_{ij}\) being the score that student \(i\) gives to course \(j\text{.}\) Let \(x_{ij}\) be 1 if student \(i\) enrolls in course \(j\) and 0 otherwise.
Depending on how you set up the objective function, a student who rates everything highly will be prioritized over a student who ranks everything more modestly. To prevent gaming the system, what could be done to ameliorate this effect?
The Dean approves one of the classes to be increased in size to a whopping 3 students. How can the dual problem inform how this choice of class should be made?
For the truly ambitious, model a scheduling problem for the offering of courses, factoring in preferred times, preferred courses, preferred classrooms, changes in staffing, fluctuating student demand and flow of courses in the future etc. 1
This is as open a problem as there can be. Someone who solves this problem will gain more recognition than if they solved all the Millennium Problems.
