# Analysing timetable clashes : the Conflict Matrix

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3 Factsheet: S1 The Conflict Matrix The art of timetabling consists of being able to resolve a number of conflicting demands. These conflicts often arise because of the composition of the teacher-teams, particularly within option blocks. For the Timetabler, and therefore for the quality of the timetable as it affects every member of staff, it is important to be able to pin-point potential difficulties early. Discussions between the Timetabler and the departments that are affected may then be used to reduce the conflicts, with the likelihood of a better timetable for all. Potential conflicts can be identified by using a Conflict Matrix or clash table. Suppose for example that one teacher-team in the Year 11 (Fifth Year) consists of two teachers, with initials AA and BB. A second teacher-team, also in Year 11, consists of teachers CC, DD, and EE. Meanwhile in (Fourth Year) there is one teacher-team of AA and CC, and another team of CC, EE, FF. By drawing a simple Conflict Matrix, we can see where the clashes occur: Year 11 Team 1 Team 2 AA, BB CC, DD, EE Team 1 AA CC AA, CC Team 2 CC, EE CC, EE, FF This shows at a glance that, of these teams, only Year-11-team-1 and Year-10-team-2 could be timetabled at the same time - all the others clash because a teacher cannot be expected to teach two classes at the same time! Even the apparent freedom of a clear cell may be illusory - for example, if one team required double periods and the other required single periods, or if both teams required the one and only Drama Studio (or another unique resource). A point worth noting is that two clashes (as in the bottom right cell of this matrix) are no worse than one clash - both represent impossibilities. By negotiating with heads of department it is often possible for the Timetabler to clear some cells of the matrix, and so improve the situation, by deliberately creating multiple clashes elsewhere. As a further example, the next sheet shows a matrix summarising the clashes of all the teams in Year 11 against all the teams in. continued... Preparing for the timetable: part 3 page 3 Keith Johnson 1990, 1999

4 X X X X X 2 X X X X 3 X X X X X Year 11 4 X X X X 5 X X X X 6 X X X X 7 X X X X X 8 X X X X 9 X X X X In this Conflict Matrix each X shows a clash. It is clear that Y10-team-6 cannot be timetabled at all -- it clashes against every Y11 team. Other teams are tight, especially as the effects of different period-styles (doubles, singles, etc) have yet to be reckoned with. If two teams need the same unique resource (eg. a drama studio, or a computer room) then this will add further clashes to the grid. Obvious difficulties like these should always be resolved (by negotiation) before the Timetabler begins the actual scheduling of the timetable. Further reading: chapter 6 of Timetabling by Keith Johnson (published by Stanley Thornes Ltd, ISBN ). For more details about timetabling, and free software, visit the web-site at: Preparing for the timetable: part 3 page 4 Keith Johnson 1990, 1999

5 Activity 1 S2 The Conflict Matrix In Laura Norder High School, the teacher-teams for and Year 11 are as shown on the diagram: Year 11 AA, BB, CC DD, EE, FF GG, HH, JJ KK, LL, MM NN, OO, PP AA, CC, KK 1 AA, CC KK AA, PP, TT 2 [S] DD, LL, MM 3 GG, LL, NN 4 EE, MM, TT 5 [D] The first row of the matrix has been completed. Please complete the remainder. Assume that the diagram shows all the teams in these two year-groups. Q1. Which team will be hardest to timetable? If that team were scheduled to Monday period 1, which other team would have to be scheduled to Monday period 1? Q2. Suppose now that Y11-team-4 requires a double period and Y10-team-2 must have single periods. What is the situation now? Q3. Discussions between the Timetabler and the Head of Faculty now reveal that teacher LL in Y10-team-4 and teacher TT in Y10-team-5 can be interchanged with no disadvantage to the pupils. How does this improve the situation? Which team would you now timetable at the same time as Y11-team-4? Q4. Now suppose also that teachers MM and TT always need the Drama Studio (or some other unique resource, eg. computer room, minibus, interactive video). What is the situation now? Which teacher would you consider first of all, with a view to negotiating his/her removal or exchange? Preparing for the timetable: part 3 page 5 Keith Johnson 1990, 1999

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