500 words essay 4 hrs with UK

Initial state: (1) From timetable1, an empty timetable contains the time period from 9:00-

18:00, from Monday to Friday, this timetable can be used to allocate modules and the specific

lecture theatres. (2) From table 2, another list shows the modules booking arrangements in

the lecture theatres.

09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00

Monday

Tuesday

Wednesday

Thursday

Friday

(timetable 1 –date and time)

We can place specific module、lecture and theatre in the timetable1 cell.

(table2 –arrangements of module and theatres)

1 hour

time

Module 1 Module 2 . . . Module n

Lecture1 Lecture2 Lecture3 Lecture4 … … Lecture2n-1 Lecture2n

Theatre 1 available occupied available available available available

Theatre 2 available available available available available available

. . . available available available available available available

Theatre

m

available available available available available available

Goal state: (1) every lecture should be allocated in theatre for 1 hour and every theatre

should only have allocated one lecture in a certain time period. (2) It is considered that many

students live far away from the school, so it’s better to allocate lectures in one day. (3) indicate

the specific theatre and module on timetable, for example, n=2, m=4.

Therefore, we need 4 theatres to allocate 2 modules at most in timetable3 and one theatre

for 2 modules at least in timetable4. (1) For best solution: If we allocate all lectures in one

day, the timetable as follow:

09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00

Monday Module1-

Lecture1

theater1

Module1-

Lecture2

Theater2

Module2-

Lecture3

Theater3

Module2-

Lecture4

Theater4

Tuesday

Wednesday

Thursday

Friday

------(Timetable3)

09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00

Monday Module1-

Lecture1

theater1

Module1-

Lecture2

theater1

Module2-

Lecture3

theater1

Module2-

Lecture4

theater1

Tuesday

Wednesday

Thursday

Friday

------(Timetable4)

Possible actions and effects:

Assume (lecture a, time b, theatre c), so that n modules have 2n lectures and there are m

theatres, which is 1<= a<=2n,9:00<=b<=18:00,1<=c<=m.

For example, if n=1, m=1:

09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00

Monday Module1-

Lecture1

theater1

Module1-

Lecture2

theater1

Tuesday

Wednesday

Thursday

Friday

From the previous timetable, if there are two lectures in theatre 1 from Monday 9:00 -10:00

and 10:00 -11:00, this action means that students can just come to university once a week. If

we allocate the lecture 2 and lecture 1 in different weekdays, for example, Tuesday 10:00, this

action means that students should come to school twice a week and it’s unfortunate for

students who live away from school.

To sum up, it’s better to allocate lectures in one day and it can reduce the times to go to

school.

Cost function：cost of actions refers to the times to school per week. The cost function

is the sum of all of actions costs.