A metaheuristic for a teaching assistant assignment-routing problem

The Flemish Ministry of Education promotes the integrated education of disabled children by providing educational opportunities in common schools. In the current system, disabled children receive ambulant help from a teaching assistant (TA) employed at an institute for extra-ordinary education. The compensation that the TAs receive for driving to visit the students is a major cost factor for the institute that provides the assistance, therefore its management desires a schedule that minimizes the accumulated distance traveled by all TAs combined. We call this optimization problem the teaching assistants assignment routing problem (TAARP). It involves three decisions that have to be taken simultaneously: (1) pupils have to be assigned to TAs; (2) pupils assigned to a given TA have to be spread over the TA's different working days; and (3) the order in which to visit the pupils on each day has to be determined. We propose a solution strategy based on an auction algorithm and a variable neighborhood search which exhibit an excellent performance both in simulated and real instances. The total distance traveled in the solution obtained for the real data set improves the current solution by about 22% which represents a saving of around 9% on the annual budget of the institute.