A determine the earliest start and finish times latest start and finish times for each activity

Draw the network and calculate the earliest start time, earliest finish time, latest start time and latest finish time of each activity and determine the Critical path of the project and duration to complete the project.

E1 = 0

E2 = 0 + 6 = 6

E3 = 0 + 5 = 5

E4 = 6 + 10 = 16

E5 = (5 + 4) or (16 + 6)

Whichever is maximum

= 22

E6 = (16 + 2) or (22 + 9)

Whichever is maximum

 = 31

L6 = 31

L5 = 31 – 8 = 22

L4 = 22 – 6 = 16 or (31 – 2)

whichever is minimum

L3 = 22 – 4 = 18

L2 = 16 – 10 = 6

L1 = 6 – 6 = 0

Since EFT and LFT is same on 1 - 2, 2 - 4, 4 - 5 and 5 - 6, the critical path is 1 - 2 - 4 - 5 - 6 and duration time taken is 31 days.

Concept: Network Analysis

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CALCULATION OF EARLIEST START TIME, LATEST FINISH TIME AND FLOATS

Problem 6.71

A project has the following activities:

Required

1. Draw the project network.
2. Find the critical path and total project duration.
3. Find earliest start time, latest start time, earliest finish time, and latest finish time.
4. Find total float, head even slack, free float, tail even slack and independent float.

Solution

Part (a)

Part (b)

Hence the critical path ...

Forward pass:

E1 = 0

E2 = 0 + 6 = 6

E3 = 0 + 5 = 5

E4 = 6 + 10 = 16

E5 = (E4 + 6) (or) (E3 + 4)

E5 = (16 + 6) (or) (5 + 4) [whichever is maximum]

E5 = 22

E6 = (E5 + 9) (or) (E4 + 2)

E6 = (22 + 9) (or) (4 + 2) [whichever is maximum]

E6 = 31

Backward pass:

L6 = 31

L5 = 31 – 9 = 22

L4 = 22 – 6 (or) 31 – 2 [whichever is minimum]

L4 = 16

L3 = 22 – 4 = 18

L2 = 16 – 10 = 6

L1 = 6 – 6 = 0

∴ EFT and LFT are the same on 1-2, 2-4, 4-5, 5-6, the vertical path is 1-2-4-5-6 and duration is 31 days to complete.

Early Start, Early Finish and Late Start, Late Finish

Why do we need to know the early and late number for an activity? By knowing how early an activity can start and how late it can finish gives you the flexibility to juggle resources between other activities that can potentially impact critical path, and hence the project completion date. The shorter a network path is in relation to critical path, more schedule flexibility you will have on activities on that path.

Early start and Early finish

Indicates the earliest time an activity on a network path can start and earliest it can finish. If you decide to start an activity on its early start (assuming previous activities on that network path are completed on their early finishes), that activity can finish on its early finish (if it does not slip). And when the last activity on a network path is completed by its early finish, you have all the resources of those activities at your disposal to deploy on other high risk activities.

Calculating Early start and finish (take a FORWARD pass through network path)

Remember!: Always start with the critical path and then go with paths with descending order of their total duration.

Step 1: Early start of first activity on critical path is always 1. Write it at the top left corner of that activity box (see the image below).

Step 2: Add its activity duration to this early start number and reduce it by one. Write the resulting number on the top right corner of activity box.

Step 3: Take the subsequent number of this early finish and write as early start for next activity. Continue this till you reach the end of critical path.

Step 4: Select the network path with second highest total duration, and calculate early starts and finishes. If you find an activity with early start and finish already written do not overwrite them. Do the same for remaining network paths.

Note: If you find two activities converging on a single activity (say, activity-G), it indicates that the activity-G will start only AFTER converging activities finish. So, you will take the largest value amongst the early finish of these two activities and write subsequent number as early start of the activity-G.

Why add duration to early start and then reduce by one, to get early finish? Because the duration of an activity includes both start and finish days (or any other unit of measurement you use). So, if first activity duration is 5 days, and early start is 1 then early finish is 1+6-1 = 6. That is 6 days including the start and finish days.

As you noticed, early start number is written at the top left corner of activity box, and early finish on the top right corner. The critical path with early start and early finish days will look like this –

Late start and Late finish

Indicates the latest time an activity on a network path can start and latest it can finish. Knowing how late the last activity on the network path can start and still finish within the time to not impact critical path, will let you decide how much of flexibility you want to exercise on its schedule. However, once the last activity on the network path starts on its late start day it should not slip, else it will impact project completion date.

Calculating Late start and finish (take BACKWARD pass through network path)

Remember!: Start with the critical path, beginning at the last activity’s late finish.

Step 1: Late finish of last activity on the critical path is same as its early finish. Write this number at the bottom right corner.

Step 2: Calculate late start of this activity as the late finish minus activity duration plus 1. This calculation has the same reason – start and finish are both included in the duration. Write this number at the bottom left corner.

Step 3: Write this late start of the activity minus 1, as the late finish of previous activity. Continue this way all way till you reach the late start of first activity on the critical path.

Step 4: Select the network path with second highest total duration, and write late starts and finishes beginning at the last activity of that path. Do the same for remaining network paths.

Notes:

• If you find two activities converging on a single activity (say, activity-C), take the smallest value amongst the late start of these activities and write previous number as late finish of the activity-C.
• If you find an activity with late start and finish already written do not overwrite them.

Late start number is written at the bottom left corner of activity box, and late finish on the bottom right corner. The critical path of our example with late starts and late finishes will look like this –

Let us go back to our example and calculate early/late start/finish for the entire schedule network diagram.

This has been a lengthy lesson, let us summarize in the next page..

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How do you find the earliest start and earliest finish?

What technique is used to calculate the early start and early finish for activities?

What is the definition of the earliest and latest start times of an activity and the earliest and latest finish times of an activity?