project networking

7/29/2019 PROJECT NETWORKING

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NETWORKING PROJECTACTIVITIES

By

Prof. (Dr.) Indrasen Singh

Professor In-Charge, NICMAR


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Crashing and Updating

o Direct cost of an activity

o The direct cost of an activity depends upon the amount ofresources employed in the execution of the activity.

o This is the cost of materials consumed, machines, equipment and

labour employed to perform the activity.

o In CPM projects, the direct cost of the activity is generally afunction of its duration.

o By increasing the resources that is the activity cost, its duration

can be decreased.

o For Example, the white washing of a building can be done in 3days by a team of 4 workers.

o If the number of men is decreased to 3, it takes 4 days.

o Thus each time 12 man-days at a cost of say Rs. 360 (Rs. 30 per

man-day) are required.


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o the number of men is further decreased to say 2, they may take

say 7 days i.e. 14 man-days at a cost of Rs. 420.

o On the other hand if the resources that is the men are increased to

say 6, the work may takes 2.5 days or 15 man-days at a cost of

Rs. 450.

o The variation of activity cost with activity duration is illustrated

in figure 1.

o The variation of cost with time is rarely linear.


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2 2.5 3 4 5 6 7

Activity Duration

Figure 1

420

450

Cost

360


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Straight Line Approximation

o The cost-time curve of the activity is rarely available. Generally,

the normal and crash durations and costs of the activities are

estimated.

o Even if the cost-time curve of an activity is known, it is very

cumbersome to analyse it for cost calculations.

o For the convenience of computations, the cost-time curve,

depending upon its curvature is approximated by straight lines.

o If the curvature is less, a single straight line approximation can

be made, as in figure 2 and if the curvature is more, multi-

straight lines (segments) approximation can be adopted, as in

figure 3.

o The slope of the straight line (or a segment of line) gives the

increase in cost per unit time for expediting the activity. This is

called cost slope (CS).


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CT NT

Figure 2

CC

NC


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CT2 CT1 NT

Figure 3

CC2

CC1

NC

DuaratinCrashdurationNoraml

CostNormalCostCrashCSSlopeCost

,


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o Indirect cost of the project.

o The indirect cost of the project can be subdivided into tow parts;

fixed indirect cost and variable indirect cost.

o The fixed indirect cost is due to the general and administrative

expenses, license fee, consultants fee, insurance cost, and taxes

etc., and does not depend upon the progress of the project.

o The variable indirect cost depends upon the project duration, but

can not be attributed to individual activities. It consists of

overhead expenses, supervision, interest on capital and

depreciation, etc.


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Crashing the Network

o A network can be crashed or contracted by identifying the least

cost slope, critical activity and the float available on the paths

parallel to the critical path.

o The smallest amount of float on the parallel paths, determines the

duration by which the selected activity can be crashed without

making it non-critical.

o This process is continued, until either all the activities become

critical or all activities with cost slopes less than the indirect cost

are crashed.

o In the former case, that is when all activities become critical, the

project duration can be reduced by crashing more than one

activities in parallel.

o The combination of activities, which together give the least cost

slope less than the indirect cost, are selected for crashing.


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o They are crashed as far as they can without making any activity

non-critical.

o The process is continued, until the total cost of the project does

not start increasing.

o The project duration corresponding to the minimum cost is the

optimum duration.

o The crashing process can be continued if required, until the

minimum possible duration is reached.

o Example:

o Let us consider the following time and cost data for a project

network.


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Activity Normal

Duration (Days

Cost (Rs.) Crash Duration

(Days)

Cost (Rs.)

1-2

1-3

2-4

2-5

3-5

4-7

5-6

6-7

6-8

7-98-9

15

7

9

0

5

6

8

12

10

1010

10,000

7,000

16,000

0

6,000

8,000

7,000

8,000

9,500

8,50015,000

11

5

6

0

2

3

5

8

7

76

12,400

8,400

20,500

0

9,000

10,400

8,350

9,400

10,850

10,00018,000

o The indirect cost of the project is Rs. 1,000 per day, and it is

required to determine the optimum project duration.


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o The project network corresponding to the normal activity times is

shown in figure 4.

o The normal activity times, along-with crash activity times in

parenthesis are written along the activity arrows. The cost slope

of each activity is computed in Table 1 and the same is shown in

the network below the corresponding activity arrow.


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ActivityDuration

(Days) Direct Cost

T C

Cost

slope

C/T

Nor

mal

Cra

sh

Normal Crash

1-2

1-3

2-42-5

3-5

4-7

5-6

6-7

6-8

7-9

8-9

15

7

90

5

6

8

12

10

10

10

11

5

60

5

3

5

8

7

7

6

10,000

7,000

16,0000

6,000

8,000

7,000

8,000

9,500

8,500

15,000

12,400

8,400

20,5000

6,000

10,400

8,350

9,400

10,850

10,000

18,000

4

2

3-

-

3

3

4

3

3

4

2400

1400

4500-

-

2400

1350

1400

1350

1500

3000

600

700

1500-

-

800

450

350

450

500

750

Table: 1


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0 0 15 15 24 29

107

35 3545 45

15 15

23 23

33 35

1

9

8

765

4

3

215(11)

600

5(5)

750

9(6)

450

7(5)

350

10(7)

500

12(8)

1500

6(3)

800

8(5)

450

10(6)10(7)

Solution

Figure 4

700


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0 0 15 15 24 27

107

33 3343 43

15 15

23 23

33 33

1

9

8

765

4

3

215(11)

600

5(5)

750

9(6)

450

7(5)

350

10(7)

500

10(8)

1500

6(3)

800

8(5)

450

10(6)10(7)

700

Figure 5


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0 0 15 15 24 24

107

30 3040 40

15 15

20 20

30 30

1

9

8

765

4

3

215(11)

600

5(5)

750

9(6)

450

7(5)

350

10(7)

500

10(8)

1500

6(3)

800

5(5)

450

10(6)10(7)

700

Figure 6


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0 0 12 12 21 21

77

27 2737 37

12 12

17 17

27 27

1

9

8

765

4

3

212(11)

600

5(5)

750

9(6)

450

7(5)

350

10(7)

500

10(8)

1500

6(3)

800

5(5)

450

10(6)10(7)

700

Figure 7


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0 0 12 12 21 21

77

27 2734 34

12 12

17 17

24 24

1

9

8

765

4

3

212(11)

600

5(5)

750

9(6)

450

7(5)

350

7(7)

500

10(8)

1500

6(3)

800

5(5)

450

10(6)7(7)

700

Figure 8


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0 0 11 11 20 20

66

26 2633 33

11 11

16 16

23 23

1

9

8

765

4

3

211(11)

600

5(5)

750

9(6)

450

6(5)

350

7(7)

500

10(8)

1500

6(3)

800

5(5)

450

10(6)7(7)

700

Figure 9


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0 0 11 11 20 20

66

24 2431 31

11 11

16 16

23 23

1

9

8

765

4

3

211(11)

600

5(5)

750

9(6)

450

6(5)

350

7(7)

500

8(8)

1500

4(3)

800

5(5)

450

8(6)7(7)

700

Figure 10


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o The critical path of the normal network is 1-2-5-6-7-9 and the

normal project duration is 45 days.

o The sum of normal costs of the activities is Rs. 95,000.

Therefore, total project cost = 95,000 + 1000 x 45 = 1,40,000

o On the critical path the least cost activity is 6-7. On the

parallel path 6-8-9, there is a slack of 2 days while on path 2-

4-7 there is a slack of 5 days. Activity 6-7 is thus crashed by 2

days. The project duration becomes 43 days.

Total cost = 1,40,000 + 350 x 2 2 x 1,000 = 1,38,700.

The corresponding network is given in figure 5.


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o Activity 5-6 can be crashed by 3 days. The project duration

becomes 40 days.

Total Cost = 1,38,700 + 3 x 450 - 3 x 1,000 = 1,37,050.

The corresponding network is given in figure 6.

o Activity 1-2 can be crashed by 3 days project duration becomes

37 days, and

Total Cost = 1,37,050 + 3 x 600

3 x 1,000 = 1,35,850.The Corresponding network is shown in figure 7.

o Activity 6-8 and 7-9 combined together can be crashed by 3

days. With this crashing, the project duration becomes 34 days

and Total cost = 1,35,850 + 3 x 950

3 x 1,000 = 1,35,700.The corresponding network is given in figure 8. Thus, for the

given cost data, the optimum project duration is 34 days and the

optimum project cost is Rs. 1,35,700.


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Updating the Project

To illustrate the procedure of updating, let us consider the

network shown in figure 11.

00 108

1715

2424

88

1210

3636

2016

1818

74

52

3 9861

8

8 8

8

1016

6

10

57

Figure 11

12


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Suppose the progress of work is checked after 15 days, that is at

the end of 15 days, and it is observed that:

- Activities 1-2, 1-3, 1-4 and 2-5 are completed.

- Activity 2-6 is in progress and needs 2 days more.

- Activity 3-6 is in progress and needs 5 days more.

- Activity 4-7 is in progress and needs 1 day more and

- Activity 5-9 is in progress and needs 14 days more.- Also it is estimated that due to the non-availability of fast setting

cement, activity 7-8 will take 12 days while due to the arrival of

a new crane, activity 8-9 will now require only 10 days.

This information can be put into a tabular form, as given below:


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Activity Status Time Required

1-2

1-31-4

2-5

2-6

3-6

4-7

5-9

6-8

7-8

8-9

Completed

CompletedCompleted

Completed

In Progress

In Progress

In Progress

In Progress

Not Started

Not Started

Not Started

0

00

0

2

5

1

14

6

12

10


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Solution

o The method, which is comparatively more convenient, is to

bunch all the activities completed up to the date of review, into

one activity and represent this by one arrow called the elapsedtime arrow.

o All the activities in progress will burst from the end node of the

elapsed time arrow and their durations will now be the times

required for their completion, from the date of review. Theremaining activities will follow in their precedence order and will

carry their revised time estimates.

o The nodes in the new network will be numbered in a different

fashion.o Then following the forward and backward computations the

network can be analysed.

o Activity 10-20 in figure 12 represents the elapsed time of 15

days.


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o Activity 20-60, 20-65, 20-70 and 20-90 represent the activities 2-

6, 3-6, 4-7 and 5-9 of the previous network, which respectively

require 2,5,1 and 14 days.

o The critical path for the revised project network is 10-20-70-80-90, which gives the project duration of 38 days.


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o Thus the updated version of the project is of increased duration,

with some change in critical activities of the project.

00

20

3838

70

1515

65

2220

10

221760

2828

80 90Elapsed Time

15

14

1616

5 610

2

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