0-1 Tamsayılı Programlama İle Ders Programı Çizelgeleme Probleminin Çözümü: Bir Yükseköğretim Kurumunda Uygulama
Yıl 2018,
Cilt: 3 Sayı: 3, 166 - 175, 31.12.2018
Tamer Eren
,
Cemre Taş
Neşet Bedir
Öz
Üniversiteler ülkelerin kalkınmalarında
çok önemli bir yer teşkil etmektedirler. Bilimsel araştırmaların yanı sıra
ülkenin eğitim, sağlık, savunma, mühendislik gibi alanlarında çalışmak üzere
gençleri yetiştirme görevini üstlenmektedir. Üniversitelerde ders programı
hazırlanması gerek öğretim üyeleri için gerek de öğrenciler için oldukça
önemlidir. Derslerin verimli olabilmesi için ders programlarının analitik bir
bakışla planlanması gerekmektedir. Ders programının hazırlanmasında ders
veren akademik personelin gün tercihlerinin dikkate alınması ve benzeri
kriterler motivasyonun dolasıyla da ders veriminin artmasına katkısı bulunur.
Bu amaçla Kırıkkale Üniversitesi Endüstri Mühendisliği Bölümü’nde ders
programı çizelgeleme problemi akademik personelin gün tercihleri gibi
kriterler dikkate alınarak ele alınmıştır. Bölümde normal ve ikinci öğretimde
toplam 58 ders, 21 öğretim elemanı bulunmaktadır. Mevcut durum analizinden
elde edilen memnuniyet oranında yaklaşık %17 artış göstermiştir. Problemi
çözmek için 438.480 değişkenli 553.044 kısıtlı 0-1 tamsayılı programlama
modeli kullanılmıştır.
|
Kaynakça
- Akkoyunlu EA. (1973). “A linear algorithm for computing the optimum university timetable”. The Computer Journal, 16(4), 347-350. Altunay, H, Eren T. (2016). “Ders programı çizelgeleme problemi için 0-1 tamsayılı programlama modeli ve bir örnek uygulama”. Uludağ Üniversitesi Mühendislik Fakültesi Dergisi, 21(6), 473-488.Altunay H, Eren T. (2017). “Ders programı çizelgeleme problemi için bir literatür taraması”. Pamukkale University Journal of Engineering Sciences, 23(1), 55-70.Avella P, Vasiliev I. “A computational study of a cutting plane algorithm for university course timetabling”. Journal of Scheduling, 8(6), 497-514, 2005Badri MA. (1996). “A two-stage multiobjective scheduling model for faculty-course-time assignments”. European Journal of Operational Research, 94(1), 16-28.Baker KR, Magazine MJ, Polak GG. (2002) “Optimal block design models for course timetabling”. Operations Research Letters, 30(1), 1-8.Bakır MA, Aksop C. (2008). “A 0-1 integer programming approach to a university timetabling problem”. Hacettepe Journal of Mathematics and Statistics, 37(1), 41-55.Boronico J. (2000). “Quantitative modeling and technology driven departmental course scheduling”. Omega, 28(3), 327-346.Burke EK, Marecek J, Parkes AJ, Rudová H. (2007). “Penalising patterns in timetables: Novel integer programming formulations”. International Conference of the German Operations Research Society (GOR), Saarbrücken, Germany, 5–7 September.Cacchiani V, Caprara A, Roberti R, Toth P. (2013).“A new lower bound for curriculum-based course timetabling”. Computers & Operations Research, 40(10), 2466-2477.Daskalaki S, Birbas T. (2005). “Efficient solutions for a university timetabling problem through integer programming”. European Journal of Operational Research, 160(1), 106-120.Dimopoulou M, Miliotis P. (2001). “Implementation of a university course and examination timetabling system”. European Journal of Operational Research, 130(1), 202-213.Dinkel JJ, Mote J, Venkataramanan MA. (1989). “An efficient decision support system for academic course scheduling”. Operations research, 37(6), 853-864.Ferland JA, Fleurent C. (1994). “SAPHIR: A decision support system for course scheduling”. Interfaces, 24(2), 105-115.Ferland JA, Roy S. (1985). “Timetabling problem for university as assignment of activities to resources”. Computers and Operations Research, 12(2), 207-218.Gosselin K, Truchon M. (1986). “Allocation of classrooms by linear programming”. The Journal of the Operational Research Society, 37(6), 561-569. Günalay Y, Şahin T. (2006). “A decision support system for the university timetabling problem with instructor preferences”. Asian Journal of Information Technology, 5(12), 1479-1484.Harwood GB, Lawless RW. (1975). “Optimizing organizational goals in assigning faculty teaching schedules”. Decision Sciences, 6(3), 513-524.Ismayilova NA, Sagir M, Gasimov RN. (2007). “A multiobjective faculty-course-time slot assignment problem with preferences”. Mathematical and Computer Modelling, 46(7-8), 1017-1029.Johnson D. (1993). “A database approach to course timetabling”. Journal of the Operational Research Society, 44(5), 425- 433.Laporte G, Desrochers S. (1986). “The problem of assigning students to course sections in a large engineering school”. Computational and Operations Research, 13(4), 387-394.Martin CH. (2004). “Ohio University’s college of business uses integer programming to schedule classes”. Interfaces, 34(6), 460-465.McClure RH, Wells CE. (1984). “A mathematical programming model for faculty course assignment”. Decision Sciences, 153(3), 409-420. Mirhassani SA. (2006). “A Computational approach to enhancing course timetabling with integer programming”. Applied Mathematics and Computation, 175(1), 814-822.Özdemir MS, Gasimov RN. (2004). “The analytic hierarchy process and multiobjective 0-1 faculty course assignment”. European Journal of Operational Research, 157(2), 398-408.Sarin SC, Wang Y, Varadarajan A. (2010). “A universitytimetabling problem and its solution using benders’ partitioning: A case study”. Journal of Scheduling, 13(2), 131-141.Sarin SC, Wang Y, Varadarajan A. (2005). “Solving a timetabling Problem Using Benders’ Decomposition”. 2nd Multidisciplinary International Conference on Scheduling: Theory and Applications (MISTA 2005), New York, USA, 18-21 July.Schimmelpfeng K, Helber S. (2007) “Application of a real-world university-course timetabling model solved by integer programming”. OR Spectrum, 29(4), 783-803.Shih W, Sullivan JA. (1977). “Dynamic course scheduling for college faculty via zero-one programming”. Decision Sciences, 8(4), 711-721.Şahin T. Goal Programming Approach to Solve the Timetabling Problem at Turkish Military Academy. Master Thesis, Bilkent University Department of Management, Ankara, Turkey, 2004Tripathy A. (1980). “A lagrangean relaxation approach to course timetabling”. Journal of Operations Research Society, 31(7), 599-603.Van Den Broek J, Hurkens C, Woeginger G. (2009). “Timetabling problems at the TU Eindhoven”. European Journal of Operational Research, 196(3), 877-885.
Yıl 2018,
Cilt: 3 Sayı: 3, 166 - 175, 31.12.2018
Tamer Eren
,
Cemre Taş
Neşet Bedir
Kaynakça
- Akkoyunlu EA. (1973). “A linear algorithm for computing the optimum university timetable”. The Computer Journal, 16(4), 347-350. Altunay, H, Eren T. (2016). “Ders programı çizelgeleme problemi için 0-1 tamsayılı programlama modeli ve bir örnek uygulama”. Uludağ Üniversitesi Mühendislik Fakültesi Dergisi, 21(6), 473-488.Altunay H, Eren T. (2017). “Ders programı çizelgeleme problemi için bir literatür taraması”. Pamukkale University Journal of Engineering Sciences, 23(1), 55-70.Avella P, Vasiliev I. “A computational study of a cutting plane algorithm for university course timetabling”. Journal of Scheduling, 8(6), 497-514, 2005Badri MA. (1996). “A two-stage multiobjective scheduling model for faculty-course-time assignments”. European Journal of Operational Research, 94(1), 16-28.Baker KR, Magazine MJ, Polak GG. (2002) “Optimal block design models for course timetabling”. Operations Research Letters, 30(1), 1-8.Bakır MA, Aksop C. (2008). “A 0-1 integer programming approach to a university timetabling problem”. Hacettepe Journal of Mathematics and Statistics, 37(1), 41-55.Boronico J. (2000). “Quantitative modeling and technology driven departmental course scheduling”. Omega, 28(3), 327-346.Burke EK, Marecek J, Parkes AJ, Rudová H. (2007). “Penalising patterns in timetables: Novel integer programming formulations”. International Conference of the German Operations Research Society (GOR), Saarbrücken, Germany, 5–7 September.Cacchiani V, Caprara A, Roberti R, Toth P. (2013).“A new lower bound for curriculum-based course timetabling”. Computers & Operations Research, 40(10), 2466-2477.Daskalaki S, Birbas T. (2005). “Efficient solutions for a university timetabling problem through integer programming”. European Journal of Operational Research, 160(1), 106-120.Dimopoulou M, Miliotis P. (2001). “Implementation of a university course and examination timetabling system”. European Journal of Operational Research, 130(1), 202-213.Dinkel JJ, Mote J, Venkataramanan MA. (1989). “An efficient decision support system for academic course scheduling”. Operations research, 37(6), 853-864.Ferland JA, Fleurent C. (1994). “SAPHIR: A decision support system for course scheduling”. Interfaces, 24(2), 105-115.Ferland JA, Roy S. (1985). “Timetabling problem for university as assignment of activities to resources”. Computers and Operations Research, 12(2), 207-218.Gosselin K, Truchon M. (1986). “Allocation of classrooms by linear programming”. The Journal of the Operational Research Society, 37(6), 561-569. Günalay Y, Şahin T. (2006). “A decision support system for the university timetabling problem with instructor preferences”. Asian Journal of Information Technology, 5(12), 1479-1484.Harwood GB, Lawless RW. (1975). “Optimizing organizational goals in assigning faculty teaching schedules”. Decision Sciences, 6(3), 513-524.Ismayilova NA, Sagir M, Gasimov RN. (2007). “A multiobjective faculty-course-time slot assignment problem with preferences”. Mathematical and Computer Modelling, 46(7-8), 1017-1029.Johnson D. (1993). “A database approach to course timetabling”. Journal of the Operational Research Society, 44(5), 425- 433.Laporte G, Desrochers S. (1986). “The problem of assigning students to course sections in a large engineering school”. Computational and Operations Research, 13(4), 387-394.Martin CH. (2004). “Ohio University’s college of business uses integer programming to schedule classes”. Interfaces, 34(6), 460-465.McClure RH, Wells CE. (1984). “A mathematical programming model for faculty course assignment”. Decision Sciences, 153(3), 409-420. Mirhassani SA. (2006). “A Computational approach to enhancing course timetabling with integer programming”. Applied Mathematics and Computation, 175(1), 814-822.Özdemir MS, Gasimov RN. (2004). “The analytic hierarchy process and multiobjective 0-1 faculty course assignment”. European Journal of Operational Research, 157(2), 398-408.Sarin SC, Wang Y, Varadarajan A. (2010). “A universitytimetabling problem and its solution using benders’ partitioning: A case study”. Journal of Scheduling, 13(2), 131-141.Sarin SC, Wang Y, Varadarajan A. (2005). “Solving a timetabling Problem Using Benders’ Decomposition”. 2nd Multidisciplinary International Conference on Scheduling: Theory and Applications (MISTA 2005), New York, USA, 18-21 July.Schimmelpfeng K, Helber S. (2007) “Application of a real-world university-course timetabling model solved by integer programming”. OR Spectrum, 29(4), 783-803.Shih W, Sullivan JA. (1977). “Dynamic course scheduling for college faculty via zero-one programming”. Decision Sciences, 8(4), 711-721.Şahin T. Goal Programming Approach to Solve the Timetabling Problem at Turkish Military Academy. Master Thesis, Bilkent University Department of Management, Ankara, Turkey, 2004Tripathy A. (1980). “A lagrangean relaxation approach to course timetabling”. Journal of Operations Research Society, 31(7), 599-603.Van Den Broek J, Hurkens C, Woeginger G. (2009). “Timetabling problems at the TU Eindhoven”. European Journal of Operational Research, 196(3), 877-885.
Toplam 1 adet kaynakça vardır.