Timetabling in constraint logic programming

In this paper we describe the timetabling problem and its solvability in a Constraint Logic Programming Language. A solution to the problem has been developed and implemented in ECLiPSe, since it deals with finite domains, it has well-defined interfaces between basic building blocks and supports good debugging facilities. The implemented timetable was based on the existing, currently used, timetables at the School of Informatics at out university. It integrates constraints concerning room and period availability

Cyclic transfers in school timetabling

In this paper we propose a neighbourhood structure based\ud on sequential/cyclic moves and a Cyclic Transfer algorithm for the high school timetabling problem. This method enables execution of complex moves for improving an existing solution, while dealing with the challenge of exploring the neighbourhood efficiently. An improvement graph is used in which certain negative cycles correspond to the neighbours; these cycles are explored using a recursive method. We address the problem of applying large neighbourhood structure methods on problems where the cost function is not exactly the sum of independent cost functions, as it is in the set partitioning problem. For computational experiments we use four real world datasets for high school timetabling in the Netherlands and England. We present results of the cyclic transfer algorithm with different settings on these datasets. The costs decrease by 8% to 28% if we use the cyclic transfers for local optimization compared to our initial solutions. The quality of the best initial solutions are comparable to the solutions found in practice by timetablers

Cyclic transfers in school timetabling

In this paper we propose a neighbourhood structure based on sequential/cyclic moves and a cyclic transfer algorithm for the high school timetabling problem. This method enables execution of complex moves for improving an existing solution, while dealing with the challenge of exploring the neighbourhood efficiently. An improvement graph is used in which certain negative cycles correspond to the neighbours; these cycles are explored using a recursive method. We address the problem of applying large neighbourhood structure methods on problems where the cost function is not exactly the sum of independent cost functions, as it is in the set partitioning problem. For computational experiments we use four real world data sets for high school timetabling in the Netherlands and England.We present results of the cyclic transfer algorithm with different settings on these data sets. The costs decrease by 8–28% if we use the cyclic transfers for local optimization compared to our initial solutions. The quality of the best initial solutions are comparable to the solutions found in practice by timetablers

The Maraca: a tool for minimizing resource conflicts in a non-periodic railway timetable

While mathematical optimization and operations research receive growing attention in the railway sector, computerized timetabling tools that actually make significant use of optimization remain relatively rare. SICS has developed a prototype tool for non-periodic timetabling that minimizes resource conflicts, enabling the user to focus on the strategic decisions. The prototype is called the Maraca and has been used and evaluated during the railway timetabling construction phase at the Swedish Transport Administration between April and September 2010

Aspects of computerised timetabling

This research considers the problem of constructing high school timetables using a computer. In the majority of high schools, termly or yearly timetables are still being produced manually. Constructing a timetable is a hard and time consuming task which is carried out repeatedly thus a computer program for assisting with this problem would be of great value. This study is in three parts. First. an overall analysis of the problem is undertaken to provide background knowledge and to identify basic principles in the construction of a school timetable. The characteristics of timetabling problems are identified and the necessary data for the construction of a timetable is identified. The first part ends with the production of a heuristic model for generating an initial solution that satisfies all the hard constraints embodied in the curriculum requirements. The second stage of the research is devoted to designing a heuristic model for solving a timetable problem with hard and medium constraints. These include constraints like the various numbers of common periods, double periods and reducing the repeated allocation of a subject within any day. The approaches taken are based on two recently developed techniques, namely tabu search and simulated annealing. Both of these are used and comparisons of their efficiency are provided. The comparison is based on the percentage fulfilment of the hard and medium requirements. The third part is devoted to one of the most difficult areas in timetable construction, that is the softer requirements which are specific to particular schools and whose satisfaction is not seen as essential. This section describes the development of an expert system based on heuristic production rules to satisfy a range of soft requirements. The soft requirements are studied and recorded as rules and a heuristic solution is produced for each of the general requirements. Different levels of rule are developed, from which the best possible solution to a particular timetable problem is expertly produced. Finally, possible extensions of the proposed method and its application to other types of the timetabling problem are discussed

Operational Research in Education

Operational Research (OR) techniques have been applied, from the early stages of the discipline, to a wide variety of issues in education. At the government level, these include questions of what resources should be allocated to education as a whole and how these should be divided amongst the individual sectors of education and the institutions within the sectors. Another pertinent issue concerns the efficient operation of institutions, how to measure it, and whether resource allocation can be used to incentivise efficiency savings. Local governments, as well as being concerned with issues of resource allocation, may also need to make decisions regarding, for example, the creation and location of new institutions or closure of existing ones, as well as the day-to-day logistics of getting pupils to schools. Issues of concern for managers within schools and colleges include allocating the budgets, scheduling lessons and the assignment of students to courses. This survey provides an overview of the diverse problems faced by government, managers and consumers of education, and the OR techniques which have typically been applied in an effort to improve operations and provide solutions

The development of a general algorithmic procedure for university examination timetabling

The problem of scheduling university examinations is becoming difficult for examination officers especially when they have to construct the timetables manually. It is largely due to the increasing number of students and greater freedom in choosing the courses. Examination officers would have to spend a considerable amount of time checking for student conflicts so that no student would have to sit for more than one exam at any one time. There are also other limitations such as the number of examination rooms, the length of the examination period and others. The examination timetabling problem varies between institutions, depending on their particular needs and limited resources. Most of the existing computerised examination timetabling systems found in the literature are developed and used by particular institutions. Therefore, the aim of the research is to produce a general computerised system for timetabling examinations which can be used by most universities. The research is done in two stages; the first stage involves carrying out a survey on the university examination timetabling systems and the second stage is the construction of a university examination timetabler incorporating the common objectives and constraints found in the survey. The survey was carried out to determine the extent to which the computerised examination timetabling procedures are used, to identify the objectives and constraints which are commonly considered when constructing examination timetables and to evaluate the effectiveness of the existing examination timetabling systems in achieving the objectives and satisfying the constraints The construction of the general examination timetabling system is done in two parts. In the first part, a new algorithmic rule is developed to assign exams to the minimum number of sessions without creating conflicts for any student. The rule adopts a clique initialisation strategy as a starting point and a graph colouring approach for assigning the exams. This rule is also quite capable of scheduling exams to the sessions which are as close as to the least number of sessions possible, without having to carry out any backtracking process. The backtracking process can sometimes be time consuming if there are a lot of exams firstly to be scheduled, and secondly clashing with each other. The second part of the work involves minimising the total number of students taking two exams on the same day and scheduling large exams early in the examination period subject to a specified time limit on the overall examination period and a maximum number of students that may be examined in any session. A swapping rule was introduced where exams in one of the sessions in any day with large number of sameday exams are interchanged with exams in other sessions which will reduce the total number of same-day exams. The experimentation showed that if the swapping procedures are repeated three times, the total number of same-day exams will be reduced by 50%. The total number of same-day exams will be reduced even more if some extra sessions can be added to the initial minimum number of sessions. A simple rule was devised to schedule large exams early in the examination period