## 1 Introduction  
Allocation problems arise in a range of fields, for example, healthcare, transportation, sports or education, which is a domain whose recognition begins to play an increasingly significant role [1; 2; 3]. Everyday practice shows that the organisation and planning of teaching that takes place every year in higher education institutions are associated with the problems of assigning teachers to courses and scheduling/timetabling the courses themselves. Within the education domain, the focal point of Assignment Problems (ASP) is determining the match (or the lack thereof) between the teacher competence (specified by competency sets) and the main subject areas (subsets of curriculum courses) that they are assigned to teach; as such, they are categorised as one of two sub-problems: Allocation (AAP) or Timetabling Problem (TTP) [4; 5; 6]. The sub-problems in question can be considered as different types of an assignment problem concerned with the assignment of available resources to various uses. Indeed, AAP can be considered as a type of ASP whose objective is to assign teacher competencies to competencies imposed by curriculum courses. In turn, TTP can be seen as a type of ASP aimed to assign allocations obtained from AAP to a limited number of timeslots and rooms subject to prescribed constraints. To assess a team of teachers' aptitude to meet the expectations of the curriculum, it is necessary to consider a stock of course requirements and the competencies of the teaching staff members. Teacher competencies are represented collectively as a personnel competency framework [7], which defines current qualifications of staff. It should be noted that course assignment planning decisions (which require specific employee competencies) to resources (teachers with given competencies) take place in dynamically changing organisational settings [8] that involve frequent changes in the scope and structure of objectives, tasks and resources. The examples of such changes include employee absenteeism, loss of qualifications, staff fluctuations and the like. Most of them are random and cannot be anticipated in advance. Such events are henceforth referred to as disruptions [9]. The most frequent reaction to disruption, e.g., caused by employee absenteeism, is to modify the current plan (in this case, the teacher allocation) so as to enable further continuation of the plan [10]. Whether or not the necessary changes can be introduced depends on the competencies of available employees, which may prove insufficient, thus preventing changes in the teacher allocation that would otherwise enable resuming the processing of conducted classes. In this context, providing for different variants of ASP sub-problems, influenced or not by various disruptions, shall follow the taxonomy of teacher assignment problems given in Figure 1: the Allocation Problem Assuming the Absence of Disruptions (AAPDA), the Timetabling Problem Assuming the Absence of Disruptions (TTPDA), the Allocation Problem Assuming the Presence of Disruptions (AAPDO) and the Timetabling Problem Assuming the Presence of Disruptions (TTPDO). The main objective of both AAPDA and AAPDO problems is the determination of the match (or its lack) between teacher competencies and the main assigned subject areas. The devised competency framework encompassing relationships linking competencies possessed by particular teachers with competencies required by student curriculum is a useful solution for assessing the suitability of teachers with respect to emerging curriculum needs. The considered sub-problems seek the balance between student needs and teacher capabilities, however, in the case of AAPDO, it is additionally required that an assumed robustness level of the resulting teacher allocation is achieved. In turn, the main objective of TTPDA and TTPDO problems is the determination of the match (or the lack thereof) between allocations linking teachers to curriculum courses and possible space-time assignment constraints, decisive to the occurrence of obstructions.