A column generation approach for the timetabling problem of Greek high schools

Abstract

A column generation (CG) approach for the solution of timetabling problems is presented. This methodology could be used for various instances of the timetabling problem, although in this paper the solution of the high-school situation in Greece is presented. The results obtained show clearly that the CG approach that has been extremely successful in recent years in the solution of airline crew scheduling problems could also be very efficient and robust for the solution of timetabling problems. Several large timetabling problems corresponding to real problems have been successfully solved, with the solutions obtained feasible and of very high quality in accordance with the problem definition. In addition, none of the solutions contained any idle hour for any of the teachers, which was one of the main goals of this optimization effort.

Tabu Search Techniques for Polish Higher Education Timetabling Problems

“…The process of constructing a class schedule involves using, among others: simulated annealing [1,35,39], evolutionary algorithms [9], neural network algorithms [13], tabu search heuristics [2,4,5,8,11,12,14,20,30], genetic algorithms [10,18,36], integer programming [6,11,15,16,27,31,33] and constraint programming [19,23,25,37].…”

Telafi̇ Dersi̇ Çi̇zelgeleme Problemi̇ni̇n (Tdçp) Matemati̇ksel Modelle Çözümü: Gerçek Bi̇r Uygulama

“…Ancak her eğitim kurumunun kendine özgü yapısı, kısıtları ve kuralları farklı olduğundan uygulanabilir standart bir çözüm yaklaşımı geliştirilememiştir. Literatürde ÜDÇP çözümü için; Matematiksel Modelleme [7][8][9][10][11][12][13][14], Yapay Arı Kolonisi Algoritması [15], Genetik Algoritma [16], Tavlama Benzetimi [17], Kısıt Programlama [18,19], Hibrit Metotlar [20][21][22][23][24][25][26][27][28][29] [9] yapmış oldukları çalışmada öğrenci grupları için seçmeli ders çakışmaları esnek kısıt olarak dikkate alınmışken, bizim çalışmamızda 2. 3. ve 4. sınıflar için tüm zorunlu derslerin, seçmeli derslerle çakışmasına izin verilmemiş, her bir sınıftaki seçmeli derslerin kendi aralarındaki çakışmaları minimize edilmeye çalışılmıştır.…”

Strong bounds with cut and column generation for class-teacher timetabling

“…The compactness requirements are particularly important in countries (like Brazil) where teachers may work in more than one institution. Those requirements were considered in [11,26,3,10,9,14,20,4,13,23,15,28]. In most of these works, compactness is treated as a soft constraint [16], i.e., this is actually considered in the objective function as a measure to evaluate timetables.…”