Planning a teacher staff competence structure robust to unexpected personnel absence

Abstract

Teachers’ absences are a common disruption to the provision of academic courses. They make it necessary to modify teacher assignment, which amounts to finding suitable substitutions. Sometimes it happens that the competences of the available teachers, with given constraints, e.g. teaching hour limits, are not sufficient to find an admissible assignment modification. Therefore, it is desirable to develop a so-called robust teaching staff competence structure. In the case of teachers’ absences, a robust competence structure is a structure that allows one to find a modification of the assignment under every possible scenario of disruption. In other words, the following question is considered: does there exist, and if so, what is the competence structure robust to the disruption caused by an unexpected personnel absence? The number of potential solution variants is related to the number of competences that can be improved. For each variant, there could exist many cases of teacher absence (absence of one teacher, two teachers, etc.). Moreover, for these, there could also exist many assignment modification variants. This an NP-hard problem. In the context of the scale of problems encountered in practice, searching for solutions using well-known algorithms (based on an exhaustive search) is a time-consuming process which does not guarantee that an admissible solution will be found. In the present study, a sufficient condition is proposed, the fulfilment of which guarantees the existence of a non-empty set of admissible solutions. Declarative modelling and computer implementation in the form of constraint logic programming (CLP) have been applied. The potential of the proposed solution is illustrated with examples.