In this paper we introduce a new algorithm for secondary school timetabling, inspired by the classical bipartite graph edge colouring algorithm for basic class-teacher timetabling. We give practical methods for generating large sets of meetings that can be timetabled to run simultaneously, and for building actual timetables based on these sets. We report promising empirical results for one real...

Cycle inequalities play an important role in the polyhedral study of the periodic timetabling problem. We give the first pseudo-polynomial time separation algorithm for cycle inequalities, and we give a rigorous proof for the pseudo-polynomial time separability of the change-cycle inequalities. The efficiency of these cutting planes is demonstrated on real-world instances of the periodic timeta...

In this paper we describe a successful case-study where a Branch-and-Cut algorithm yields the “optimal” solution of a real-world timetabling problem for university courses (University Course Timetabling problem). The polyhedral structure of the problem is studied in conection with a polytope of the Set Packing problem. Several families of cutting planes are introduced, these being crutial to fi...

Planning, scheduling, and timetabling problems are typically solved using different techniques despite the fact that all these areas seem very similar and they are definitely connected. In this paper we propose a generic model covering scheduling and timetabling problems as well as some problems from planning under time and resource constraints. Our model is motivated by reallife problems and o...

Local Search is an emerging paradigm for combinatorial search, which has been recently shown to be very effective for a large number of combinatorial problems. Educational timetabling problems consist in scheduling a sequence of lectures or examinations between teachers and students in a prefixed period of time (typically a week), satisfying a set of constraints of various types. Problems in th...

This paper introduces a new timetabling problem on universities, called interview timetabling. In this problem, some constant number, say three, of referees are assigned to each of 2n graduate students. Our task is to construct a presentation timetable of these 2n students using n timeslots and two rooms, so that two students evaluated by the same referee must be assigned to different timeslots...

The university course timetabling problem is a combinatorial optimisation problem in which a set of events has to be scheduled in time slots and located in suitable rooms. The design of course timetables for academic institutions is a very difficult task because it is an NP-hard problem. This paper proposes a genetic algorithm with a guided search strategy and a local search technique for the u...

For many problems in Scheduling and Timetabling the choice of a mathematical programming formulation is determined by the formulation of the graph colouring component. This paper briefly surveys seven known integer programming formulations of vertex colouring and introduces a new formulation using “supernodes”. In the definition of George and McIntyre [SIAM J. Numer. Anal. 15 (1978), no. 1, 90–...

The examination timetabling problem represents a major administrative activity for academic institutions. An increasing number of student enrolments, a wider variety of courses and increasing number of combined degree courses contribute to the growing challenge of developing examination timetabling software to cater for the broad spectrum of constraints required by educational institutions. In ...

Timetabling problems have been frequently studied due to their wide range of applications. However, they are often solved manually because of the lack of appropriate computer tools. Although many approaches mainly based on local search or constraint programming seem to have been quite successful in recent years, they are often highly dedicated to specific problems and encounter difficulties to ...