Project Scheduling

Critical Path Method (CPM)

Critical Path Method technique was developed by Du Pont in 1950 and was first used in missile defense construction projects.

Critical Path: In project management, a critical path is the sequence of project network activities which add up to the longest overall duration, regardless if that longest duration has float or not. This determines the earliest possible time to complete the project. The activities that lie on the critical path are known as critical activities. These are those activities which do not have any cushion time to either postpone or prepone its starting time from its original starting time. Each non-critical activity will have some cushion time so it can be postponed or preponed its starting time from its original time. If the activity of the critical path is delayed, the project completion time will also be delayed.

 Steps to find out critical path:

  1. Break down the project into various activities and arrange all activities in logical sequence.
  2. Number all the events and activities.
  3. Calculate the earliest start time, earliest finish time, latest start time and latest finish time of each event.
    1. Earliest start time for activity (Es): it is the time at which the activity can start without affecting the total project time.
    2. Earliest finish time for activity (Ef):
    3. Latest start time for activity (Ls):
    4. Latest finish time for activity (Lf): it is the latest time by which an activity must get completed without delaying the project completion.
    5. Total Float: the total float of an activity represents the amount of time by which an activity can be delayed without delay in the project completion date. In other words, it refers to the amount of the free time associated with an activity which can be used before, during or after the performance of this activity.

Total Float TF = Lf – Ef or Ls – Es

  1. Free Float: the free float indicates the value by which an activity can be delayed without causing any delay in its immediate successor activities.

Free Float FF =

  1. Independent Float: it is the time by which an activity can be delayed for start without affecting floats of the preceding activities.

Independent Float IF =

Difference between Float and Slack: Slack is event related whereas float is related to activities.

  1. Determine the slack for each activity by taking difference between earliest and latest time.
  2. Identify the critical activities (with zero slack) and connect them by double arrow. This shows the critical path.
  3. Calculate the total project duration.
Critical Path Method Project Scheduling

A – D – G – K            10+12+20+6 = 48 days

A – D – H – L            10+12+3+18 = 43 days

A – E – I – L              10+4+9+18 = 41 days

B – I – L                    9+9+8 = 36 days

C – J – N                     12+13+9 = 34 days

C – F – I – L              12+8+9+18 = 47 days

C – J – M – L            12+13+7+18 = 50 days*

C – J – M – L  is the critical path and the project duration is 50 days.

Project Scheduling

Example 1: Construct the network and find out the critical path.

Critical Path Method Project Scheduling
Critical Path Method Project Scheduling

Example 2: Draw the network and find out the critical path and total float using Critical Path Method (CPM)

Critical Path Method Project Scheduling
Critical Path Method Project Scheduling

By Hassham

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