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Line Of Balance
Q1:
Activity Predecessor Duration Rate
Z W,X,Y 10 4
W R 14 2
R - 8 4
X R 20 8
Y R 12 4
For the 65 units Construction Project using the one unit net work it
is required to:
1) Draw LOB Chart.
2) Check project situation at 46th week.
3) What’s your recommendation if at 60th week activity Z finished in
39 unit ?
R
0 8
8
X
8 28
20
W
8 22
14
Y
8 20
12
Z
28 38
10
A.O.N For the first unit at (N=1)
𝒕 𝒐
𝒕 𝒇
Rate= slope =
𝑵−𝟏
𝒕 𝒇− 𝒕 𝒐
N – 1 = R (𝒕 𝒇 − 𝒕 𝒐 )
𝑵 – 𝟏
𝑹
= 𝒕 𝒇 − 𝒕 𝒐
𝑵 – 𝟏
𝑹
= 𝒕 𝒇 − 𝒕 𝒐
𝒕 𝒇 = 𝒕 𝒐 +
𝑵 – 𝟏
𝑹
𝒕 𝑶 = 𝒕 𝒇 -
𝑵 – 𝟏
𝑹
𝟏
𝑵
𝒕𝒊𝒎𝒆
𝒕𝒊𝒎𝒆
𝑨𝒄𝒕𝒊𝒗𝒊𝒕𝒚
For Activity (R) :
𝒕 𝟎 = 𝟖
𝒕 𝒇 = 𝒕 𝒐 +
𝑵 – 𝟏
𝑹
𝒕 𝒇 = 𝟖 +
𝟔𝟓 – 𝟏
𝟒
= 24
Unit Time
Time
24
8
R
N= 65
N= 1
For Activity (w) :
R(w) < 𝑹(R)
2 4
𝒕 𝟎(𝒘) = 𝒕 𝒐 (𝑹) + 𝑫(𝑾)
𝒕 𝒐 = 𝟖 + 14 = 22
𝒕 𝒇 = 𝒕 𝒐 +
𝑵 – 𝟏
𝑹
𝒕 𝒇 = 𝟐𝟐 +
𝟔𝟓 – 𝟏
𝟐
= 54
Unit Time
Time
24
8
R
22
54
w
For Activity (x) :
R(x) > 𝑹(R)
8 4
𝒕 𝒇(𝒙) = 𝒕 𝒇 (𝑹) + 𝑫 𝑿
𝒕 𝒇 = 𝟐𝟒 + 20 = 44
𝒕 𝒐 = 𝒕 𝒇 -
𝑵 – 𝟏
𝑹
𝒕 𝒐 = 𝟒𝟒 -
𝟔𝟓 – 𝟏
𝟖
= 36
Unit Time
Time
24
8
R
22
54
w
36
44
X
For Activity (Y) :
R(Y) = 𝑹(R)
4 4
𝒕 𝒇(𝒀) = 𝒕 𝒇 (𝑹) + 𝑫 𝒀
𝒕 𝒇 = 𝟐𝟒 + 12 = 36
𝒕 𝒐 = 𝒕 𝒇 -
𝑵 – 𝟏
𝑹
𝒕 𝒐 = 𝟑𝟔 -
𝟔𝟓 – 𝟏
𝟒
= 20
Unit Time
Time
24
8
R
22
54
w
36
44
X
36
20
Y
1) Act. (Z) with Act. (X)
R(Z) < 𝑹(𝑿)
4 8
𝒕 𝟎(𝒛) = 𝒕 𝒐 (𝒙) + 𝑫 𝒁
𝒕 𝒐 = 𝟑𝟔 + 10 = 46
𝒕 𝒇 = 𝒕 𝒐 +
𝑵 – 𝟏
𝑹
𝒕 𝒇 = 𝟒𝟔 +
𝟔𝟓 – 𝟏
𝟒
= 62
2) Act. (Z) with Act. (w)
R(Z) > 𝑹(𝑾)
4 2
𝒕 𝒇(𝒁) = 𝒕 𝒇 (𝑾) + 𝑫 𝒁
𝒕 𝒇 = 𝟓𝟒 + 10 = 64
𝒕 𝒐 = 𝒕 𝒇 -
𝑵 – 𝟏
𝑹
𝒕 𝒐 = 𝟔𝟒 -
𝟔𝟓 – 𝟏
𝟒
= 48
For Activity (Z):
Unit Time
Time
24
8
R
22
54
w
36
44
X
36
20
Y
64
48
Z
Unit Time
Time
24
8
R
22
54
w
36
44
X
36
20
Y
64
48
Z
46
46
N = ???
w
46
46
N = ???
Time
Time
22
54
R =
𝑵−𝟏
𝒕 𝒇− 𝒕 𝒐
2 =
𝑵−𝟏
𝟒𝟔−𝟐𝟐
N =49
2) The project situation at 46th week.
Activities R, Y AND X has been finished
Activity W finished in 49 unit
Activity Z not finished yet in any unit
Unit Time
Time
24
8
R
24
54
w
36
44
X
36
20
Y
64
48
Z
60
60
N = ???
Unit Time
Time
48
Z
60
60 64
N = 49
N = 39
𝑹
𝒏𝒆𝒘=
𝟔𝟓 −𝟑𝟗
𝟔𝟒 − 𝟔𝟎
=6.5
𝑹 𝒐𝒍𝒅
𝒕 𝒇𝒏𝒆𝒘
𝑹 𝒐𝒍𝒅=
𝟑𝟗−𝟏
𝟔𝟎−𝟒𝟖
= 3.1666 < 4

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Lob management

  • 2. Q1: Activity Predecessor Duration Rate Z W,X,Y 10 4 W R 14 2 R - 8 4 X R 20 8 Y R 12 4 For the 65 units Construction Project using the one unit net work it is required to: 1) Draw LOB Chart. 2) Check project situation at 46th week. 3) What’s your recommendation if at 60th week activity Z finished in 39 unit ?
  • 3. R 0 8 8 X 8 28 20 W 8 22 14 Y 8 20 12 Z 28 38 10 A.O.N For the first unit at (N=1)
  • 4. 𝒕 𝒐 𝒕 𝒇 Rate= slope = 𝑵−𝟏 𝒕 𝒇− 𝒕 𝒐 N – 1 = R (𝒕 𝒇 − 𝒕 𝒐 ) 𝑵 – 𝟏 𝑹 = 𝒕 𝒇 − 𝒕 𝒐 𝑵 – 𝟏 𝑹 = 𝒕 𝒇 − 𝒕 𝒐 𝒕 𝒇 = 𝒕 𝒐 + 𝑵 – 𝟏 𝑹 𝒕 𝑶 = 𝒕 𝒇 - 𝑵 – 𝟏 𝑹 𝟏 𝑵 𝒕𝒊𝒎𝒆 𝒕𝒊𝒎𝒆 𝑨𝒄𝒕𝒊𝒗𝒊𝒕𝒚
  • 5. For Activity (R) : 𝒕 𝟎 = 𝟖 𝒕 𝒇 = 𝒕 𝒐 + 𝑵 – 𝟏 𝑹 𝒕 𝒇 = 𝟖 + 𝟔𝟓 – 𝟏 𝟒 = 24 Unit Time Time 24 8 R N= 65 N= 1
  • 6. For Activity (w) : R(w) < 𝑹(R) 2 4 𝒕 𝟎(𝒘) = 𝒕 𝒐 (𝑹) + 𝑫(𝑾) 𝒕 𝒐 = 𝟖 + 14 = 22 𝒕 𝒇 = 𝒕 𝒐 + 𝑵 – 𝟏 𝑹 𝒕 𝒇 = 𝟐𝟐 + 𝟔𝟓 – 𝟏 𝟐 = 54
  • 8. For Activity (x) : R(x) > 𝑹(R) 8 4 𝒕 𝒇(𝒙) = 𝒕 𝒇 (𝑹) + 𝑫 𝑿 𝒕 𝒇 = 𝟐𝟒 + 20 = 44 𝒕 𝒐 = 𝒕 𝒇 - 𝑵 – 𝟏 𝑹 𝒕 𝒐 = 𝟒𝟒 - 𝟔𝟓 – 𝟏 𝟖 = 36
  • 10. For Activity (Y) : R(Y) = 𝑹(R) 4 4 𝒕 𝒇(𝒀) = 𝒕 𝒇 (𝑹) + 𝑫 𝒀 𝒕 𝒇 = 𝟐𝟒 + 12 = 36 𝒕 𝒐 = 𝒕 𝒇 - 𝑵 – 𝟏 𝑹 𝒕 𝒐 = 𝟑𝟔 - 𝟔𝟓 – 𝟏 𝟒 = 20
  • 12. 1) Act. (Z) with Act. (X) R(Z) < 𝑹(𝑿) 4 8 𝒕 𝟎(𝒛) = 𝒕 𝒐 (𝒙) + 𝑫 𝒁 𝒕 𝒐 = 𝟑𝟔 + 10 = 46 𝒕 𝒇 = 𝒕 𝒐 + 𝑵 – 𝟏 𝑹 𝒕 𝒇 = 𝟒𝟔 + 𝟔𝟓 – 𝟏 𝟒 = 62 2) Act. (Z) with Act. (w) R(Z) > 𝑹(𝑾) 4 2 𝒕 𝒇(𝒁) = 𝒕 𝒇 (𝑾) + 𝑫 𝒁 𝒕 𝒇 = 𝟓𝟒 + 10 = 64 𝒕 𝒐 = 𝒕 𝒇 - 𝑵 – 𝟏 𝑹 𝒕 𝒐 = 𝟔𝟒 - 𝟔𝟓 – 𝟏 𝟒 = 48 For Activity (Z):
  • 15. w 46 46 N = ??? Time Time 22 54 R = 𝑵−𝟏 𝒕 𝒇− 𝒕 𝒐 2 = 𝑵−𝟏 𝟒𝟔−𝟐𝟐 N =49
  • 16. 2) The project situation at 46th week. Activities R, Y AND X has been finished Activity W finished in 49 unit Activity Z not finished yet in any unit
  • 18. Unit Time Time 48 Z 60 60 64 N = 49 N = 39 𝑹 𝒏𝒆𝒘= 𝟔𝟓 −𝟑𝟗 𝟔𝟒 − 𝟔𝟎 =6.5 𝑹 𝒐𝒍𝒅 𝒕 𝒇𝒏𝒆𝒘 𝑹 𝒐𝒍𝒅= 𝟑𝟗−𝟏 𝟔𝟎−𝟒𝟖 = 3.1666 < 4