44 CHAPTER 5 CONCLUSION First semester course unit timetable of FAS, USJP has been modeled in this study. For the model formulation, both graph theoretic and ILP approach has been used. For the three years of studies, timetables were modeled separately and finally three of them were joined together to analyze the feasibility. Using graph vertex coloring algorithm course units were grouped such a way that two course units in the same group can be scheduled simultaneously while two course units in two groups cannot. For the first year, graph coloring algorithm results 20 groups and for the second and third years there are 23 and 24 groups respectively. Using those resulted groups of course units a binary ILP model has been defined for each of the three years. The uniqueness property and the completeness property were defined as the hard constraints which are the essential parts for a feasible timetable while the objective (soft constraint) of optimizing the timetable is given as the objective function of the ILP. Hence the objective is to minimize the cost of assigning courses to time periods. When constructing the timetable it was assumed that teacher will not become a constraint to the solution where allocation of teachers to course units is a responsibility of the department which the subject is offering. Further it was assumed that lecture halls belong to each department is accessible to all departments. With those assumptions, it was able to model a conflict free efficient timetable for the FAS. The model was able to optimize the idle time of the students by reducing the maximum idle time to three hours. Further it was able to implement the result with the currently available lecture halls. Hence this model helps to utilize both physical and human (student) resources in the faculty. The problem was solved effectively for the first semester which can be extended to the second semester and it can be used for other faculties as well.However, the size of the problem creates complications in achieving an optimum solution. It is therefore necessary to find a way of decreasing machine time, which has not been discussed here. 45 5.1 Limitations of the Study This study was conducted with the data collected in 2015. But this data can be changed year by year. Some combinations have been introduced in 2015 which are not offered to third year students. But for the comparison it is assumed that those are offering to all students. The number of students in each subject depends on the year of the study. Here it has taken to be fixed for all three years for the categorization of subjects and lecture halls. The ordering of course unit groups are taken to be arbitrary, since one cannot give preferences to the subjects. But in departmental level they have their own preferences which are difficult to absorb. If some ordering method can be applied, one would obtain more efficient results. This study has not considered the distance that the students have to walk when they transferring from one lecture to the other. Here we have assumed that any student is able to access to any of the lecture halls within 10 minutes. But the present some physical science subjects are not conducted in some biology lecture halls and vice versa. 5.2 Further Improvements and Suggestions This study only searched for a feasible and efficient course unit timetable. Basically it was suggested for the optimization of lecturing hours. The analysis revealed that it can be implemented with the available resources, but it does not allocate each course unit to a lecture hall. As a suggestion it would be assigned using an assignment algorithm such as Hungarian algorithm by further analysis. Another problem that the faculty management faces is the scheduling the practical sessions. For the subjects, MAT, PHY, CHE, ZOO, PST, ARM, BIO, STA, CSC, ICT and FST, students are having practical. With the limited capacity of laboratories the same practical is repeated several times per week by grouping students. This situation has not been considered in this study, since it requires the data separately from the departments. Hence one can further develop this result by scheduling the practicalsessions. 46 The timetable which has been modeled only resulted the scheduling of general lectures. But for the fourth year students their special course units have not been scheduled. Mostly the special timetable is decided by the department involved. But if one interests it can be also scheduled by offering a departmental timetable. One objective of this study is to minimize the wastage of the resources used in the timetabling process, both human and physical resources. An automated system will probably reduce such wastage of human resources, but a detailed cost analysis has not done due to the difficulties in getting information. Having such data a cost analysis can be done and the adequacy of this model would be further verified. 47 BIBLIOGRAPHY [1] A. Borges, R. Ospina, G. Cristina, “Binary integer programming model for university courses timetabling: a case study”. [2] D. Werra,“An Introduction to Timetabling” European Journal ofOperation Research 19 (1985), 151-162. [3] E.K. Burke, J.H. Kingston and D. de Werra. (2004). “Applications to timetabling”.In: J. Gross and J. Yellen (eds.) The Handbook of Graph Theory, Chapman Hall/CRC Press, 2004, 445-474. [4] E.K. Burke, S. Petrovic, “Recent research directions in automated timetabling”, European Journal of Operational Research 140 (2002), pp 266-280. [5] EnzheYu , Ki Seok, “A genetic algorithm for a university weekly course timetabling problem”, international transaction in operational research, 9 (2002), pp 703-717. [6] F. Zibran, “A multi-phaseapproach to university course timetabling”, M.Sc.Thesis , 2007. [7] J. Rickman, J. Yellen, “Course Timetabling Using Graph Coloring and A.I. Techniques”, 10th International Conference of the Practice and Theory of Automated Timetabling, 2014, 26-29. [8] Khaled M. Mahar, “automatic generation of university timetables: an evolutionary approach”.ISBN: 972-8924-09-7 © 2006 IADIS http://www.researchgate.net/publication/267770949. [9] M. Dimopoulou , P. Miliotis, “Theory and Methodology - Implementation of a university course and examination timetabling system”, European Journal of Operational Research 130 (2001), pp 202-213. [10] M. Bakır, C. Aksop, “A0-1 integer programming approach to a university timetabling problem”, Hacettepe Journal of Mathematics and Statistics, Volume 37 (1) (2008), pp41 – 55. 48 [11] M. Carter, G. Laporte (1996), “Recent Developments in Practical Exam Timetabling”, In: Burke E.K. and Ross P. (eds.), Selected Papers from the 1st International Conference on the Practice and Theory of Automated Timetabling, Lecture Notes in Computer Science 1153, pp. 3-21. [12] Phillips, D. Ryan, “Solving the Classroom Assignment Problem Using Integer Programming”, University of Auckland, New Zealand, 2013. [13] S. Daskalaki ,T. Birbas , E. Housos , “An integer programming formulation for a case study in university timetabling”, European Journal of Operational Research 153 (2004), pp 117-135. [14] S. Chacha, “Mathematical programming formulations for optimization of university course timetabling problem”, The Case of Makwawa University College of Education, M.Sc. (Mathematical Modeling) Dissertation, University of Dares Salaam September, 2012. [15] Shoshana H. Goldberg, “Defining, Modeling, and Solving a Real University Course Timetabling Problem”, Master thesis, 2007. [16] T. Muller, “Constraint-based Timetabling”, Ph.D. Thesis, Prague, Charles University in Prague, Faculty of Mathematics and Physics, 2005. [17] Tim B. Cooper and Jefferey H. Kingston,“The Solution of Real Instances of the Timetabling Problem”, The Computer Journal vol. 36, no. 7, Australia, 1993. 49 APPENDIX A-QUESTIONNAIRE Questionnaire on the faculty time table This questionnaire is part of a research which intends to gather responses from students at the Faculty of Applied Sciences related to the master time table of the faculty. By completing this form you will be making an important contribution to redesign the time table in an efficient way. 1. Your year of Study First Second Third Special 2. Your Stream Of Study Physical Biological Other 3. You are coming to the university from: Home Boarding Hostel Other 4. Time taken to travel from your residence to the university Less than a half an hour Around an hour More than an hour 5. Rank the following lecture halls as you prefer for lectures for a group with more than 100 students (1-for highest preference, 2 for the next, etc.) Science Auditorium (S1) Biology Auditorium (A1) Chemistry Lecture Theatre 1 (C1) New Faculty Complex Chemistry Lecture Theatre 2 (C2) Physics Lecture Theatre 1 (P1) Background information Preferences of Lecture Halls 50 6. Your most preferred time to attend the lectures Morning (8-12) Afternoon (1-3) After 3 p.m. 7. Rank the days of the week for morning lectures in your preference order. Monday Thursday Tuesday Friday Wednesday 8. Rank the days of the week for evening lectures in your preference order. Monday Thursday Tuesday Friday Wednesday 9. Your most preferred time for practical classes Morning (8-12) Afternoon (1-3) After 3 p.m. 10. Your preference on maximum time gap between two consecutive lectures 30 minutes 60 minutes More than 60 minutes 11. Do you prefer to have a free day within the week days while having frequent lectures on other days? Yes No 12. State any other issues that you are facing with the current time table. Many thanks for your time. Time of Lectures 1 2 3 51 Responses of the second year physical science students: Note: The numbers represent the rankings of the students for each time periods and days. Student no lecture-time Monday morning Tuesday morning Wednesday morning Thursday morning Friday morning gap 1 1 4 1 3 4 5 2 2 2 2 1 3 4 5 2 3 1 1 1 2 4 5 2 4 1 4 1 2 3 5 1 5 1 3 1 3 3 4 1 6 1 1 2 3 3 4 1 7 1 3 1 3 2 4 1 8 2 1 2 2 2 4 3 9 1 1 1 2 3 4 2 10 2 2 1 3 3 4 2 11 1 4 2 3 3 4 1 12 1 4 3 3 3 5 2 13 1 1 2 3 3 4 2 14 1 1 1 3 3 5 1 15 1 2 2 3 3 5 2 16 1 3 1 3 3 5 2 17 1 4 1 2 3 5 2 18 1 3 1 2 3 5 2 19 1 2 2 2 3 5 2 20 1 2 2 2 3 5 2 21 1 2 2 2 3 5 1 22 1 3 2 2 2 5 3 23 1 3 1 2 2 5 1 24 2 3 1 2 4 5 1 25 2 3 1 3 4 5 1 26 1 3 2 3 2 5 1 27 2 3 2 3 3 5 2 28 1 3 2 3 4 5 2 29 1 4 1 3 2 5 2 30 1 1 1 3 3 5 2 31 1 4 1 3 3 5 1 32 2 4 2 3 3 5 2 33 1 4 3 3 4 5 2 34 1 3 1 3 4 5 1 35 1 2 1 2 4 5 1 36 1 3 1 2 4 5 1 37 1 2 2 2 3 5 2 52 38 1 2 2 2 4 4 1 39 2 2 2 2 3 4 2 40 2 2 2 2 3 5 2 41 1 2 2 2 3 5 2 42 1 4 2 3 3 5 2 43 1 4 3 3 3 5 2 44 1 4 1 3 3 5 2 45 1 4 1 3 3 5 2 46 1 4 1 3 3 5 1 47 2 4 1 3 3 5 1 48 1 4 1 3 3 5 1 49 1 4 1 3 3 5 2 50 1 3 1 3 4 5 1 51 1 1 2 3 4 5 1 52 2 3 1 3 3 5 2 53 1 3 2 3 3 5 2 54 2 3 1 2 3 4 2 55 2 2 1 2 3 4 2 56 2 1 1 2 3 4 2 57 2 1 2 2 3 3 2 58 1 3 3 2 4 4 3 59 1 3 1 2 4 4 2 60 1 1 1 2 3 5 2 61 1 1 2 2 3 5 2 62 1 3 2 2 3 5 2 63 1 3 1 3 3 5 2 64 1 3 1 3 3 5 2 65 1 3 2 3 3 5 1 66 1 3 2 2 3 5 3 67 1 4 1 3 3 5 1 68 1 4 2 3 3 5 1 69 1 3 1 3 3 5 2 70 1 2 1 3 3 5 1 71 1 3 1 2 3 5 2 72 1 4 2 2 3 5 2 73 1 2 2 2 3 5 2 74 1 1 2 2 3 5 1 75 1 1 2 2 4 4 1 76 1 4 1 2 2 4 2 77 1 3 1 2 3 5 3 78 1 1 2 2 3 5 3 79 1 3 1 2 3 5 1 80 1 3 1 2 3 5 1 81 1 2 1 2 4 5 1 53 82 1 2 1 2 4 5 2 83 1 1 1 2 4 5 1 84 1 4 1 2 4 5 2 85 1 3 1 2 4 5 2 86 1 2 2 2 4 4 3 87 1 2 1 2 4 4 1 88 1 2 1 2 4 4 1 89 1 2 1 2 4 4 1 90 1 2 1 2 3 4 2 91 1 3 2 3 3 4 1 92 1 1 2 3 3 4 2 93 2 2 1 3 3 4 2 94 1 2 2 2 3 4 2 95 1 2 1 3 3 4 2 96 1 2 2 3 2 4 2 97 1 3 2 2 3 4 2 98 2 3 2 2 3 5 2 99 1 3 2 2 3 5 1 100 1 3 1 2 3 5 1 101 1 2 1 2 3 5 1 102 1 2 1 3 3 5 1 103 1 2 1 3 4 5 1 104 1 2 1 2 4 4 2 105 1 2 1 2 4 4 1 106 1 2 2 2 4 5 2 107 1 2 2 2 4 5 1 108 1 2 1 2 3 5 2 109 1 3 2 2 3 5 2 110 1 2 1 2 3 5 2 111 1 3 1 2 3 5 2 112 1 4 1 3 3 5 2 113 1 3 1 2 2 5 2 114 1 4 1 2 3 5 1 115 1 4 1 3 3 5 1 116 1 3 1 3 3 5 1 117 1 3 1 3 3 5 1 118 1 3 1 3 3 5 1 119 1 4 2 3 3 5 1 120 1 1 2 2 3 5 1 121 1 2 2 2 3 5 1 122 2 2 2 2 3 5 2 123 1 3 1 3 3 5 2 124 1 4 1 3 4 5 2 125 1 3 1 3 4 5 1 54 126 1 4 1 3 2 5 3 127 1 3 1 2 3 5 1 128 1 4 1 2 3 5 2 129 1 4 1 2 3 5 1 130 1 4 1 2 3 5 2 131 1 3 2 2 3 5 2 132 1 2 2 2 3 5 2 133 2 3 2 3 3 5 1 134 1 2 2 3 3 5 2 135 1 3 2 3 4 5 2 136 1 2 1 3 4 5 1 137 1 3 2 2 4 5 2 138 1 2 1 2 2 5 1 139 1 3 1 2 3 5 2 140 1 3 1 1 3 5 1 141 1 3 1 1 3 5 2 142 1 3 2 2 3 5 1 143 1 4 1 2 3 5 2 144 1 2 1 2 3 5 2 145 1 2 2 2 3 5 1 146 1 2 1 2 4 5 1 147 1 3 2 2 2 5 1 148 1 2 2 2 3 5 1 149 2 2 1 1 3 5 1 150 1 3 1 1 3 4 2 55 Responses of the second year Biological science students: Stud ent no lectu re- time Mondaymo rning Tuesdaymo rning Wednesdaym orning Thursdaym orning Fridaymo rning gap 2 2 3 1 2 4 5 2 3 1 1 2 3 4 5 1 4 1 1 2 3 5 4 1 5 1 1 2 3 4 5 1 6 1 1 2 3 4 5 2 7 1 1 2 3 4 5 2 8 2 1 2 3 4 5 2 9 1 1 2 3 4 5 1 10 2 1 2 3 5 4 1 11 2 1 2 3 4 5 1 12 2 1 2 3 4 5 3 13 2 1 2 3 4 5 2 14 1 2 1 3 4 5 2 15 1 2 1 3 4 5 1 16 1 2 1 3 4 5 1 17 1 3 1 2 4 5 3 18 1 1 3 2 4 5 3 19 1 3 1 2 4 5 1 20 1 3 1 2 5 4 3 21 1 3 1 2 4 5 1 22 1 3 1 2 4 5 1 23 1 2 1 3 4 5 2 24 2 2 1 3 4 5 2 25 2 1 2 3 4 5 2 26 1 1 2 3 4 5 2 27 2 1 2 3 4 5 2 28 1 3 2 1 4 5 2 29 1 2 3 1 4 5 1 30 1 2 1 3 4 5 3 31 1 1 2 3 4 5 3 32 2 2 1 3 4 5 1 33 1 1 2 3 4 5 1 34 1 3 1 2 4 5 2 35 1 1 3 2 4 5 3 36 1 2 1 3 4 5 1 37 2 1 2 3 4 5 1 38 2 2 1 3 4 5 2 56 39 2 1 2 3 4 5 2 40 2 3 1 2 4 5 2 41 1 2 1 3 4 5 1 42 1 1 2 3 4 5 2 43 1 2 1 3 4 5 1 44 1 3 1 2 4 5 2 45 1 2 1 3 4 5 1 46 1 1 2 3 4 5 2 47 2 1 2 3 4 5 1 48 1 1 2 3 4 5 3 49 1 2 1 3 4 5 2 50 1 1 2 3 4 5 1 51 1 3 1 2 4 5 2 52 2 2 1 3 4 5 2 53 1 1 2 3 4 5 3 54 2 1 2 3 4 5 1 55 2 1 2 3 4 5 1 56 1 1 2 3 4 5 2 57 1 2 1 3 4 5 1 58 1 1 2 3 4 5 2 59 1 1 2 3 4 5 2 60 1 3 1 2 4 5 3 61 1 2 1 3 4 5 2 62 1 2 1 3 4 5 2 63 1 1 2 3 4 5 2 64 1 1 2 3 4 5 2 65 1 1 2 3 4 5 1 66 1 3 1 2 4 5 1 67 1 3 1 2 4 5 2 68 1 3 1 2 4 5 1 69 1 3 1 2 4 5 2 70 1 2 1 3 4 5 1 71 1 1 2 3 4 5 1 72 1 2 1 3 4 5 2 73 1 1 2 3 4 5 1 74 1 2 1 2 4 5 2 75 1 1 2 3 4 5 1 76 1 3 1 2 4 5 2 77 1 1 2 3 4 5 1 78 1 2 1 3 4 5 1 79 1 2 1 3 4 5 2 80 1 1 3 2 4 5 1 81 1 1 2 3 4 5 2 82 1 3 1 2 4 5 1 83 1 1 2 3 4 5 2 57 84 1 2 1 3 4 5 1 85 1 1 2 3 4 5 2 86 1 1 2 3 4 5 1 87 2 1 2 3 4 5 2 88 2 1 2 3 4 5 1 89 2 2 1 3 4 5 2 90 1 2 1 3 4 5 1 91 1 1 2 3 4 5 2 92 2 1 2 3 4 5 1 93 2 3 1 2 4 5 2 94 1 1 2 3 4 5 2 95 1 2 1 3 4 5 2 96 1 3 1 2 4 5 2 97 1 3 1 2 4 5 2 98 2 3 1 2 4 5 2 99 2 3 1 2 4 5 2 100 1 2 1 3 4 5 1 101 1 2 1 3 4 5 1 102 1 2 1 3 4 5 1 103 1 1 2 3 4 5 1 104 1 1 2 3 4 5 2 105 1 2 1 3 4 5 2 58 Responses of the first year students Stude nt no lecture -time Mondaym orning Tuesdaym orning Wednesda ymorning Thursdaymo rning Fridaym orning Gap 1 1 3 1 2 4 5 2 2 2 3 1 2 4 5 2 3 1 3 1 4 2 5 2 4 1 2 1 3 4 5 3 5 1 2 1 4 3 5 3 6 1 2 1 5 3 4 1 7 2 2 1 3 4 5 2 8 1 1 2 3 4 5 3 9 2 1 2 3 4 5 2 10 2 2 1 3 4 5 2 11 2 1 2 3 4 5 2 12 2 3 1 2 5 4 2 13 2 2 1 3 4 5 2 14 1 2 1 3 4 5 2 15 2 3 1 2 4 5 2 16 2 3 1 2 4 5 2 17 2 2 1 3 4 5 1 18 2 2 1 3 4 5 2 19 1 1 2 3 4 5 3 20 1 3 1 2 4 5 2 21 2 3 1 2 5 4 3 22 1 1 3 2 4 5 3 23 2 3 1 2 4 5 1 24 1 2 1 3 4 5 1 25 1 3 2 1 4 5 1 26 2 3 1 2 4 5 1 27 2 3 1 2 4 5 1 28 2 2 3 1 4 5 1 29 1 2 1 3 4 5 3 30 1 1 2 3 4 5 2 31 1 1 2 3 4 5 1 32 1 1 2 3 4 5 3 33 2 1 2 3 4 5 3 34 1 1 2 3 4 5 3 35 1 2 1 3 4 5 1 36 1 2 1 3 4 5 1 37 2 2 1 3 4 5 2 59 38 1 2 1 3 4 5 2 39 2 2 1 3 4 5 3 40 1 2 3 1 4 5 2 41 1 4 3 1 2 5 3 42 1 1 2 3 4 5 2 43 1 1 2 3 4 5 3 44 1 2 1 3 4 5 2 45 1 2 1 3 4 5 3 46 2 3 1 2 4 5 2 47 2 1 2 3 4 5 3 48 2 2 3 1 4 5 2 49 1 2 1 3 4 5 1 50 1 3 1 2 4 5 2 51 1 3 1 2 4 5 1 52 2 3 1 2 4 5 1 53 1 3 1 2 4 5 1 54 2 3 1 2 4 5 2 55 1 1 2 3 4 5 1 56 2 1 2 3 4 5 2 57 1 2 1 3 4 5 2 58 2 1 2 3 4 5 2 59 1 1 2 3 4 5 2 60 2 3 2 1 4 5 2 61 1 3 1 2 4 5 3 62 2 1 2 3 4 5 1 63 1 2 1 3 4 5 2 64 2 1 2 3 4 5 2 65 1 2 1 3 4 5 3 66 2 1 2 3 4 5 3 67 1 2 3 1 4 5 2 68 1 2 1 3 4 5 2 69 1 2 1 3 4 5 1 70 1 2 1 3 4 5 1 71 1 2 1 3 4 5 1 72 1 2 1 3 4 5 3 73 1 2 1 3 4 5 2 74 1 2 1 3 4 5 2 75 1 2 1 3 4 5 2 76 2 2 1 3 4 5 2 77 2 2 1 3 4 5 2 78 2 2 1 3 4 5 2 79 2 2 1 3 4 5 1 80 2 2 1 3 4 5 1 81 1 3 1 3 4 5 1 82 2 3 1 3 4 5 3 60 83 1 1 2 4 3 5 2 84 1 2 1 4 3 5 2 85 1 1 2 3 4 5 2 86 1 2 1 3 4 5 2 87 2 1 2 3 4 5 2 88 1 3 2 1 4 5 2 89 2 3 1 2 4 5 3 90 1 3 1 2 4 5 3 91 2 2 1 3 4 5 2 92 1 2 1 3 4 5 2 93 2 1 2 3 4 5 1 94 1 2 1 3 4 5 2 95 2 2 1 3 4 5 2 96 1 2 1 3 4 5 2 97 2 2 3 1 4 5 1 98 1 2 1 3 4 5 1 99 1 3 1 2 4 5 2 100 1 3 2 1 4 5 1 101 1 3 1 2 4 5 1 102 1 1 2 3 4 5 1 103 1 2 1 3 4 5 1 104 2 1 2 3 4 5 1 105 2 2 1 3 4 5 1 106 1 1 2 3 4 5 2 107 2 2 1 3 4 5 1 108 1 2 1 3 4 5 2 109 2 3 1 2 4 5 3 110 1 3 1 2 4 5 1 111 2 3 1 2 4 5 1 112 1 1 2 4 3 5 2 113 2 1 2 3 4 5 2 114 1 1 2 3 4 5 2 115 2 1 2 3 4 5 1 116 1 2 1 4 3 5 2 117 2 2 1 3 4 5 1 118 1 2 1 3 4 5 2 119 2 3 1 2 4 5 2 120 2 3 2 1 4 5 2 121 2 3 2 1 4 5 2 122 2 3 2 1 4 5 2 123 2 1 2 4 3 5 2 124 1 1 2 3 4 5 2 125 1 2 1 3 4 5 2 126 1 1 2 3 4 5 1 127 2 2 1 3 4 5 1 61 128 1 1 2 3 4 5 1 129 2 2 1 4 5 1 130 1 2 1 3 4 5 1 131 2 1 2 3 4 5 2 132 1 2 1 3 4 5 2 133 2 3 1 2 4 5 2 134 1 3 2 1 4 5 1 135 2 2 1 3 4 5 2 136 2 1 2 3 4 5 1 137 2 1 2 3 4 5 2 138 1 2 1 3 4 5 1 139 1 2 1 3 4 5 3 140 1 2 1 3 4 5 1 141 1 3 1 2 4 5 1 142 2 1 2 3 4 5 1 143 1 2 1 3 4 5 1 144 2 1 2 3 4 5 1 145 1 2 1 3 4 5 1 146 2 1 2 3 4 5 1 147 1 2 1 3 4 5 1 148 2 1 2 3 4 5 1 149 1 2 1 3 4 5 1 150 2 2 1 3 4 5 1 151 1 2 1 3 4 5 1 152 2 2 1 3 4 5 1 153 1 3 2 1 4 5 2 154 2 3 1 2 4 5 2 155 2 1 2 3 4 5 2 156 1 3 1 2 4 5 2 157 1 2 1 3 4 5 2 158 2 1 2 3 4 5 1 159 2 3 1 2 4 5 1 160 1 1 2 3 4 5 1 161 2 2 1 3 4 5 1 162 1 2 1 3 4 5 1 163 2 2 1 3 4 5 3 164 2 2 1 3 4 5 2 165 2 2 1 3 4 5 1 166 1 2 1 3 4 5 2 167 1 2 1 3 4 5 1 168 1 3 2 1 4 5 2 169 1 3 1 2 4 5 1 170 1 1 2 3 4 5 2 171 1 1 2 3 4 5 1 172 2 3 1 2 4 5 2 62 173 2 3 1 2 4 5 2 174 1 2 1 3 4 5 2 175 2 2 1 3 4 5 2 176 2 3 2 1 4 5 2 177 2 1 2 3 4 5 2 178 1 1 2 3 4 5 2 179 2 3 1 2 4 5 2 180 2 2 1 3 4 5 2 181 1 2 1 3 4 5 2 182 1 2 1 3 4 5 1 183 1 2 1 3 4 5 1 184 1 2 1 3 4 5 1 185 1 3 1 2 4 5 1 186 1 3 1 3 4 5 1 187 1 3 1 2 4 5 1 188 2 3 1 2 4 5 1 189 1 1 2 3 4 5 3 190 1 2 3 1 4 5 2 191 1 2 1 3 4 5 2 192 2 3 2 1 4 5 2 193 2 2 1 2 4 5 3 194 1 1 2 3 4 5 2 195 1 2 1 3 4 5 2 196 1 3 1 2 4 5 2 197 1 2 1 3 4 5 2 198 1 1 2 3 4 5 2 199 1 2 1 3 4 5 2 200 1 2 1 3 4 5 2 63 APPENDIX B Maple 12 coding for graph coloring Maple results of initial coloring > restart; with(GraphTheory); >A := matrix([[CHE, ZOO, PHY, PBT, EMF, ARM, BIO, ICT, MAN, PST, MAT, CSC, STA, ECN, FSC]]); >G2 := Graph(A, ARM, BIO, ARM, CHE, ARM, MAN, ARM, ZOO, BIO, CHE, BIO, FSC, BIO, ICT, CHE, EMF, CHE, FSC, CHE, ICT, CHE, MAN, CHE, MAT, CHE, PBT, CHE, PHY, CHE, PST, CHE, STA, CHE, ZOO, CSC, MAT, CSC, PHY, CSC, STA, ECN, MAT, ECN, STA, EMF, MAN, EMF, PBT, EMF, PHY, EMF, ZOO, ICT, MAT, ICT, PHY, MAN, MAT, MAN, PBT, MAN, PHY, MAN, ZOO, MAT, PHY, MAT, STA, PBT, ZOO, PHY, PST, PHY, STA, PHY, ZOO); >IsVertexColorable(G2, 5, ’Co’); true > Co; [[CHE, CSC, ECN], [ARM, EMF, FSC, ICT, PST, STA], [BIO, MAN], [PBT, PHY], [MAT, ZOO]] Maple results of the coloring the first year course units. Gnew1 := Graph(V1, E1) Gnew1 := ‘Graph 3: a directed unweighted graph with 55 vertices and 1183 arc(s)‘ >IsVertexColorable(Gnew1, 20, ’Co1’); true > Co1; [1, 6, 9], [2, 7, 10], [3, 8], [4], [5], [11, 14, 27, 36, 39], [12, 15, 28, 37, 40], [13, 16, 29,38, 41],[17, 23, 30, 32, 42], [18, 24, 31, 33], [19, 25, 34, 64 43], [20, 26, 35, 44],[21, 45, 46], [49, 52], [50, 53], [51, 54], [55], [22, 47], [48]] Maple results of the coloring the Second year course units. >Gnew2 := Graph(V2, E2); Gnew2 := ‘Graph 2: a directed unweighted graph with 62 vertices and 1482 arc(s)‘ >IsVertexColorable(Gnew2, 23, ’Co2’); true; > Co2; [[1, 6, 9], [2, 7, 10], [3, 8], [4], [5], [11, 15, 22, 30, 33], [12, 16, 23, 31, 34], [13, 17, 24, 32, 35], [14, 25, 36, 46], [18, 26, 27, 37, 56], [19, 28, 38, 57], [20, 29, 39, 58], [21, 40, 42, 59], [41, 43, 60], [47, 50, 61], [48, 51, 62], [49, 52], [53], [54], [55], [44], [45]] Maple results of the coloring the Third year course units. >Gnew3 := Graph(V3, E3); Gnew3 := ‘Graph 2: a directed unweighted graph with 65 vertices and 1719 arc(s)‘ >IsVertexColorable(Gnew3, 24, ’Co3’); true [1, 7, 12], [2, 8, 13], [3, 9], [4, 10], [5, 11], [6], [14, 19, 29, 40, 44], [15, 20, 30,41, 45], [16, 31, 42, 46], [17, 32, 43], [18, 33, 52], [21, 25, 34, 36], [22, 26, 35,37], [23, 27, 38, 47], [24, 28, 39, 48], [49, 53], [50, 54], [51, 55], [56, 61], [57,62], [58, 63], [59, 64], [60, 65],[57]] 65 MATLAB 14 codes to execute the linear programming model and to generate the time table. function Time=SemesterI_TimeTable(Year) Time=Year; if Time==1 %import data [l1]=xlsread('Grouping.xlsx','onehr'); [l2]=xlsread('Grouping.xlsx','twohr'); [T1]=xlsread('Grouping.xlsx','Timeslots'); C1=length(l1); C2=length(l2); t_courses=length(l1)+length(l2); % total no of courses n_times=length(T1); %total no of time slots variables=t_courses*n_times; % First constraint-matrix A1 for the completness property l=1;u=n_times; A1=zeros(t_courses,variables); %initializing fori=1:t_courses for q=l:u A1(i,q)=1; end l=u+1; u=u+n_times; end % H is the array representimg the duration for each course H=ones(C1+C2,1); %initializing 66 fori=C1+1:t_courses H(i)=2; end %Second constraint-matrix A2 represents conflicts free A2=zeros(n_times,variables);% initializing fori=1:n_times for q=1:t_courses A2(i,n_times*q+i-n_times)=1; end end % B is the array with ones-r.h.s. of the constraints B=ones(n_times,1); % integer linear program intcon=1:756; % all decision variables are integers % z is the objective function z=zeros(variables,1); k=1; fori=1:t_courses for q=1:n_times z(k)=sqrt(q)+1; k=k+1; end end % giving lower and upper bounds for decision variables(binary) lb=zeros(variables,1); ub = ones(variables,1); % y is the solution of the ILP y=intlinprog(z,intcon,A2,B,A1,H,lb,ub); % representing the solution in to matrix 67 n=1;X=zeros(C1+C2,n_times); for p=1:C1+C2 for q=1:42 X(p,q)=y(n); n=n+1; end end TT=zeros(1,45);%dummy timetable %Courses=1:C1+C2; fori=1:C1+C2 for j=1:n_times if X(i,j)==1 TT(j) = i; end end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% TimeTable1=zeros(9,5);%represent only the group numbers %Table gives values for each timeperiod according to preferences Table1=[1,2,3,4,5;6,7,8,9,10;11,12,13,14,15;16,17,18,19,2 0;21,22,23,24,25,;26,27,28,29,30;31,32,33,100,35;36,37,10 0,100,100;41,42,100,100,100]; fori=1:9 for j=1:5 for k=1:45 if Table1(i,j)==k TimeTable1(i,j)= TT(k); end 68 end end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %following loop will assign consecutive time periods fori=C1+1:t_courses for p=1:9 for q=1:5 if TimeTable1(p,q)==i for t=1:9 for s=1:5 if (t~=p && s~=q) if TimeTable1(t,s)==i TimeTable1(t,s)=TimeTable1(p+1,q); TimeTable1(p+1,q)=i; end; end end end end end end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Adjust the two hrs in 11-12 i=4; for k=C1+1:t_courses for j=1:5 if (TimeTable1(i,j)==k && TimeTable1(i+1,j)==k) TimeTable1(i,j)=0; TimeTable1(i+2,j)=k; end end 69 end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% GUI Table [credit,courseunit,compose]=xlsread('Grouping.xlsx','Shee t2'); NewTable=cell(9,5); fori=1:9 for j=1:5 for p=1:t_courses if compose{p,2}==TimeTable1(i,j) NewTable{i,j}=compose{p,1}; end end end end f = figure('Position',[0 0 1 1]); set(f,'unit','normalized'); % Column names and column format columnname = {'Monday','Tuesday','Wednesday','Thursday','Friday'}; %columnformat = {'char','char','char','char','char'}; columnformat = {'numeric','numeric','numeric','numeric','numeric'}; FontSize = 9; FontWeight='bold'; 70 rownames = {'8.00-8.50','8.55-9.45','10.15-11.05','11.10- 12.00','1.00-2.00','2.00-3.00','3.00-4.00','4.00- 5.00','5.00-5.45'}; % Define the data fori=1:9 for j=1:5 d{i,j}=NewTable{i,j}; end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Create the uitable t = uitable('Data', d,... 'ColumnName', columnname,... 'ColumnFormat', columnformat,... 'ColumnWidth',{300 },... 'FontSize',FontSize,... 'FontWeight',FontWeight,... 'RowName',rownames); %set(t,'BackgroundColor',[0 0.9 1]); end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% if Time==3 [l1_3]=xlsread('Grouping3.xlsx','onehr'); [l2_3]=xlsread('Grouping3.xlsx','twohr'); [T1_3]=xlsread('Grouping.xlsx','Timeslots'); C1_3=length(l1_3); C2_3=length(l2_3); t_courses3=length(l1_3)+length(l2_3); % total no of courses n_times=length(T1_3); %total no of time slots l=1;u=n_times; 71 A1_3=zeros(t_courses3,t_courses3*n_times); %initializing fori=1:t_courses3 for q=l:u A1_3(i,q)=1; end l=u+1; u=u+n_times; end H_3=ones(C1_3+C2_3,1); %initializing fori=C1_3+1:t_courses3 H_3(i)=2; end A2_3=zeros(n_times,t_courses3*n_times);% initializing fori=1:n_times for q=1:t_courses3 A2_3(i,n_times*q+i-n_times)=1; end end B_3=ones(n_times,1); % integer linear program intcon=1:1008; % all decision variables are integers % z is the objective function z=zeros(n_times*t_courses3,1); k=1; fori=1:t_courses3 for q=1:n_times z(k)=sqrt(q)+1; k=k+1; 72 end end % giving lower and upper bounds for decision variables(binary) lb=zeros(n_times*t_courses3,1); ub = ones(n_times*t_courses3,1); % y is the solution of the ILP y=intlinprog(z,intcon,A2_3,B_3,A1_3,H_3,lb,ub); % representing the solution in to matrix n=1;X=zeros(C1_3+C2_3,n_times); for p=1:C1_3+C2_3 for q=1:42 X(p,q)=y(n); n=n+1; end end TT=zeros(1,45); Courses=1:C1_3+C2_3; fori=1:C1_3+C2_3 for j=1:n_times if X(i,j)==1 TT(j) = i; end end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% TimeTable3=zeros(9,5); Table3=[1,2,3,13,14;4,5,6,15,16;7,8,9,17,18;10,11,12,19,2 0;21,22,23,36,37;24,25,26,38,39;27,28,29,100,100;30,31,32 ,100,100;33,34,100,100,100]; 73 fori=1:9 for j=1:5 for k=1:45 if Table3(i,j)==k TimeTable3(i,j)= TT(k) end end end end fori=C1_3+1:t_courses3 for p=1:9 for q=1:5 if TimeTable3(p,q)==i for t3=1:9 for s=1:5 if (t3~=p && s~=q) if TimeTable3(t3,s)==i TimeTable3(t3,s)=TimeTable3(p+1,q); TimeTable3(p+1,q)=i; end; end end end end end end end i=4; for k=C1_3+1:t_courses3 for j=1:5 if (TimeTable3(i,j)==k && TimeTable3(i+1,j)==k) TimeTable3(i,j)=0; TimeTable3(i+2,j)=k; end 74 end end TimeTable3(3,1)=23;TimeTable3(9,1)=11;TimeTable3(6,3)=16; TimeTable3(8,2)=9;TimeTable3(5,4)=17;TimeTable3(6,4)=17; TimeTable3(4,4)=12;TimeTable3(7,2)=18;TimeTable3(9,2)=8;T imeTable3(4,1)=4; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% [credit3,courseunit3,compose3]=xlsread('Grouping3.xlsx',' groups3'); NewTable3=cell(9,5); fori=1:9 for j=1:5 for p=1:t_courses3 if compose3{p,3}==TimeTable3(i,j) NewTable3{i,j}=compose3{p,1}; end end end end f3 = figure('Position',[200 400 400 400]); % Column names and column format columnname = {'Monday','Tuesday','Wednesday','Thursday','Friday'}; %columnformat = {'char','char','char','char','char'}; columnformat = {'numeric','numeric','numeric','numeric','numeric'}; FontSize = 9; FontWeight='bold'; 75 rownames = {'8.00-9.00','9.00-10.00','10.00- 11.00','11.00-12.00','1.00-2.00','2.00-3.00','3.00- 4.00','4.00-5.00','5.00-6.00'}; % Define the data fori=1:9 for j=1:5 d3{i,j}=NewTable3{i,j}; end end % Create the uitable t3 = uitable('Data', d3,... 'ColumnName', columnname,... 'ColumnFormat', columnformat,... 'ColumnWidth',{300 },... 'FontSize',FontSize,... 'RowName',rownames); set(t3,'BackgroundColor',[0 1 0.7]); end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% if Time==2 [l1_2]=xlsread('Grouping2.xlsx','onehr'); [l2_2]=xlsread('Grouping2.xlsx','twohr'); [T1_2]=xlsread('Grouping.xlsx','Timeslots'); C1_2=length(l1_2); C2=length(l2_2); t_courses2=length(l1_2)+length(l2_2); % total no of courses n_times=length(T1_2); %total no of time slots l=1;u=n_times; 76 A1_2=zeros(t_courses2,t_courses2*n_times); %initializing fori=1:t_courses2 for q=l:u A1_2(i,q)=1; end l=u+1; u=u+n_times; end H_2=ones(C1_2+C2,1); %initializing fori=C1_2+1:t_courses2 H_2(i)=2; end A2_2=zeros(n_times,t_courses2*n_times);% initializing fori=1:n_times for q=1:t_courses2 A2_2(i,n_times*q+i-n_times)=1; end end B_2=ones(n_times,1); % integer linear program intcon=1:882; % all decision variables are integers % z is the objective function z=zeros(n_times*t_courses2,1); k=1; fori=1:t_courses2 for q=1:n_times z(k)=sqrt(q)+1; 77 k=k+1; end end % giving lower and upper bounds for decision variables(binary) lb=zeros(n_times*t_courses2,1); ub = ones(n_times*t_courses2,1); % y is the solution of the ILP y=intlinprog(z,intcon,A2_2,B_2,A1_2,H_2,lb,ub); % representing the solution in to matrix n=1;X=zeros(C1_2+C2,n_times); for p=1:C1_2+C2 for q=1:42 X(p,q)=y(n); n=n+1; end end TT=zeros(1,45); Courses=1:C1_2+C2; fori=1:C1_2+C2 for j=1:n_times if X(i,j)==1 TT(j) = i; end end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% TimeTable2=zeros(9,5); 78 Table2=[11,13,15,17,19;12,14,16,18,20;1,3,5,7,9;2,4,6,8,1 0;21,23,25,27,29;22,24,26,28,30;31,32,33,100,34;35,36,37, 100,100;38,39,40,100,100]; fori=1:9 for j=1:5 for k=1:45 if Table2(i,j)==k TimeTable2(i,j)= TT(k); end end end end fori=C1_2+1:t_courses2 for p=1:9 for q=1:5 if TimeTable2(p,q)==i for t2=1:9 for s=1:5 if (t2~=p && s~=q) if TimeTable2(t2,s)==i TimeTable2(t2,s)=TimeTable2(p+1,q); TimeTable2(p+1,q)=i; end; end end end end end end end 79 i=4; for k=C1_2+1:t_courses2 for j=1:5 if (TimeTable2(i,j)==k && TimeTable2(i+1,j)==k) TimeTable2(i,j)=0; TimeTable2(i+2,j)=k; end end end TimeTable2(4,5)=22;TimeTable2(7,5)=3;TimeTable2(4,2)=5;Ti meTable2(8,3)=15; [credit2,courseunit2,compose2]=xlsread('Grouping2.xlsx',' groups2'); NewTable2=cell(9,5); fori=1:9 for j=1:5 for p=1:t_courses2 if compose2{p,2}==TimeTable2(i,j) NewTable2{i,j}=compose2{p,1}; end end end end f2 = figure('Position',[200 400 400 400]); % Column names and column format 80 columnname = {'Monday','Tuesday','Wednesday','Thursday','Friday'}; %columnformat = {'char','char','char','char','char'}; columnformat = {'numeric','numeric','numeric','numeric','numeric'}; FontSize = 9; FontWeight='bold'; rownames = {'8.00-8.50','8.55-9.45','10.15-11.05','11.10- 12.00','1.00-2.00','2.00-3.00','3.00-4.00','4.00- 5.00','5.00-5.45'}; % Define the data fori=1:9 for j=1:5 d2{i,j}=NewTable2{i,j}; end end % Create the uitable t2 = uitable('Data', d2,... 'ColumnName', columnname,... 'ColumnFormat', columnformat,... 'columnWidth',{300},... 'FontSize',FontSize,... 'RowName',rownames); %set(t2,'BackgroundColor',[1 0 0.9]); end 81 MATLAB Results 82 First Year Timetable 83 Second Year Timetable Third Year Timet 84 APPENDIX C -FACULTY OF APPLIED SCIENCES - MASTER TIME TABLE 2016 Time MON TUE WED THU FRI 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 8.00 - 8.50 CHE MAT PHY CHE MAN CHE MAT EMF CHE CSC ZOO CHE STA ZOO MAT CSC PST PBT CSC STA CSC PBT CSC CSC EMF MAT MAN MAT PBT ECN ARM ICT BIO ARM ECN ECN PST ZOO FSC FSC PBT ICT BIO PBT 8.55 - 9.45 CSC MAT PHY CHE STA ZOO MAT CSC EMF PHY ZOO PBT MAT ECN PST PBT CSC PST CSC EMF EMF CSC FSC MAT CHE MAT PHY ICT PHY PST ICT ECN PST BIO ARM EMF BIO 10.15 - 11.05 STA MAN ZOO PHY PHY STA CSC CHE MAT PBT STA STA MAN CSC MAT PBT ECN MAN PST CSC ZOO PHY MAN MAN FSC PST BIO FSC ECN ECN BIO FSC PST ZOO ICT PST ICT ICT PST 11.10 - 12.00 STA MAN ZOO PHY PHY STA CSC CHE MAT MAN EMF STA MAN CSC MAT PBT MAN ZOO CSC ZOO PBT AQS STA FSC PST PST ARM ECN BIO PHY PST ICT BIO FSC PST ICT ZOO PST ECN FSC 01.00 - 02.00 ARM FSC CSC ZOO MAT MAT STA PBT CSC MAN CHE MBL EMF MAT MAT EMF BIO ZOO ZOO PBT MAN FSC ECN EMF STA MBL EMF BIO PST ICT ICT STA FSC BIO PST PST FSC 02.00 - 03.00 ARM FSC MAT MAN MBL PHY CSC EMF STA EMF EMF ZOO CSC CHE STA MAN MBL MAT PST STA MAN ECN FSC AQS FSC ZOO BIO PBT PBT FSC STA MAT BIO ICT ICT FSC 03.00 - 04.00 PHY PHY STA EMF ICT PBT EMF MAN STA ZOO ICT PBT STA STA STA MAN 04.00 - 05.00 ZOO PHY STA IT MAN PHY MAT PHY CHE STA BIO MAN CHE ICT PBT PBT EMF ICT PBL PBT 05.00 - 05.45 MAN MAN CHE CHE MAN MAT MAN PST PST Time Slots for Student Activities 85 FACULTY OF APPLIED SCIENCES –PROPSOED MASTER TIME TABLE 2016 Time MON TUE WED 1 2 3 1 2 3 1 2 3 8.00 - 8.50 CHE 110 1.0 ARM 202 1.0 MAT 304 1.0 BIO 103 1.0 PBT 226 1.0 MAT 302 2.0 CHE 107 2.0 PBT 227 1.0 CHE 320 1.0 EMF 204 1.0 ZOO 338 1.0 MAN 104 1.0 PHY 225 2.0 ZOO 322 2.0 CSC 107 2.0 PHY 226 1.0 CSC 313 2.0 ICT 202 1.0 STA 115 1.0 FST 270 1.0 ECN 102 2.0 FST284 1.0 PST 104 1.0 8.55 - 9.45 ARM 106 1.0 BIO 202 2.0 ZOO 320 2.0 PBT 226 1.0 MAT 302 2.0 CHE 107 2.0 ZOO 227 1.0 CHE 320 1.0 EMF 115 1.0 MAN 202 2.0 PHY 225 2.0 ZOO 322 2.0 CSC 107 2.0 CSC 313 2.0 MAT 103 1.0 STA 215 2.0 FST 270 1.0 ECN 102 2.0 PST 207 1.0 10.15 - 11.05 MAT 102 2.0 BIO 202 2.0 ZOO 320 2.0 PBT 122 2.0 CHE 204/211 CHE 302 1.0 MAT 101 2.0 CHE 209 2.0 PBT 381 2.0 ZOO 118/120 MAN 202 2.0 PHY 104/105 CSC 203 1.0 CSC 314 2.0 CSC 201 2.0 STA 215 2.0 ECN 201 2.0 ECN 202 2.0 PST 207 1.0 11.10 - 12.00 MAT 102 2.0 BIO 203 1.0 PBT 382 1.0 PBT 122 2.0 CHE 204/211 ZOO 340 1.0 MAT 101 2.0 CHE 209 2.0 PBT 381 2.0 ZOO 118/120 EMF 201 1.0 PHY 325 PHY 104/105 CSC 203 1.0 CSC 314 2.0 CSC 201 2.0 STA 214 1.0 ECN 201 2.0 ECN 202 2.0 MAT 201 1.0 01.00 - 02.00 BIO 101 1.0 PBT 231 1.0 PBT 383 2.0 CHE 112 1.0 MAT 204 2.0 BIO 304 1.0 ARM 104 1.0 ARM203 2.0 BIO 301 2.0 MAN 101 2.0 PHY 222 2.0 PHY 326 1.0 ZOO 215 2.0 EMF 312 1.0 FSC 191 1.0 EMF 220 1.0 MAN 327 2.0 PST 102 1.0 STA 324 1.5 EMF 101 1.0 ICT 203 2.0 STA 322 1.5 STA 113 2.0 ICT 104 1.0 FST 256 1.0 PST 307 1.0 02.00 - 03.00 BIO 101 1.0 PBT 231 1.0 PBT 383 2.0 PBT104 1.0 MAT 204 2.0 ARM308 2.0 ZOO 128 1.0 ARM203 2.0 BIO 301 2.0 MAN 101 2.0 PHY 222 2.0 PHY 326 1.0 PHY 131 1.0 ZOO 215 2.0 FSC 361 1.0 EMF 220 1.0 MAN 327 2.0 PST 102 1.0 EMF 317 1.0 ICT 203 2.0 STA 322 1.5 STA 113 2.0 ICT 326 2.0 FST 256 1.0 PST 307 1.0 03.00 - 04.00 BIO221 1.0 CHE 319 1.0 ARM308 2.0 BIO 201 1.0 ARM 307 1.0 MAN 203 1.0 CSC 319 2.0 FSC 361 1.0 MAN 201 2.0 FSC 332 1.0 PST 216 1.0 EMF 317 1.0 STA 213 2.0 EMF 316 1.0 STA 214 1.0 ICT 326 2.0 PST 206 1.0 ICT 327 1.5 04.00 - 05.00 CHE 319 1.0 BIO 302 1.0 BIO 201 1.0 PBT 380 1.0 CSC 319 2.0 MAN 326 1.0 MAN 201 2.0 PHY 381 1.0 STA 321 1.5 STA 213 2.0 PST 301 1.0 PST 206 1.0 05.00 - 05.45 ARM 306 1.0 FSC 361 1.0 EMF 315 1.0 ICT 328 1.5 86 THU FRI 1 2 3 1 2 3 ARM 101 1.0 ARM 207 2.0 PBT 384 2.0 CHE 108 /110 CHE 205 1.0 CHE 312 1.0 FSC 122 2.0 EMF 221 1.0 PHY 321/322 CSC 106 1.5 EMF 103 1.0 MAT 202 2.0 ICT102 2.0 FST 281 2.0 PST 102 2.0 ARM 101 1.0 ARM 207 2.0 PBT 384 2.0 CHE 108 /110 MAT 205 1.0 ARM 311 1.0 FSC 122 2.0 EMF 221 1.0 PHY 321/322 CSC 106 1.5 ZOO 217 1.0 FSC 353 1.0 EMF 103 1.0 MAT 202 2.0 EMF 319 1.0 ICT102 2.0 FST 281 2.0 ICT 329 1.5 PST 102 2.0 ARM 107 1.0 ZOO 220 1.0 CSC 312 2.0 ARM 102 1.0 CSC 207 1.0 BIO 303 1.0 PBT 121 2.0 ECN 202 2.0 FSC111 1.0 CHE 208 1.0 EMF 311 1.0 PHY 103 2.0 CHE309/340 EMF 106 1.0 STA 323 1.5 ICT 101 1.0 PST 313 1.0 PST 101 1.0 ARM 107 1.0 ZOO 218 1.0 CSC 312 2.0 CHE 102 1.0 MAT 303 1 .0 PBT 121 2.0 ECN 202 2.0 CSC 105 1.0 ZOO 323 1.0 PHY 103 2.0 CHE309 /340 ECN 101 1.0 BIO 102 2.0 PBT 221 1.0 BIO 305 1.0 ZOO 126 1.0 PST 217 1.0 CHE 302 1.0 MAN 102 2.0 PHY 221 2.0 EMF 314 1.0 ARM 203 2.0 CSC 314 2.0 STA 114 2.0 FST 278/283 MAT 3012.0 EMF213 1.0 PST 101 2.0 ICT 201 2.0 FST 252 1.0 BIO 102 2.0 PBT 221 1.0 BIO 305 1.0 PST 217 1.0 CHE 302 1.0 MAN 102 2.0 PHY 221 2.0 EMF 314 1.0 ARM 2032.0 CSC 314 2.0 STA 114 2.0 FST 278/283 MAT 301 2.0 EMF213 1.0 PST 101 2.0 ICT 201 2.0 FST 252 1.0 Time Slots for Student Activities 87