Application of a real-world university-course timetabling model solved by integer programming

摘要

In this case study, we describe an integer programming (IP) approach, which has been implemented at the School of Economics and Management at Hannover University, Germany, to create the complete timetable of all courses for a term. Approximately 150 different weekly lectures, tutorials and seminars ranging from 5 to 650 students are taught by about 100 teachers. The decision problem is to assign these teaching groups to time slots and rooms so that several soft and hard constraints are met. It is modeled as an assignment problem with numerous types of constraints and about 100,000 binary or integer variables. An open source mixed-integer solver can be used to solve the problem to optimality within minutes whereas the commercial CPLEX solver takes only seconds. We also describe the implementation process and report results from an anonymous satisfaction survey among the faculty with respect to the new planning approach.