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# ANALYSIS OF UNIVERSITY TIMETABLE SCHEDULING PARAMETERS TOWARDS PREVENTION OF CLASHES

The three main parameters towards timetable scheduling are the Day, Time and Room. The course, lecture-in-charge, number-of-times –per-lecture, course-type (practical or theoretical), population of student, are regarded as lurking variables which should be considered during the scheduling process. However, in this paper, we set to demonstrate the derivation of unique number of resources which will fit into the scheduling process even if the lurking variables are considered or not.

MATHEMATICAL MODEL

Resource means {Room,Day,Time}

Let R be the Room

Let D be the Day

Let T be the Time

By various arrangement possibilities, we can derive:

Same R, Same D and different T — — i

Same R Same D and Same T — — ii x cannot be considered since the constraint avoids clash

Same R Different D and Different T — -iii

Same R different D and Same T — -iv

Different R different D and Same T — — v

Different R Same D and Same T — -vi

Different R Same D and Different T — -vii

Different R Different D and Different T — -viii

These are all possible ways in which we can arrange R,D and T such that they are unique.

However because of the Constraints involved in scheduling, we would sieve out the arrangements as it would fit the constraint.

CONSTRAINTS

1. For two different courses offered by a particular level

<They both must not be at same T and same D>

Hence possible resource that can fit this would be

All the arrangements except ii and vi (clash case)

2. Same level of different department offering common course

<Considering their respective level course, resource that fit this common course will be>

I, iii, iv, v, vii and viii

<Considering other departments, resource that fit will be>

All arrangement with different R

3. For a course taken twice in a week by a particular level

<considering the first course has been assigned with rule 1. The resource that will fit the second course scheduling will be >

Iii, iv, v

<Considering other departments, resource that fit will be>

Same as constraint 2’s consideration of other department

DETERMINING THE TOTAL NUMBER OF ALLOCATABLE RESOURCE

Considering that a resource has been taken, determining the total number of allocatable resource will be:

For the minimum, if number of Room is 1 and the timeslot happen to spread about 5 per day, the total unique allocatable resources or total number of courses that can be allocated to these resources will be:

Runique = 10(1–1)+29

= 29

PROOF

Suppose as we have earlier considered a resource(Room, Day, Time) been scheduled i.e (ETF, MON, 7–9); here our timeslot is [7–9,9–11,11–1,1–3,3–5]

We try to determine how many unique resources can there be:

1. EFT MON 9–11

2. ETF MON 11–1

3. ETF MON 1–3

4. ETF MON 3–5

5. ETF TUE 7–9

6. ETF TUE 9–11

7. ETF TUE 11–1

8. ETF TUE 1–3

9. ETF TUE 3–5

10. ETF WED 7–9

11. ETF WED 9–11

12. ETF WED 11–1

13. ETF WED 1–3

14. ETF WED 3–5

15. ETF THUR 7–9

16. ETF THUR 9–11

17. ETF THUR 11–1

18. ETF THUR 1–3

19. ETF THUR 3–5

20. ETF FRI 7–9

21. ETF FRI 9–11

22. ETF FRI 11–1

23. ETF FRI 1–3

24. ETF FRI 3–5

25. ETF SAT 7–9

26. ETF SAT 9–11

27. ETF SAT 11–1

28. ETF SAT 1–3

29. ETF SAT 3–5

This shows that our model was able to derive how many unique resources that can be allocated to various courses while satisfying the constraints.

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## Kingsley Izundu

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