Generation of Teacher Timesheets via Mixed Integer Programming: A 17-Year Longitudinal Experience

The generation of teachers' timesheets in educational institutions is a challenging problem both from a computational and organizational perspective. In general, it is impossible to simultaneously meet all the operational constraints and individual preferences of faculty, many of them of a personal nature, although their attendance may contribute to a more appropriate and collaborative work environment. This scenario becomes even more complex in institutions that offer courses at different levels, modalities, and forms of offer, such as integrated high school, subsequent technical courses, higher technology courses, and graduate studies. When these courses belong to the same technological axis, the sharing of physical and human resources, especially teachers, naturally occurs, so that changes in the availability or preferences of a subset of resources can trigger a ripple effect in the overall configuration of the timetable. Considering the case of the Industrial Technical College of Santa Maria (CTISM), linked to the Federal University of Santa Maria, the problem involves the allocation of 90 teachers and 38 laboratories to serve 44 classes distributed among integrated high school, post-secondary, undergraduate and graduate courses, offered in the morning, afternoon and night shifts. The methodology adopted combines a computer interface implemented in Java for collecting, visualizing and eventual manual adjustment of information with a mathematical model based on mixed integer programming, solved through IBM ILOG CPLEX