| |||||||||

Timetable for courses and teachers Description We want to establish the weekly timetable for two classes of
a college. The two classes have the same teachers, except
for mathematics and sport. All lessons have a duration of
two hours. All students of the same class attend exactly
the same courses. Every class may only have one two-hour
lesson per subject on a single day. Some teachers are only
available on certain days. Some time slots are reserved
for certain subjects. Further explanation of this example:
'Applications of optimization with Xpress-MP',
Section 14.3 'Establishing a college timetable'
Source Files Data Files timetable_graph.mos (!****************************************************** Mosel Example Problems ====================== file timetable.mos `````````````````` TYPE: Timetabling problem DIFFICULTY: 2 FEATURES: MIP problem, many specific constraints, tricky (pseudo-) objective function, `finalize' DESCRIPTION: We want to establish the weekly timetable for two classes of a college. The two classes have the same teachers, except for mathematics and sport. All lessons have a duration of two hours. All students of the same class attend exactly the same courses. Every class may only have one two-hour lesson per subject on a single day. Some teachers are only available on certain days. Some time slots are reserved for certain subjects. FURTHER INFO: `Applications of optimization with Xpress-MP', Section 14.3 `Establishing a college timetable' (c) 2008 Fair Isaac Corporation author: S. Heipcke, 2002, rev. Sep. 2017 *******************************************************!) model "School timetable" uses "mmxprs", "mmsvg" declarations TEACHERS: set of string ! Set of teachers CLASS = 1..2 ! Set of classes NP = 4 ! Number of time periods for courses ND = 5 ! Days per week SLOTS=1..NP*ND ! Set of time slots for the entire week COURSE: array(TEACHERS,CLASS) of integer ! Lessons per teacher and class end-declarations initializations from 'timetable.dat' COURSE end-initializations finalize(TEACHERS) declarations teach: array(TEACHERS,CLASS,SLOTS) of mpvar ! teach(t,c,l) = 1 if teacher t gives a ! lesson to class c during time period l end-declarations ! Objective: number of "holes" in the class timetables Hole:= sum(t in TEACHERS, c in CLASS, d in 0..ND-1) (teach(t,c,d*NP+1) + teach(t,c,(d+1)*NP)) ! Plan all courses forall(t in TEACHERS, c in CLASS) PlanAll(t,c):= sum(l in SLOTS) teach(t,c,l) = COURSE(t,c) ! For every class, one course at a time forall(c in CLASS, l in SLOTS) OneCourseClass(c,l):= sum(t in TEACHERS) teach(t,c,l) <= 1 ! Teacher teaches one course at a time forall(t in TEACHERS, l in SLOTS) OneCourseTeacher(t,l):= sum(c in CLASS) teach(t,c,l) <= 1 ! Every subject only once per day forall(t in TEACHERS, c in CLASS, d in 0..ND-1) OncePerDay(t,c,d):= sum(l in d*NP+1..(d+1)*NP) teach(t,c,l) <= 1 ! Sport Thursday afternoon (slot 15) teach("Mr Muscle",1,15) = 1 teach("Mrs Biceps",2,15) = 1 ! No course during first period of Monday morning forall(t in TEACHERS, c in CLASS) teach(t,c,1) = 0 ! No course by Mr Effofecks Monday morning forall(l in 1..2) teach("Mr Effofecks",2,l) = 0 ! No Biology on Wednesday forall(c in CLASS, l in 2*NP+1..3*NP) teach("Mrs Insulin",c,l) = 0 forall(t in TEACHERS, c in CLASS, l in SLOTS) teach(t,c,l) is_binary ! Solve the problem minimize(Hole) ! Solution printing declarations DAYS=1..ND NAMES: array(DAYS) of string end-declarations initializations from 'timetable.dat' NAMES end-initializations writeln("Courses at begin or end of day: ", getobjval) forall(c in CLASS) do writeln("Class ",c) forall(d in DAYS) do write(NAMES(d), ": ") forall(l in (d-1)*NP+1..d*NP) if (getsol(sum(t in TEACHERS) teach(t,c,l))>0) then forall(t in TEACHERS) write( if(getsol(teach(t,c,l))>0, strfmt(t,-14), "")) else write(strfmt("",14)) end-if writeln end-do end-do ! Solution drawing forall(t in TEACHERS) do svgaddgroup(t,t) svgsetstyle(SVG_FILL,SVG_CURRENT) svgsetstyle(SVG_STROKE,SVG_GREY) end-do svgaddgroup("msg","text",SVG_BLACK) pos:=CLASS.size*NP+5 svgsetgraphviewbox(0,0,ND*2+2,pos+2) svgsetgraphscale(20) forall(c in CLASS) do svgaddtext("msg", 0, pos, "Class "+c) svgsetstyle(svggetlastobj, SVG_FONTWEIGHT, "bold") pos-=1 forall(d in DAYS) do svgaddtext("msg", d*2+1,pos+0.2,NAMES(d)) svgsetstyle(svggetlastobj,SVG_TEXTANCHOR,"middle") forall(l in (d-1)*NP+1..d*NP) do if d=1 then svgaddtext("msg", 0,pos+0.2-(l-(d-1)*NP),"Slot "+l); end-if if (getsol(sum(t in TEACHERS) teach(t,c,l))>0) then forall(t in TEACHERS | getsol(teach(t,c,l))>0) svgaddrectangle(t, d*2, pos-(l-(d-1)*NP), 2, 1) end-if end-do end-do pos-=(NP+1) end-do svgsave("timetable.svg") svgrefresh svgwaitclose("Close browser window to terminate model execution.", 1) end-model | |||||||||

© Copyright 2021 Fair Isaac Corporation. |