Allocation of Students to Laboratory Groups Taking into Account Constraints from Timetables and Student Availabilities at Niederrhein University of Applied Sciences

Organizing lab groups in a University of Applied Sciences is a challenging task that is often done by manually assigning students to groups. For sufficiently large cohorts of students, the optimal allocation is often not reached, which is achieved by minimizing the teaching effort of instructors and minimizing the occupancy of laboratories. In this contribution, an integer programming approach is employed to allocate students to lab groups across the Faculty of Mechanical Engineering, while minimizing the total number of groups needed. The algorithm particularly addresses the challenge of the availability of professors and laboratories, aligning the availability of students from four different bachelor programs with their personal preferences for certain weekdays, which they provide in advance. Additionally, the flexibility or restrictions required by part-time and dual study programs in terms of lab participation are integrated into the model. The developed algorithm uses an iterative procedure that checks all relevant constraints in each iteration using IP. If the constraints lead to an infeasible solution, the less important constraints, which are the weekday choises of students, are dropped until a feasible solution is found. The choice of an objective function ensures minimal teaching effort and lab usage, but does not take advantage of group sizes. In a second iterative process, all group sizes are equalized as long as the problem is feasible. The example computes 862 lab group assignments with a solution vector of 32,344 components, 7116 inequalities and 1208 equality constraints to model the lab group assignment.