A Model to Optimize University Course Timetable Using Graph Coloring and Integer Linear Programming

Abstract

This paper presents the design and construction of a faculty course timetable. The system uses an Integer Linear Programming model which attempts to assign groups of course units to time periods where each group is a result of a graph coloring approach. Limited number of lecture halls, large number of subject combinations and growing number of student registration have made the problem very tight which results thousands of variables and constraints to the model. The quality of the solution depends on the location of the time period assigned to the set of course units. Hence the objective function is defined to optimize the allocation of time periods to course units. The model results a feasible solution which has reduced the maximum idle time of students to three hours and it can be implemented with the lecture halls currently available in the faculty of Applied Sciences, University of Sri Jayewardenepura. The model is flexible and allows to change the constraints depending on the faculty requirements and other factors and if necessary, construct alternative schedules.

Honours course timetabling and classroom assignment

“…The most commonly used techniques encountered in the literature include the method of simulated annealing algorithm, tabu search, and genetic algorithms [1,7,8]. Some research has also been done on the application of graph colouring to solve timetabling problems [12].…”

Efisiensi Pengaturan Jadwal Perkuliahan Menggunakan Pendekatan Pewarnaan Graf

“…Selanjutnya Winda dkk [7] meneliti optimasi penjadwalan waktu kerja dengan integer programming, Burke dkk [8] menggunakan metode hyperheuristic untuk mengkonstruksi jadwal ujian dan jadwal perkuliahan. Penelitian lain terkait pengaturan jadwal perkuliahan dilakukan oleh Perera yang menggunakan pemodelan graf dan pewarnaan graf serta dilanjutkan dengan integer linear programming (ILP) [9].…”

Penerapan Model Integer Linear Programming Dalam Optimasi Penjadwalan Perkuliahan Secara Otomatis

“…Dalam organisasi dengan sumber daya yang besar, penjadwalan adalah salah satu faktor terpenting dari strategi manajemen dan yang paling rentan terhadap kesalahan atau masalah [1]. Masalah penjadwalan melibatkan beberapa sumber tertentu seperti orang, ruangan atau kendaraan yang dialokasikan ke sekumpulan objek tertentu seperti pekerjaan, periode waktu, rute, dan sebagainya sedemikian sehingga akan memenuhi beberapa tujuan yang disesuaikan pada beberapa kendala [2]. Penjadwalan merupakan salah satu masalah yang sering dihadapi dalam mengatur penugasan pada suatu organisasi termasuk lembaga pendidikan, diantaranya tentang penjadwalan perkuliahan.…”