EVA Problems with Solutions March 2020 PDF

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Example 13.The progress observed at the end of the 7th day from the beginning of a 12-day durationproject is given in Table 13. The actual cost incurred till date is reported to be Rs. 3,100.Draw a Gantt chart for the project and find the project performance on the basis of cost andschedule performa...

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Example 13.7 The progress observed at the end of the 7th day from the beginning of a 12-day duration project is given in Table 13.8. The actual cost incurred till date is reported to be Rs. 3,100.00 Draw a Gantt chart for the project and find the project performance on the basis of cost and schedule performance indices. (Assume the activity costs are incurred uniformly over its duration). % of

Estimated Activity A B C D E F G H I J

Immediate Predecessor A B B D E C F G

Duration in Days 3 1 4 4 5 2 3 4 2 3

Budget of Activity (Rs.) 600 200 800 700 500 200 500 400 600 300

Completion at End of 7 Days 100 100 75 100 95 80 50 0 0 0

Table 13.8 Project-related details (MMS, VI Sem, Mumbai Univ 2003,2012)

Solution: We have to construct the network, find the ES and EF for all activities and estimate the duration of the project. Path 1: A – C – H, duration = 11 days Path 2: B – D – F – I, duration = 9 days Path 3: B – E – G – J, duration = 12 days Path 3 is the longest duration path and hence the critical path. The budgeted project duration is 12 days.

Activity

Immediate Predecesso r

Duration in Days

ES

EF

A B C D E F G H I J

A B B D E C F G

3 1 4 4 5 2 3 4 2 3

0 0 3 1 1 5 6 7 7 9

3 1 7 5 6 7 9 11 9 12

Total

Budgeted cost of Activity 600 200 800 700 500 200 500 400 600 300 4,800

% of Completio n at End of 7 Days 100 100 75 100 95 80 50 0 0 0

BCWS

BCWP

600 200 800 700 500 200 167 3,167

600 200 600 700 475 160 250 2,985

Figure 13.3 Gantt chart at the end of the 7th day

The budgeted cost for the work scheduled is Rs. 3,167 The budgeted cost for work performed is Rs. 2,985 The actual cost of work performed is Rs. 3,100 (data given in the problem). Cost performance indices (CPI) =

BCWP ACWP

Schedule performance indices (CPI) =

=

BCWP BCWS

2,985 3,100 =

= 0.96

2,985 3,167

= 0.94

Cost of completion = Budgeted cost / CPI = 4,800/0.96 = Rs. 5,000 Time of completion = Scheduled duration/SPI = 12/0.94 = 12.76 ≈ 13 days.

Problem 13.8 A project consisting of eight activities was reviewed on completing of 12 days after its start. Find the project performance on the basis of cost and schedule performance indices. What is the estimated duration of the project?

Actual Cost (Rs. ‘000)

Actual % Completion at the End of Day 12

Activity

Duration (Days)

Budgeted Cost (Rs. ‘000)

A1–2

5

60

62

100

B2–3

7

70

70

100

C2–4

5

75

73

100

D2–5

7

82

70

90

E3–6

6

69

0

0

F4–6

8

54

10

20

G5–7

6

50

0

0

H6–7

5

40

0

0

Table 13.10 Activity related details (MMM, VI SEM, Mumbai Univ 2007)

Solution: We will have to construct the network (Figure 13.4) and identify the critical path to know the project duration. Path 1: A – B – E – H, 23 Days Path 2: A – C – F – H, 23 Days Path 3: A – D – G, 18 Days

The project duration is 23 days. The evaluation of the ES and EF times is as shown in Table 13.11.

Activity

Duration in Days

A1–2 B2–3 C2–4 D2–5 E3–6 F4–6 G5–7 H6–7

5 7 5 7 6 8 6 5 Total

Notes:

Actual % Actual Completion Cost ES EF at the End (Rs. of Day 12 ‘000) 0 5 60 62 100 5 12 70 70 100 5 10 75 73 100 5 12 82 70 90 12 18 69 0 0 10 18 54 10 20 12 18 50 0 0 18 23 40 0 0 500 285 Table 13.11 Project activity-related details Budgeted Cost (Rs. ‘000)

BCWP

BCWS

60 70 75 73.8 0 10.8 0 0 289.6

60 70 75 82 0 13.5 0 0 300.5

1. BCWP is the percentage of the budgeted cost converted into actual work or the earned value. 2. BCWS is the budgeted cost of work that should be performed up to the day of review i.e., 12. In case of activity F, up to day 12, 2 days (out of a total 8 days) should be 54 completed as per schedule. Hence, BCWS for activity F is ( x 2 = days) = 13.5. 8 Budgeted cost of work performed = 289.6 Budgeted cost of work scheduled = 300.5 Actual cost of work performed = 285 CPI =

BCWP ACWP

=

289.6 285

= 1.02

SPI =

BCWP BCWS

=

289.6 300.5

= 0.96

The project is delayed but is working within the cost estimates. The estimated project duration is: Project duration SPI

23

= 0.96

= 23.96 ≈ 24 days

Example 13.10 The progress observed at the end of the 7th day from the beginning of the project is as given in Table 13.12.

Actual Cost (Rs. Lakhs)

Actual % Completion at the End of Day 7

Activity

Duration (Days)

Budgeted Cost (Rs. Lakhs)

A1–2

3

5

4

100

B2–3

4

8

9

90

C2–4

3

4

5

95

D2–5

8

5

3

60

E3–6

5

3

0

0

F4–6

4

2

1

30

G5–7

5

10

0

0

H6–7

3

7

0

0

Table 13.12 Activity-related details If the costs are incurred linearly in proportion to activity completion, then find the following: i) ii) iii) iv) v)

Cost variance Cost performance index Scheduled performance index Estimated cost of project completion Estimated duration of the project MMM, VI Sem, Mumbai Univ, 2008

Solution: The first step is to construct the network (Figure 13.5) and identify the critical path to know the budgeted project duration.

Path 1: A – B – E – H, 15 days. Path 2: A – C – F – H, 13 days. Path 3: A – D – G, 16 days. The project duration is 16 days. The evaluation of the ES and EF times is shown in Table 13.13.

Activity

Duration (Days)

A1–2 B2–3 C2–4 D2–5 E3–6 F4–6 G5–7 H6–7

3 4 3 8 5 4 5 3 Total

Actual % Actual Cost Completion ES EF (Rs. at the End of Day 7 Lakhs) 0 3 5 4 100 3 7 8 9 90 3 6 4 5 95 3 11 5 3 60 7 12 3 0 0 6 10 2 1 30 11 16 10 0 0 12 15 7 0 0 44 22 Table 13.13 Project activity related details Budgeted Cost (Rs. Lakhs)

BCWP

BCWS

5 7.2 3.8 3 0 0.6 0 0 19.6

5 8 4 2.5 3 0.5 0 0 23

Notes: 1. BCWP is the percentage of the budgeted cost converted into actual work or the earned value. 2. BCWS is the budgeted cost of work that should be performed up to the day of review i.e., 7. In case of activity F, up to day 7, 1 day (out of a total 4 days) should be completed as per schedule. Hence, BCWS for activity F is (

2 4

x 1 = days) = 0.5.

Budgeted cost of work performed = 19.6 Budgeted cost of work scheduled = 23 Actual cost of work performed = 22 i) Cost variance = BCWP – ACWP = 19.6 – 22 = -2.4 BCWP 19.6 ii) CPI = ACWP = 22 = 0.89 BCWP 19.6 iii) SPI = BCWS = 23 = 0.85 Budgeted cost of totalwork iv) Estimated cost of project on completion = CPI 44 = 0.89 = 49.43 ≈ 50 lakhs Project duration 16 = 0.85 = 18.82 ≈ 19 days v) SPI Hence, the project is likely to be delayed and completed in 19 days.

Example 13.11 Consider the data given in Table 13.14 for a small project. The actual performance is measured at the end of 5 months in terms of % actual completion and actual cost incurred. Assume all activities will begin at the earliest, determine the following: a) Cost performance index and schedule performance index b) Revised project duration and cost

Activity

Predecessor(s )

Normal Time

Normal Cost

Actual Cost

% Actual Completion

A

-

4

6

6

100

B

-

12

15

6

40

C

-

4

3

3

95

D

A

10

15

2

7

E

C

6

10

0

0

F

A

14

11

8

7

G

B, D, E

8

10

0

0

Table 13.14 Small project data MMS, IV Sem, Mumbai Univ, 2018

Solution: a) Although there is no requirement to draw the network diagram for the calculations, we will as a matter of practice still draw the network diagram as shown in figure 13.6. The Early Start (ES) and Early Finish (EF) besides BCWP and BCWS calculations are shown in Table 13.15. CPI = BCWP / ACWP = 16.67 / 25 = 0.67 SPI = BCWP / BCWS = 16.67 / 19.21 = 0.87 b) Revised project cost = Budgeted cost / CPI = 70 / 0.67 = 104.48 Revised project duration = Budgeted duration / SPI = 22 / 0.87 = 25.29 ≈ 26 months Activity Predecessor(s) A

-

B

-

C

-

D

A

E

C

F

A

G

B, D, E Total

% Actual Normal Normal Actual ES EF BCWP BCWS Time Cost Cost Completion 4 6 6 100 0 4 6 6 1 6 6.25 12 15 6 40 0 2 4 3 3 95 0 4 2.85 3 1 1.05 1.5 10 15 2 7 4 4 1 0 1.67 6 10 0 0 4 0 1 0.77 0.79 14 11 8 7 4 8 1 2 0 0 8 10 0 0 4 2 70 25 16.67 19.21 Table 13.15 BCWP and BCWS calculations...