Abstract
Exam scheduling problems are one of the major problems faced by universities. Despite the increase in the number of students in recent years, the existing classroom resources remain the same. Because of that, there are various problems in the examination programs. In the present case, the exam schedules are prepared manually based on the experience of the programmer without using any scientific method. As a result, there may occur many problems such as entering several exams or more than one hard exam on the same day. In order to overcome such problems, a mixed integer mathematical model for exam scheduling is proposed in this study. The proposed model is applied to Erciyes University, Department of Industrial Engineering and the final program of the 2016-2017 fall semester is established by using the CPLEX 12.6.1 optimization package program. The obtained exam schedule is compared with the schedule prepared by the research assistants. The final program obtained by the proposed method used fewer classrooms than the current final program, so the number of supervisors is reduced. On the other hand, the number of empty desks in the classrooms is minimized, hard exams are not scheduled on the same day and the time laps between exams are created in order to increase the performance of students.
Keywords
References
- PINEDO, Michael L.; (2008), Scheduling: Theory, Algorithms, and Systems, 3rd Edition, Prentice Hall. BABAEI, Hamed; KARIMPOUR, Jaber and HADİDİ, Amin; (2015), “A Survey of Approaches for University Course Timetabling Problem”, Computers & Industrial Engineering, 86, pp. 43-59. DIMOPOULOU, M. and MILIOTIS, P.; (2001), “Implementation of a University Course and Examination Timetabling System”, European Journal of Operational Research, 130, pp. 202-212. AL-YAKOOB, Salem M. and SHERALI, Hanif D.; (2015), “Mathematical Models and Algorithms for a High School Timetabling Problem”, Computers & Operations Research, 61, pp. 56-68. DORNELES, Arton P.; ARAUJO, Olinto C.B. and BURIOL, Luciana S.; (2017), “A Column Generation Approach to High School Timetabling Modeled as a Multicommodiy Flow Problem”, European Journal of Operational Research, 256, pp. 685-695. DAMMAK, Abdelaziz; ELLOUMI, Abdelkarim and KAMOUN, Hichem; (2006), “Classroom Assignment for Exam Timetabling”, Advances in Engineering Software, 37, pp. 659-666. UÇAR, Ukbe Üsame ve İŞLEYEN, Selçuk Kürşat; (2016), “Telafi Dersi Çizelgeleme Probleminin (TDÇP) Matematiksel Modelle Çözümü: Gerçek bir Uygulama”, Gazi Üniv. Müh. Mim. Fak. Der., 31(2), pp. 331-346. DEMİR, Yunus ve ÇELİK, Cafer; (2016), “Müfredat Bazlı Akademik Zaman Çizelgeleme Probleminin Çözümüne Tamsayılı Doğrusal Programlama Yaklaşımı”, Gazi Üniv. Müh. Mim. Fak. Der., 31(1), pp. 145-159. KAHAR, Mohd Nizam Mohmad and KENDALL, Graham; (2009), “The Examination Timetabling Problem at Universiti Malaysia Pahang: Comparison of a Constructive Heuristic with an Existing Software Solution”, European Journal of Operational Research, 207, pp. 557-565. QU, Rong; BURKE, Edmund K. and MCCOLLUM, Barry; (2010), “Adaptive Autoated Construction of Hybrid Heuristics for Exam Timetabling and Graph Colouring Problems”, European Journal of Operational Research, 198, pp. 392-404. SANTIAGO-MOZOS, Ricardo; SALCEDO-SANZ, Sancho; DEPRADO-CUMPLIDO, Mario and BOUSONO-CALZON, Carlos; (2005), “A Two-phase Heuristic Evolutionary Algorithm for Personalizing Course Timetables: A Case Study in a Spanish University”, Computers & Operations Research, 32, pp. 1761-1776. BURKE, Edmund K.; ECKERSLEY, A.J.; MCCOLLUM, Barry; PETROVIC, S. and QU, Rong; (2010), “Hybrid Variable Neighbourhood Approaches to University Exam Timetabling”, European Journal of Operational Research, 206, pp. 46-53. LI, Jingpeng; BAI, Ruibin; SHEN, Yindong and QU, Rong; (2015), “Search with Evolutionary Ruin and Stochastic Rebuild: A Theoretic Framework and a Case Study on Exam Timetabling”, European Journal of Operational Research, 242, pp. 798-806. ELLOUMI, Abdelkarim; KAMOUN, Hichem; JARBOUI, Bassem and DAMMAK, Abdelaziz; (2014), “The Classroom Assignment Problem: Complexity, Size Reduction and Heuristics”, Applied Soft Computing, 14, pp. 677-686. ARBAOUI, Taha; BOUFFLET, Jean-Paul and MOUKRIM, Aziz; (2016), “A Matheuristic for Exam Timetabling”, IFAC-PapersOnLine, 49(12), pp. 1289-1294.
Abstract
Sınav çizelgeleme problemleri üniversitelerin karşılaştığı önemli problemlerden biridir. Son yıllarda bölümlerdeki öğrenci sayılarındaki artışa rağmen mevcut derslik kaynaklarının aynı kalması sebebiyle oluşturulan sınav programlarında çeşitli sıkıntılar ortaya çıkmaktadır. Mevcut durumda sınav çizelgeleri herhangi bir bilimsel yöntem kullanmadan programı yapan kişinin tecrübelerine dayanarak manuel olarak hazırlanmaktadır. Bunun sonucunda da öğrencilerin aynı günde çok sayıda sınava girmesi, aynı sınıfa ait zor olarak nitelenebilecek derslerin sınavının aynı güne atanması gibi problemler ortaya çıkabilmektedir. Bu tarz sorunların üstesinden gelmek amacıyla, bu çalışmada sınav çizelgeleme problemine yönelik karma tamsayılı bir matematiksel model geliştirilmiştir. Önerilen model Erciyes Üniversitesi Endüstri Mühendisliği Bölümü’ne uygulanarak, 2016-2017 güz yarıyılı final programı CPLEX 12.6.1 optimizasyon paket programı kullanılarak çözülmüştür. Model sonucu elde edilen final programı, bölüm araştırma görevlilerince hazırlanan program ile karşılaştırılmıştır. Önerilen yöntem ile elde edilen final programı mevcut final programına göre daha az sayıda derslik kullanmış dolayısıyla gözetmen sayısı azaltılmış, sınavın yapıldığı dersliklerdeki boş yer sayısı minimize edilmiş, öğrencilerin performanslarını düşürmemek adına zor olarak belirtilen dersler aynı güne çizelgelenmemiş ve öğrencilerin sınavlar arası dinlenmelerine olanak sağlayan zaman boşlukları oluşturulmuştur.
References
- PINEDO, Michael L.; (2008), Scheduling: Theory, Algorithms, and Systems, 3rd Edition, Prentice Hall. BABAEI, Hamed; KARIMPOUR, Jaber and HADİDİ, Amin; (2015), “A Survey of Approaches for University Course Timetabling Problem”, Computers & Industrial Engineering, 86, pp. 43-59. DIMOPOULOU, M. and MILIOTIS, P.; (2001), “Implementation of a University Course and Examination Timetabling System”, European Journal of Operational Research, 130, pp. 202-212. AL-YAKOOB, Salem M. and SHERALI, Hanif D.; (2015), “Mathematical Models and Algorithms for a High School Timetabling Problem”, Computers & Operations Research, 61, pp. 56-68. DORNELES, Arton P.; ARAUJO, Olinto C.B. and BURIOL, Luciana S.; (2017), “A Column Generation Approach to High School Timetabling Modeled as a Multicommodiy Flow Problem”, European Journal of Operational Research, 256, pp. 685-695. DAMMAK, Abdelaziz; ELLOUMI, Abdelkarim and KAMOUN, Hichem; (2006), “Classroom Assignment for Exam Timetabling”, Advances in Engineering Software, 37, pp. 659-666. UÇAR, Ukbe Üsame ve İŞLEYEN, Selçuk Kürşat; (2016), “Telafi Dersi Çizelgeleme Probleminin (TDÇP) Matematiksel Modelle Çözümü: Gerçek bir Uygulama”, Gazi Üniv. Müh. Mim. Fak. Der., 31(2), pp. 331-346. DEMİR, Yunus ve ÇELİK, Cafer; (2016), “Müfredat Bazlı Akademik Zaman Çizelgeleme Probleminin Çözümüne Tamsayılı Doğrusal Programlama Yaklaşımı”, Gazi Üniv. Müh. Mim. Fak. Der., 31(1), pp. 145-159. KAHAR, Mohd Nizam Mohmad and KENDALL, Graham; (2009), “The Examination Timetabling Problem at Universiti Malaysia Pahang: Comparison of a Constructive Heuristic with an Existing Software Solution”, European Journal of Operational Research, 207, pp. 557-565. QU, Rong; BURKE, Edmund K. and MCCOLLUM, Barry; (2010), “Adaptive Autoated Construction of Hybrid Heuristics for Exam Timetabling and Graph Colouring Problems”, European Journal of Operational Research, 198, pp. 392-404. SANTIAGO-MOZOS, Ricardo; SALCEDO-SANZ, Sancho; DEPRADO-CUMPLIDO, Mario and BOUSONO-CALZON, Carlos; (2005), “A Two-phase Heuristic Evolutionary Algorithm for Personalizing Course Timetables: A Case Study in a Spanish University”, Computers & Operations Research, 32, pp. 1761-1776. BURKE, Edmund K.; ECKERSLEY, A.J.; MCCOLLUM, Barry; PETROVIC, S. and QU, Rong; (2010), “Hybrid Variable Neighbourhood Approaches to University Exam Timetabling”, European Journal of Operational Research, 206, pp. 46-53. LI, Jingpeng; BAI, Ruibin; SHEN, Yindong and QU, Rong; (2015), “Search with Evolutionary Ruin and Stochastic Rebuild: A Theoretic Framework and a Case Study on Exam Timetabling”, European Journal of Operational Research, 242, pp. 798-806. ELLOUMI, Abdelkarim; KAMOUN, Hichem; JARBOUI, Bassem and DAMMAK, Abdelaziz; (2014), “The Classroom Assignment Problem: Complexity, Size Reduction and Heuristics”, Applied Soft Computing, 14, pp. 677-686. ARBAOUI, Taha; BOUFFLET, Jean-Paul and MOUKRIM, Aziz; (2016), “A Matheuristic for Exam Timetabling”, IFAC-PapersOnLine, 49(12), pp. 1289-1294.
Details
| Journal Section | Makaleler |
|---|---|
| Authors | |
| Publication Date | June 30, 2019 |
| Acceptance Date | January 9, 2019 |
| Published in Issue | Year 2019 Issue: 53 |
Cited By
SINAV ÇİZELGELEME PROBLEMİNDE SINIF VE GÖZETMEN ATAMALARI İÇİN İKİ AŞAMALI BİR ÇÖZÜM YAKLAŞIMI
Uludağ University Journal of The Faculty of Engineering
Merve KÖSE KÜÇÜK
https://doi.org/10.17482/uumfd.713329
DEVELOPING A DECISION SUPPORT SYSTEM FOR EXAM SCHEDULING PROBLEM USING GENETIC ALGORITHM
Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering
Ahmet DOĞAN
https://doi.org/10.18038/estubtda.890307
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