7 Timetable test 1 The Combing Chart

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1 7 Timtabl tst 1 Th Combing Chart 7.1 Introduction 7.2 Tachr tams two workd xampls 7.3 Th Principl of Compatibility 7.4 Choosing tachr tams workd xampl 7.5 Ruls for drawing a Combing Chart 7.6 Th Combing Chart workd xampl 7.7 Th Combing Chart for mor than on dpartmnt workd xampls 7.8 Th principl of compatibility and tim 7.9 Th principl of compatibility and class-combinations 7.10 Th principl of compatibility and room-combinations 7.11 Summary Th First Law of Timtabling stats that: th sts of data rcivd on th Data Collction Forms ar almost crtainly incompatibl! Bcaus of th wid rang of options that w offr in our schools and bcaus w usually allow dpartmnts som frdom in choosing th staff to tach th groups, th sts of data w rciv almost crtainly contain som mathmatical impossibilitis. Th Scond Law stats: Any impossibilitis in th data will forc th Timtablr to mak compromiss during th actual schduling stag of th timtabl, and any compromiss thn ar likly to damag th quality of th timtabl! All schduling is likly to involv som compromis, although obviously w wish th compromising to b as inconsquntial as possibl. Compromiss mad in a logical way at this prsnt stag ar likly to hav lss consqunc and b mor accptabl to th staff than compromiss forcd on th timtablr during th schduling stag. Th compromiss that hav com to b accptd by th taching staff vary somwhat from school to school. Timtablrs naturally vary in th amount of patinc and ingnuity thy can maintain in ordr to obtain a bttr solution. Som of th compromiss that may b forcd during schduling ar listd in th box on th nxt pag. Thr is no known mthod of dtrmining whthr a givn st of data can b timtabld without compromis (othr than by complting a full timtabl). Howvr, thr ar tsts which will dtct som of th impossibilitis and pinpoint th rasons for thm. This chaptr covrs th fi rst of ths tsts. Chaptr 7 - Th Combing Chart 85

2 Som of th compromiss that may occur during schduling: 1 Altration to th rqustd priod sprad. This happns most frquntly to English, Maths and Modrn Languags. g. Frnch schduld for 5 priods on 4 days instad of 1 priod pr day. 2 Altration to th rqustd priod brakdown. g. Art or Scinc schduld as singl priods in Yar 7 although doubls wr rqustd. 3 Spcialist subjcts taught in ordinary classrooms. g. all four priods of Scinc taught in a classroom. 4 Th rqustd tachr rplacd by an altrnativ in th sam dpartmnt. g. a young nw tachr rplacs th Had of Dpartmnt for a tough Yar 10 class. 5 Th rqustd tachr rplacd by an altrnativ in th sam dpartmnt for som priods during th wk. g. class 9A has two tachrs for Maths (calld split taching ). 6 Th rqustd tachr rplacd by a mmbr of anothr dpartmnt. g. som tim ago, a Dputy was hard to say (at th schduling stag): Thos two Tchnology tachrs will hav to tach Maths. 7 Stting schduld for only som of th priods. g. Yar 9 Maths sttd for only 3 out of th 4 priods. 8 Multipl priods spanning a brak or a lunchtim. g. a doubl priod of Scinc across a brak. 9 Altration to th xpctd numbr of priods. g. Yr 12 Chmistry allocatd only 4 priods instad of th usual 5 priods. 10 Inability to allocat any tachr. g. a Dputy was hard to say (at th schduling stag): This Yar 10 subjct will hav to b canclld. In considring th fasibility tsts in this chaptr (and th nxt thr chaptrs) it is important to rmmbr that it is tachrs that clash, not subjcts. i. confl icts ar not introducd dirctly by th curriculum on which w hav dcidd, but only indirctly by way of th staff who ar chosn to tach th groups. For som groups th Subjct Ladr s choic of a tachr will b mad for sound ducational rasons; for othr groups th choic may b arbitrary. Onc th fasibility tsts hav pinpointd an ara of diffi culty, on can look for simpl and accptabl modifi cations to th data on th Data Collction Forms. Ths modifi cations may b crucial but simpl. Prhaps, by happnstanc, a crtain tachr is du to tach 7A, according to th Data Collction Form. For timtabling, th fasibility tsts show that it would b far bttr if h taught 7B instad. Th Had of Dpartmnt dos not mind, th tachr dos not mind, but for th timtablr th diffrnc could b crucial. 86 Timtabling

3 7.2 Tachr tams Tams of tachrs ar obviously mor diffi cult to schdul than singl tachrs. Th numbr and siz of th tachr tams in our schools tnd to incras as Subjct Ladrs rqust thm for a varity of rasons: to allow tam taching or stting (by attainmnt or ability lvl), g. in Mathmatics, English, Languags, to allow a choic of subjcts, g. in th option pools, to allow sparation by sx, g. for PE, to rduc class siz, g. if two classs ar schduld togthr and allocatd thr tachrs, to allow a cycl of rotation during th yar, g. in Tchnology. Th way in which ths tams ar chosn can hav a hug ffct on th schduling diffi culty and fi nal quality of th timtabl. In choosing th tams for ths activitis, w want th tams to b compatibl so thy can b timtabld within th numbr of priods in th timtabl cycl. Workd Exampl 1 Considr a small dpartmnt consisting of thr tachrs, AA, BB, and CC. Each is du to tach for 20 priods, in a 25-priod wk. On th Data Collction Form, th Subjct Ladr rqusts that: tachrs AA and BB tach togthr for 10 priods and tachrs BB and CC tach togthr for 10 priods and tachrs AA and CC tach togthr for 10 priods Qustion: is this possibl? To s if this is a rasonabl rqust, w can draw a tim-chart (s blow). Th vrtical axis (s blow) shows th thr tachrs. Th horizontal axis shows a lngth of tim in priods. By drawing a horizontal bar for ach tachr in a tachr-tam, w can s th total numbr of priods ndd for this small dpartmnt: pds: AA BB CC W can s that this arrangmnt rquirs 30 priods (vn though ach tachr tachs only 20 priods). It could not possibly fi t into th 25-priod wk, just bcaus th staff ar in tams. Th rd ara shows th priods ndd byond th 25-priod wk th staff would hav to tach at th wknd! Th chosn tams wr not compatibl with th availabl timfram. Chaptr 7 - Th Combing Chart 87

4 Workd Exampl 2 A small Mathmatics dpartmnt consists of 6 tachrs, numbrd 1 to 6. Each tachr is to tach for 20 priods. Thy ar in an school (Yars 7 11) whr ach of th fi v yar-groups is dividd into 2 half-yar bands (calld A and B). Each band rquirs a tam of 3 tachrs, for 4 priods. Th Had of Maths might rqust th tams shown hr: priods: t a c h r s A 11B 10A 10B 9A 9B 8A 8B 7A 7B Th chart shows that th tam for Yar 11 band A is mad of tachrs 1, 2, 3. For band 11B, th tachrs ar 1, 4, 5. Ths two tams cannot tach at th sam tim bcaus thy hav tachr 1 in common (and tachr 1 cannot tach two classs at th sam tim). For 10A th tachrs ar 3, 4, 6. This tam cannot tach at th sam tim as th 11A tam (bcaus of tachr 3), nor can this tam tach at th sam tim as th 11B tam (bcaus of tachr 4). Th thr tams considrd so far would nd 3 x 4 = 12 priods of th wk. Inspcting th othr tams on by on shows that non of thm can tach at th sam tim as any othr tam. Each tam ovrlaps vry othr tam. Each tachr tachs fi v classs, ach of 4 priods, and so tachs 20 priods pr wk. Howvr, sinc no tam can xist at th sam tim as any othr tam, th total lngth of tim ndd for th tams to tach all 10 bands is 10 x 4 = 40 priods. In a 25-priod wk this is clarly impossibl. That xampl was an xtrm cas whr all th tams clash. Now considr an idal situation, unlikly to b obtaind in practic but somthing to aim for. Th diagram blow shows th sam Maths dpartmnt with th sam 6 tachrs taching th sam numbr of groups: priods: t a c h r s A 11B 10A 10B 9A 9B 8A 8B 7A 7B 88 Timtabling

5 In th diagram th tam for 11A dos not ovrlap th tam for 11B. Th tams ar said to b non-ovrlapping or disjoint or compatibl. This mans that 11A and 11B can b timtabld at th sam tim. Similarly with 10A, 10B tc. Comparing th two diagrams abov for this Maths dpartmnt, w can s th diffrnc btwn thm: th scond diagram can b squzd up by sliding th 4, 5, 6 tams to th lft, undr th 1, 2, 3 tams. Th whol diagram will thn fi t into a tim of only 20 priods, as shown blow: priods: t a c h r s A 10A 9B 8A 8B 11B 10B 9A 7A 7B It is clar that ths non-ovrlapping ( disjoint ), compatibl tams giv much gratr fl xibility at th schduling stag. In fact thr ar two advantags with non-ovrlapping tams: Non-ovrlapping tams will fi t into a smallr numbr of priods (ovrlapping tams may not fi t into th school wk). Thr is a gratr numbr of diffrnt ways of fi tting non-ovrlapping tams. In th last diagram, th labls show 11A paird with 11B, but 11A could wll b paird with 10B whil 11B could b paird with 8A tc. This intrchangability givs you much gratr fl xibility at th schduling stag. Ths diagrams ar calld Combing Charts. Th horizontal bars for th tams can b thought of as th tth of combs which allow or prvnt othr tams moving or combing to th lft. 7.3 Th Principl of Compatibility In th light of th prvious sction lt us s how a dpartmnt might choos idal tachr tams. Considr a larg dpartmnt English, Maths or prhaps Scinc consisting of 12 tachrs, numbrd Suppos that for on of th yar-groups w nd a tam of 6 tachrs. Clarly thr ar many ways of choosing 6 tachrs, but suppos w choos th tachrs numbrd from 1 to 6. This tam is markd as 6-tam-A in th diagram on th nxt pag. Suppos now that w nd a tam of 6 tachrs for anothr yar-group. Thr ar only two possibilitis if w want non-ovrlapping tams ithr w choos th tam of th sam 6 tachrs (6-tam-A) or w choos th tam of th othr 6 tachrs (6-tam-B). continud... Chaptr 7 - Th Combing Chart 89

6 Th chaptr continus with: 7.3 Th Principl of Compatibility and how to us it to gt mor flxibility 7.4 Choosing tachr tams a workd xampl 7.5 Ruls for drawing a Combing Chart 7.6 Th Combing Chart workd xampl 7.7 Th Combing Chart for mor than on dpartmnt workd xampls 7.8 Th principl of compatibility and tim 7.9 Th principl of compatibility and class-combinations 7.10 Th principl of compatibility and room-combinations 7.11 Summary 90 Timtabling

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