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4. CRITICAL PATH BASED TIME

ANALYSISObjective:

To learn the principles of activity network based preliminary time analysis, calculating: – project duration, – critical path, – activity floats, and – event times.

In addition, introduce:– lead and lag times;– conversion into time-scaled charts.

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Summary:

4.1 Computing the Project Duration4.2 Determining the Critical Path(s)4.3 Determining the Activity Floats4.4 Lead and Lag Times and Ladder Constructs4.5 Representing Time Graphically4.6 Determining Activity Durations

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4.1 COMPUTING THE PROJECT

DURATION

Once the logical dependencies between the activities have been established, a time analysis can be performed.

The preliminary time analysis will consider only logical constraints on the timing of activities, and determines:– preliminary project duration, and

– activity floats.

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The floats assist in scheduling activities in a way that satisfies all project objectives, taking into account all resource constraints.

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• The duration of a project is given by the longest time path through the network:

Fig. 4-1: Addition of Durations to Foundation Network

clear site

excav. pad found.

constr. temp. haul road

constr. form

position form & fix steel

clean up

pour conc.

add activity durations

5

7

10

0

6

10

0

5

7

6

Fig. 4-2: Computation of Early Event Times

5

7

10

0

6

10

0

5

7

add event numbers

eventnumber

eventnumber

1 2

3

4

5

6

7

calculate early event times

earlyevent time

earlyevent time

0

0 + 5 = 50 + 5 = 5

5

12

merge events use largestcomputed value

merge events use largestcomputed value

15 25

25

32

projectduration

= 32

projectduration

= 32

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4.2 Determining the Critical Path(s)

The next step is to determine which activities are critical.

The critical activities will always form at least one path connecting the initial and final events.

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Fig. 4-3: Computation of Late Event Times

5

7

10

0

6

10

0

5

7

1 2

3

4

5

6

70 5

12

15 25

25

32

calculate late event times

lateeventtime

lateeventtime

32

32 - 5 = 27 32 - 5 = 27

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burst events use smallestcomputed value

burst events use smallestcomputed value

2515

15

50

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Fig. 4-4: Identification of Critical Path

5

7

10

0

6

10

0

5

7

1 2

3

4

5

6

70 5

12

15 25

25

32 32

27

2515

15

50

eve = evl?

if yes then critical event

eve = evl?

if yes then critical event

evlf - eves - d = 0 ?

if yes thencritical activity

evlf - eves - d = 0 ?

if yes thencritical activity

= critical path = critical path

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• Knowledge of the critical path is useful for:– reducing the project duration;

– scheduling activities to meet resource constraints; and

– focusing management efforts to minimize the possibility of delay to the project.

Note, a non-critical activity could be very susceptible to delays and thus easily become critical (eg: activities susceptible to inclement weather).

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• Activity times and event times should not be confused.

StartEvent

FinishEvent

Activity A

d

early event time

(eventes)

late event time

(eventls)

early event time

(eventef)

late event time

(eventlf)

early activity start = eventes

early activity finish = eventes + d

late activity start = eventlf - d

late activity finish = eventlf

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Table 4-I: Activity Start and Finish Times for the Foundation Operation

ActAct EarlyEarly LateLate EarlyEarly LateLateIDID StartStart StartStart FinishFinish FinishFinish1-21-22-42-43-43-43-53-54-64-65-75-76-56-56-76-7

00 00 55 55 55 55 1515 1515 1212 1515 1212 1515 1212 2121 1818 2727 1515 1515 2525 2525 2525 2727 3030 3232 2525 2727 2525 2727 2525 2525 3232 3232

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4.3 Determining the Activity Floats

Non critical activities can experience some delay before they will cause other activities to be delayed and/or the project completion time to be delayed.

– This leeway is termed float or slack.

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• Total Float. The maximum amount of time by which an activity’s completion can be delayed without extending the completion date of the project.

15Fig. 4-5: Computation of Total Float

(a) interpretation of total float

(b) total floats for foundation operation

START EVENTSTART EVENT FINISH EVENTFINISH EVENTearly late early late

TIME

Activity Duration = d TOTALFLOAT

5

7

10

0

6

10

0

5

7

1 2

3

4

5

6

70 5

12

15 25

25

32 32

27

2515

15

50

TF = 0

TF = 3

TF = 0

TF = 9

TF = 3

TF = 0

TF = 2

TF = 2

TF = 0

criticalactivitieshave zeroor -ve TF

criticalactivitieshave zeroor -ve TF

dummy activitiescan have TF > 0

dummy activitiescan have TF > 0

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• Free Float. The maximum amount of time by which the activity’s completion can be delayed without delaying succeeding activities.

17Fig. 4-6: Computation of Free Float

(a) interpretation of free float

(b) free floats for foundation operation

START EVENTSTART EVENT FINISH EVENTFINISH EVENTearly late early late

TIME

Activity Duration = d FREEFLOAT

5

7

10

0

6

10

0

5

7

1 2

3

4

5

6

70 5

12

15 25

25

32 32

27

2515

15

50

FF = 0

FF = 0

FF = 0

FF = 7

FF = 3

FF = 0

FF = 2

FF = 0

FF = 0

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• Independent Float. The maximum amount of time by which the activity’s duration can be extended without delaying other activities, even if all float in the preceding activities has been consumed.

19Fig. 4-7: Computation of Independent Float

(a) interpretation of independent float

(b) independent floats for foundation operation

START EVENTSTART EVENT FINISH EVENTFINISH EVENTearly late early late

TIME

Activity Duration = d

INDEPENDENTFLOAT

5

7

10

0

6

10

0

5

7

1 2

3

4

5

6

70 5

12

15 25

25

32 32

27

2515

15

50

IF = 0

IF = 0

IF = 0

IF = 4

IF = 0

IF = 0

IF = 0

IF = 0

IF = 0

Independent floatcan be -ve even ifthere are no delays

Independent floatcan be -ve even ifthere are no delays

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• Shared Float. Shared float is that which is common to connected activities.

• Shared float is computed as the difference between the late and early event times at an event.

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4.4 Lead and Lag Times and Ladder Constructs

Sometimes, it is necessary to impose a delay between events using dummy activities:– Lead time when the delay follows the start of

an activity, and

– Lag time where the delay follows the finish of an activity.

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• Lead and lag times can be used in a ladder to simplify representation of phased sequential activities.

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Fig. 4-8 The Use of Lead and Lag Dummies to Simplify Network Construction continued...

(a) phased lengthy sequential activities

excav. trn. 1

excav. trn. 2 excav. trn. 3

shore 1 shore 2

shore 3 lay pipe 1 lay

pipe 3

laypipe 2

1 day 2 days

2 days2 days

3 days2 days

2 days

2 days 2 days

0 1 3

3 3 6

6

6

8 10 108

6

6

633

310

totalduration

= 10

totalduration

= 10

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Fig. 4-8 The Use of Lead and Lag Dummies to Simplify Network Construction

(b) ladder construction

excav. trn.

shore

lay pipe

lead 1lag 1

lead 2

lag 2

5 days

7 days

6 days

1 day

2 days

2 days

2 days

0 5

1 8

3 10 10

8

4

1

60

Againtotal

duration= 10

Againtotal

duration= 10

Some loss of logic:In (a), excav. and lay pipe

are partially critical

Some loss of logic:In (a), excav. and lay pipe

are partially critical

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4.5 Representing Time Graphically

• Activity-on-the-arrow networks can be conveniently scaled to represent time graphically:

26Fig. 4-9: Time-Scaled Representation of Activity Network ...

(b) time scaled activity-on-the-arrow-network

(a) original activity-on-the-arrow-network

5

7

10

0

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10

0

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1 2

3

4

5

6

70 5

12

15 25

25

32 32

27

2515

15

50

0 5 12 15 18 25 30 32TIME

5 71 2 3

4

5

6

7

10

6

10 7

5

Free Float

Free Float

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• Alternatively, activity networks (including precedence networks) can be converted into linked bar charts to show time graphically.

Fig. 4-9: Time-Scaled Representation of Activity Network(c) linked bar chart

0 5 12 15 18 25 30 32TIME

1-2 (5)1-2 (5)

2-3 (7)2-3 (7)

3-5 (6)3-5 (6)

5-7 (5)5-7 (5)

2-4 (10)2-4 (10)

4-6 (10)4-6 (10)

6-7 (7)6-7 (7)

progress can beconveniently indicated

progress can beconveniently indicated

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4.6 Determining Activity Durations

• An accurate estimate of project duration requires accurate estimates of the activity durations.

• The duration for an activity is dependent on many things.• Often, a good approximation for an activity duration can be estimated

from just 3 factors:– the quantity of work to be performed;– the production rates of the productive resources (crews and equipment); and– the numbers of productive resources employed on the task.

• The data for this can be based on:– personal experience;– company historic data;– published data (for example, R.S. Means)

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• Example 1: Determine the time required to drive 25 no. 12” diameter 50 ft steel piles (step tapered, round, and concrete filled).

• An approximation:Duration = Quantity of work per crew / (Production rate per crew × No. of crews)Quantity of work = 50 (v.l. ft / pile) × 25 piles = 1250 v.l. ftProduction rate per crew = 630 (v.l. ft / (crew ∙ day)) (RS Means)No. of crews = 2 (available)

• note:Quantity of work per crew = 1250 / 2 = 625 v.l ft per crew.Each pile = 50 v.l. ft.So, one crew would sink 650 v.l. ft, and the other 600 v.l. ft.

• therefore:Duration (to complete all piles) = 650 / 630 = 1.032 days (approximately 1 day).

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• Note, this does not include:– mobilization;– demobilization;– moving equipment; and setting-out.

• Such factors would be significant and need to be taken into account

• Also, the more crews you have operating in an area, the greater the interference leading to extensions in duration.

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• Example 2: Determine the time required to excavate 2,000 cubic yards of earth using a scraper-based system:

– An approximate estimate requires a lot more information than in the previous example, most notably:

• number of scrapers and their capacities;• policy on % of bowl to be filled at each load operation;• load growth curves;• power of the tractor and whether or not bulldozers are used to assist scraper

loading;• distance the scrapers have to travel to dump their loads;• slopes on the haul roads;• type of soil to be excavated and its moisture content;

other factors that are important but are more difficult to quantify include:• condition of the haul road;• experience of the operator;• balance in the numbers of scrapers and bulldozers;

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• Problems of this type can be solved by:- Tables published by equipment manufacturers,

such as Caterpillar Handbook.- Simulation software:

generic construction simulation software, such as CYCLONE; or

manufacturer specific (again, such as that provided by Caterpillar).

- Beware, the data published by some companies represents idealized rates exclusive of unavoidable inefficiencies:

fueling; start-up conditions; and interference between items of equipment.

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• An activity’s duration will vary from repetition to repetition.

• The reasons for this can be divided into two categories:(1) stochastic causes of variance:

these are random and thus impossible to predict;

(2) deterministic causes of variance:these can be predicted, at least in principle. For example:

• patterns have been observed between the day of the week when a task is performed and the rate at which that task progresses; and

• learning effects whereby, the time required to repeat a task decreases that task (discussed in a later lecture).