Application of a real-world university-course timetabling model solved by integer programming

Schimmelpfeng, Katja; Helber, Stefan

doi:10.1007/s00291-006-0074-z

Cited by 61 publications

(30 citation statements)

References 14 publications

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“…However, thanks to strong advances in computer software and hardware, and in IP formulations, mathematical programming approaches for timetabling problems have become more popular ( [1], [23]). Examples of IP formulations for UCTPs can be found in [24], [1], [25] and [26]. One advantage of mathematical programming approaches is the ease of incorporating additional soft constraints ( [2]).…”

Section: Solution Techniquesmentioning

confidence: 99%

“…Dimopoulo and Miliotis [24] report on the implementation of a computer system for the joint development of a course and examination timetable at The Athens University of Economics and Business. Schimmelpfeng and Helber [26] describe the implementation of an integer programming approach to create a complete timetable of all courses for a term at the School of Economics and Management at Hannover University. Badri [28] develops a twostage optimization model to solve a faculty-course-time timetabling problem at United Arab Emirates University.…”

Section: Solution Techniquesmentioning

confidence: 99%

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Developing compact course timetables with optimized student flows

Vermuyten

Lemmens

Marqués

et al. 2016

European Journal of Operational Research

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In university buildings with many rooms spread over different floors, large student flows between two consecutive lectures might cause congestion problems. These congestions result in long queues at elevators or at stairwells, which might lead to delays in lecture starts. The course timetable clearly has an important impact on these congestions. This paper presents a two-stage integer programming approach for building a university course timetable that aims at minimizing the resulting student flows. The first stage minimizes the violation of the teacher and educational preferences by assigning lectures to timeslots and rooms. The second stage reassigns classrooms to lectures of the timetable of the first stage and minimizes the student flow. The conceptual model is applied to the dataset of the Faculty of Economics and Business of the KU Leuven Campus Brussels and is tested and validated with 21 adapted instances from the literature. In contrast to a monolithic model, the two-stage model consistently succeeds in finding good quality feasible solutions. Moreover, the generated timetables entail significantly reduced student flows compared to the flows of the manually developed course timetable.

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Section: Solution Techniquesmentioning

confidence: 99%

Section: Solution Techniquesmentioning

confidence: 99%

Developing compact course timetables with optimized student flows

Vermuyten

Lemmens

Marqués

et al. 2016

European Journal of Operational Research

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Estudo de caso de programação inteira para automação de grade de horários do departamento de estatística da Universidade Federal de Pernambuco

Borges

Leite

Ospina

et al. 2015

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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A otimização de grade de horáriosé um problema de grande interesse e muitos algoritmos foram desenvolvidos nosúltimos anos [1,2,3,4], principalmente para o caso particular de cursos de graduação. Neste trabalho, descreve-se uma aplicação de otimização combinatória para a automação da grade de horários dos professores do departamento de estatística da Universidade Federal de Pernambuco. Considera-se o problema, semestral, de alocação de professoresà disciplinas de acordo com suas preferências individuais e satisfazendo a uma série de restrições. As variáveis de decisão consideram os seguintes conjuntos (com respectivas dimensões): professor (40), a disciplina (50), o dia (5), o turno (3), o período (2) e a sala onde será ministrado o curso (15).O departamento oferece disciplinas de duas naturezas: internas e externas. As disciplinas internas são aquelas relacionadas ao curso de graduação e de responsabilidade do departamento, de modo que se tem flexibilidade na determinação de horários e salas. As disciplinas externas podem ser de dois tipos: as ministradas em outros cursos com horários predefinidos, sendo permitido apenas a escolha do professor; e as ministradas ao curso de graduação em estatística por outros departamentos, com horários pré-definidos e nos quais não se pode alocar outras disciplinas.A preferência dos professores por disciplinaé estabelecida por meio de uma relação de preferência (ordinal) dos professores a partir de um questionário me que cada professor selecionará um subconjunto próprio das possíveis disciplinas, de cardinalidade predefinida e bem menor que o número total de disciplinas, e estabelecerá uma ordem neste subconjunto.A variável de decisão, x[i, j, k, l, m, n], binária, assumirá valor 1 se o professor i for alocado para a disciplina j no dia k, no turno l, no período m e na sala n; e valor zero caso contrário. Precisaremos das seguintes estruturas:(parâmetro) Utilidade ordinal do professor i em relaçãoà disciplina j. Representa a preferência do professor para com as disciplinas. Note-se que ele precisa atribuir um valor diferente de zero apenas para um subconjunto próprio de disciplinas.y [i, j]. (variável auxiliar). Variável binária que determina se o professor i será alocado na disciplina j. * Bolsista de Iniciação Científica, PIBIC/PROPESQ/UFPE.

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“…Meta heuristics clearly constitute the main solution approach, see [2,12,14], and the references therein. Several integer programs were suggested as well [5,6,7,15,17], however, optimally solvable problem instances are (i) smaller than ours by at least an order of magnitude, or (ii) are much simpler (and thus less realistic) than ours. Interestingly, complete polyhedral descriptions of problems closely related to finding transversals are well known.…”

Section: Related Workmentioning

confidence: 99%

“…Much has been written about practical details [7], and the non-negligible human factor of timetabling [17]. Meta heuristics clearly constitute the main solution approach, see [2,12,14], and the references therein.…”

Section: Related Workmentioning

confidence: 99%

Optimal University Course Timetables and the Partial Transversal Polytope

Lach

Lübbecke

Experimental Algorithms

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University course timetabling is the conflict-free assignment of courses to weekly time slots and rooms subject to various hard and soft constraints. One goal is to meet as closely as possible professors' preferences. Building on an intuitive integer program (IP), we develop an exact decomposition approach which schedules courses first, and matches courses/times to rooms in a second stage. The subset of constraints which ensures a feasible room assignment defines the well-known partial transversal polytope. We describe it as a polymatroid, and thereby obtain a complete characterization of its facets. This enables us to add only strong valid inequalities to the first stage IP. In fact, for all practical purposes the number of facets is small. We present encouraging computational results on real-world and simulated timetabling data. The sizes of our optimally solvable instances (respecting all hard constraints) are the largest reported in the literature by far.

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Application of a real-world university-course timetabling model solved by integer programming

Cited by 61 publications

References 14 publications

Developing compact course timetables with optimized student flows

Developing compact course timetables with optimized student flows

Estudo de caso de programação inteira para automação de grade de horários do departamento de estatística da Universidade Federal de Pernambuco

Optimal University Course Timetables and the Partial Transversal Polytope

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