Elective course planning

Efficient planning increasingly becomes an indispensable tool for management of both companies and public organizations. This is also the case for high school management in Denmark, because the growing individual freedom of the students to choose courses makes planning much more complex. Due to reforms, elective courses are today an important part of the curriculum, and elective courses are a good way to make high school education more attractive for the students. In this article, the problem of planning the elective courses is modeled using integer programming and three different solution approaches are suggested, including a Branch-and-Price framework using partial Dantzig–Wolfe decomposition. Explicit Constraint Branching is used to enhance the solution process, both on the original IP model and in the Branch-and-Price algorithm. To the best of our knowledge, no exact algorithm for the Elective Course Planning Problem has been described in the literature before. The proposed algorithms are tested on data sets from 98 of the 150 high schools in Denmark. The tests show that for the majority of the problems, the optimal solution can be obtained within the one hour time bound. Furthermore the suggested algorithms achieve better results than the currently applied meta-heuristic.

► Important high school real-life problem is modeled using Integer Programming. ► Dantzig-Wolfe decomposition is applied and a Branch-and-Price algorithm is implemented. ► Explicit Constraint Branching is used to enhance the solution process. ► The developed algorithms are tested on real-world datasets.