Gerçek bir sınav çizelgeleme problemi için iki aşamalı çözüm yaklaşımı

Üniversitelerde, ilgili fakültelerde veya bölümlerde sınav çizelgelerinin hazırlanması oldukça uzun süreler alabilmekte, oluşturulan sınav çizelgeleri çoğu zaman ne öğrencileri, ne öğretim üyelerini ne de yöneticileri memnun etmektedir. Bu çalışmada bir üniversitenin bir bölümüne ait yılsonu sınavı çizelgesi oluşturma problemi ele alınmıştır. Tanımlanan problem için, ilk aşamada sınavlar bir tam sayılı programlama modeli ile zorluk derecelerine göre gruplandırılmıştır. İkinci aşamada ise öğrencilerin çalışma ve odaklanabilme verimlerini en üst düzeye çıkaracak sınav çizelgesini elde etmek üzere bir tam sayılı programlama modeli geliştirilmiştir. Modelin amacı, aynı günde birden fazla sınava girme durumu olan öğrenci sayısını, ilgili sınavların zorluk dereceleri toplamı ile ağırlıklandırarak en küçüklemektir. Gerçek verilerden yola çıkarak bir öğretim dönemi için veri kümesi oluşturulmuştur. Oluşturulan veri kümesi üzerinden önerilen çözüm yaklaşımı uygulanarak çözümler alınmış ve elle yapılan çizelgeyle karşılaştırılarak, önerilen yaklaşımla oluşturulan çizelgenin üstünlükleri tartışılmıştır.

Anahtar Kelimeler:

Sınav çizelgeleme, Tam sayılı programlama, Öğrenci/Öğretim üyesi memnuniyeti, Zorluk derecesi

A two-phase solution approach for a real-life examination timetabling problem

In the faculties or departments of universities, preparing the examination timetables takes quite a long time, and often could not satisfy neither the students nor the instructors or managers. In this study, the final exam timetabling problem of a department of a university is considered. For the problem, in the first stage, the exams are classified into the groups according to their difficulty levels by an integer programming model. In the second stage, an integer programming model is proposed in order to find an exam timetable which will increase the concentration and study efficiency of the students. In the model, the number of students taking more than one exam on the same day is minimized by weighting the difficulty levels of the relevant exams. The proposed solution approach is applied by using a real data set of a semester. By comparing the exam timetable obtained with the schedule prepared by hand, the advantages of the proposed solution approach are presented.

Keywords:

Examination timetabling, Integer programming, Student /Instructor satisfaction, Difficulty level,

PDF

___

Turabieh H, Abdullah S. “An integrated hybrid approach to the examination timetabling problem”. Omega, 39(6), 598-607, 2011.
Carter MW. “Or Practice-a survey of practical applications of examination timetabling algorithms”. Operations Research, 34(2), 193-202, 1986.
Burke E, Elliman D, Ford P, Weare R. Examination Timetabling in British Universities: A Survey. Editors: Burke E, Ross, P. Practice and Theory of Automated Timetabling, LNCS, 1153, 76-90, Berlin, Heidelberg, Springer, 1996.
Cowling P, Kendall G, Hussin NM. “A Survey and Case Study of Practical Examination Timetabling Problems”. 4th international Conference on the Practice and Theory of Automated Timetabling (PATAT 2002), Gent, Belgium, 21-23 August 2002.
Burke E, Jackson K, Kingston JH, Weare R. “Automated university timetabling: the state of the art”. The Computer Journal, 40(9), 565-571, 1997.
Qu R, Burke EK, McCollum B, Merlot LT, Lee SY. “A survey of search methodologies and automated system development for examination timetabling”. Journal of Scheduling, 12(1), 55-89, 2009.
Broder S. “Final examination scheduling”. Communications of the ACM, 7(8), 494-498, 1964.
Lotfi V, Cerveny R. “A final-exam-scheduling package”. Journal of the Operational Research Society, 42(3), 205-216, 1991.
Bullnheimer B. An Examination Scheduling Model to Maximize Students’ Study Time. Editors: Burke E, Carter M. Practice and Theory of Automated Timetabling II, LNCS, Vol. 1408, 78-91, Berlin, Heidelberg, Springer, 1998.
Wong T, Côté P, Gely P. “Final Exam Timetabling: A Practical Approach”. IEEE Canadian Conference on Electrical and Computer Engineering, (CCECE 2002), Manitoba, Canada, 12-15 May 2002.
Mushi AR. “Mathematical programming formulations for the examinations timetable problem: the case of the University Of Dar Es Salaam”. AJST, 5(2), 34-40, 2004.
MirHassani SA. “Improving paper spread in examination timetables using integer programming”. Applied Mathematics and Computation, 179(2), 702-706, 2006.
McCollum B, McMullan P, Parkes AJ, Burke EK, Qu R. “A new model for automated examination timetabling”. Annals of Operations Research, 194(1), 291-315, 2012.
Wang S, Bussieck M, Guignard M, Meeraus A, O’Brien F. “Term-end exam scheduling at United States Military Academy/West Point”. Journal of Scheduling, 13(4), 375-391, 2010.
Al-Yakoob SM, Sherali HD. “A mixed-integer programming approach to a class timetabling problem: a case study with gender policies and traffic considerations”. European Journal of Operational Research, 180(3), 1028-1044, 2007.
Kahar MNM, Kendall G. “The examination timetabling problem at Universiti Malaysia Pahang: comparison of a constructive heuristic with an existing software solution”. European Journal of Operational Research, 207(2), 557-565, 2010.
Ayob M, Hamdan AR, Abdullah S, Othman Z., Nazri MZA, Razak KA, ... Sabar NR. “Intelligent examination timetabling software”. Procedia-Social and Behavioral Sciences, 18, 600-608, 2011.
Komijan AR, Koupaei MN. “A new binary model for university examination timetabling: a case study”. Journal of Industrial Engineering International, 8(1), 1-7, 2012.
Ahmad F, Mohammad Z, Hassan H, Rose ANM, Muktar D. “Quadratic assignment approach for optimization of examination scheduling”. Applied Mathematical Sciences, 9(130), 6449-6460, 2015.
Koksalmış E, Gracia C, Rabadi G. “The optimal exam experience: a timetabling approach to prevent student cheating and fatigue”. International Journal of Operational Research, 21(3), 263-278, 2014.
Arbaoui T, Boufflet JP, Moukrim A. “A matheuristic for exam timetabling”. IFAC-PapersOnLine, 49(12), 1289-1294, 2016.
Cataldo A, Ferrer JC, Miranda J, Rey PA, Sauré A. “An integer programming approach to curriculum-based examination timetabling”. Annals of Operations Research, 258(2), 369-393, 2016.
Woumans G, De Boeck L, Beliën J, Creemers S. “A column generation approach for solving the examination-timetabling problem”. European Journal of Operational Research, 253(1), 178-194, 2016.
Cavdur F, Kose M. “A fuzzy logic and binary-goal programming-based approach for solving the exam timetabling problem to create a balanced-exam schedule”. International Journal of Fuzzy Systems, 18(1), 119-129, 2016.
Ergul Z, Kamisli Ozturk, Z. “A new mathematical model for multisession exams-building assignment”. Acta Physica Polonica A, 132(3), 1207-1210, 2017.
Sağlam B, Salman FS, Sayın S, Türkay M. “A mixed-integer programming approach to the clustering problem with an application in customer segmentation”. European Journal of Operational Research, 16, 173(3), 866-879, 2006.
ILOG, IBM. IBM ILOG CPLEX Optimization Studio, V12.6.2., 2013.