todo: write a proper readme file
Given a number of courses each organized once or multiple times in a number of sessions. For each session a course has a specific capacity depending on its location. Also given is a group of people that have listed which courses they are interested in and hence would like to go to a session of that specific course.
Hence we need to assign people to specific courses in specific sessions in some optimal fashion. Ideally everyone could follow the courses that he would like to follow having a perfect match of demand and supply. Practical considerations however necessarily entail that there will be some mismatch between demand and supply. Meaning that some people won't be able to be assigned to a specific course because their is not enough capacity. E.g. only a limited number of people can enter a lecture room at once. While other session might have room to spare.
To try and solve this problem, people are also requested to list some secondary choices of courses they would like to follow in case they can't be assigned to their preferred courses.
Several consideration might play a role in defining a good or optimal distribution:
- people would like to be assigned their first choice instead of their second choice. So any distribution where less people are assigned their second choice is preferred over any other.
- people that list their preferences early should have a lower chance of being assigned a second choice then people that list their preferences later on.
- the number of people attending a course should be relatively similar over all sessions. No sense in having a full class room in session 1 and only one person attending in session 2.
- Obviously a person can't be assigned to more then one course in the same session because one can only be in one place at a time.
Such a problem is known in optimisation as an assignment problem and can be modelled using Mixed Integer Programming (MIP) for which dedicated solvers are available.
In this project we will make us of the Gnu MathProg modeling language to model the problem which is part of the Gnu Linear Programming Kit or GLPK for short. The GLPK also includes a solver which can be used to actually solve the problem. Other solvers that support the Gnu Mathprog modeling language could of course also be used to read and solve the model files developed in this project.
- description of the models
- structure of data files
- organization of the project
- example data file?
- test cases?
???
See the test directory. Each test should have a Readme file explaining the case.