IEEE Systems, Man and Cybernetics Magazine - April 2021 - 28

number of popular seats varies depending on the in situ
occupied-seat rate.
Take the first four rows of a classroom as an example. As
illustrated in Figure 8, if a seat is occupied, it is marked with
an orange color; otherwise, it is blue. Assume that there are
currently six occupants sitting in orange seats in rows 1, 2,
and 4, and the third row is unoccupied. At this time, if the
seventh student takes seat 41 (as depicted in Figure 8), the
number of available popular seats is zero; if the seventh student takes seat 40 or 43 (as demonstrated in Figure 9), the
number of popular seats that remains is one.
The available popular seats are affected by changes in
the status of their left and right adjacent seats. Take a row of
seats in a classroom as an example. In Figure 10, there are
nine seats, where seats 1 and 9 are occupied. Now, seats 4-6
all meet the popular seating conditions, but the actual situation is that after a third occupant sits in any of seats 4-6, the
number of available popular seats is zero.
Let T1 , T2 , and T3 denote the total time of powering on
lecture halls, large classrooms, and small classrooms,
respectively. Let E 1 , E 2 , and E 3 denote the hourly power
consumption of each lecture hall, large classroom, and small
classroom, respectively. Thus, the objective function is
f ^T1, T2, T3 h = |E z Tz .(9)
3

	

z=1

Row 1

1

2

3

4

5

Row 2

20

21

22

23

24

Row 3

39

40

41

42

43

Row 4

58

59

60

61

62

Figure 8. Case 1.

Row 1

1

2

3

4

5

Row 2

20

21

22

23

24

Row 3

39

40

41

42

43

Row 4

58

59

60

61

62

Figure 9. Case 2.

Row 1

1

2

3

4

5

6

7

8

9

Figure 10. Case 3.
28	

IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE Apri l 2021

The average power of air conditioners is 18.15 W/m2, and
the average power of other facilities is 2.659 W/m2. The total
power consumption is 20.809 W/m2. The areas of a lecture
hall, large classroom, and small classroom are 209.25,
122.40, and 81.60 m2, respectively. Thus, E 1 = 4,354.28 W,
E 2 = 2,536.41 W, and E 3 = 1,698.01 W.
Let S 1 , S 2 , and S 3 denote the total number of available
popular seats in lecture halls, large classrooms, and small
classrooms, respectively. Let rs 1 , rs 2 , and rs 3 denote the
number of available popular seats in a lecture hall, large
classroom, and small classroom, respectively.
Let R 1 , R 2, and R 3 represent the number of power-on
lecture halls, large classrooms, and small classrooms,
respectively, that need scheduling. Let t 1,y, t 2,y, and t 3,y
denote the power-on hours of a lecture hall, large classroom,
and small classroom, respectively. It is supposed that the
upper limit of a power-on classroom is 5 h.
	

Rz

Tz = |t z,y , 0 ≤ t z,y # 5, z = 1, 2, 3. (10)
y=1

It is supposed that 20 classrooms of each type are
reserved for lectures or events. They are not available for
student self-study and thus need no scheduling. R z ( z = 1,
2, 3) meets the constraints of (11)-(13). Similarly, rs z
( z = 1, 2, 3) and S z ( z = 1, 2, 3) meet the constraints of
(14)-(16).
	

0 # R 1 # 48, (11)

	

0 # R 2 # 74, (12)

	

0 # R 3 # 23, (13)

	

0 # rs 1 # S 1 # 82, (14)

	

0 # rs 2 # S 2 # 46, (15)

	

0 # rs 3 # S 3 # 14. (16)

Because many students simultaneously arrive at the
classrooms for self-study in a short period of time (such
as 1 min), it is impossible to power on one classroom until
the number of popular seats in a certain type of classroom is
zero at that time.
Let i i with i ! " 1, 2, 3 , denote the threshold numbers of
available popular seats in a lecture hall, large classroom, and
small classroom, respectively. Let H i with i ! " 1, 2, 3 ,
denote the threshold numbers of total available popular
seats in lecture halls, large classrooms, and small classrooms, respectively.
Essentially, in (9), T1 , T2 , and T3 depend on the time
when each classroom is powered on, i.e., the conditions for
powering on a classroom are satisfied. In the case of small
classrooms, when rs 1 # i 1 and S 1 # H 1 , one more small
classroom is scheduled to be powered on. Therefore, i i
and H i with i ! " 1, 2, 3 , should be figured out to determine the conditions for powering on a classroom. This is
discussed next.



IEEE Systems, Man and Cybernetics Magazine - April 2021

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