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What is the critical path method

The Critical Path Method is a technique used to estimate the duration of a project by analyzing which sequence of activities has the least amount of planning flexibility. Gantt meaning.

The critical path is represented by the sequence of activities for which no delay is allowed, otherwise the project end date shifts by the same amount as the delay (so it is the longest path).

It was developed in the 1959 by James E. Kelly Jr. and Morgan R. Walker and then improved. Through the CPM algorithm applied to the sequence of activities, the following information is obtained:

  • The minimum start and end dates for each activity;
  • The maximum start and end dates for each activity;
  • The project end date
  • The critical route (s)
  • The possible admissible slips of the activities that lie on the other paths 

The critical path method is a modeling process that defiends all critical project tasks that must be completed on time. The start and finish dates of the tasks in the project are calculated in two steps: 

  • The first step calculates the start and end dates anticipated from the first start date;
  • The second pass calculates the delayed start and end activities from the last end date backwards;

The difference between the start and end date pairs for each activity is the floating or slack time for the activity. Loosening is the amount of time an activity can be delayed without delaying the completion date of the project. By experimenting with different logical sequences and / or durations it is possible to determine the optimal planning of the project.

Project Plan: CPM, Early Start and Finish Date

The minimum start date (Early Start Date - ES-) of an activity represents the date calendar to which it is possible to start the activity considered as soon as possible, the shortest time within which the activity can start if the previous activities do not have delays in completing them.

The minimum end date (Early Finish Date –EF-) of an activity represents the date calendar to which it is possible to complete as soon as possible the activity considered, the shortest time within which the activity can end if the previous activities do not have delays in completing them. 

The maximum start date (Late Start Date –LS-) of an activity represents the date calendar to which the activity under consideration must start at the latest, the maximum time within which the activity must start in order not to compromise the total time at the end of the project.

The maximum end date (Late Finish Date –LF-) of an activity represents the date calendar to which the activity under consideration must be completed, the maximum time within which the activity must end in order not to compromise the time total end of project.

To calculate the maximum dates, proceed backwards.

The maximum end date of the project corresponds to the End node and is often the date proposed by the client.

Example of a grid

The flows

The difference between the minimum and maximum dates is a measure of the flexibility of an activity and indicates how long the completion of an activity can be delayed without thereby affecting the project end date.

The measure of this time interval is properly defined with the term "sliding" (float or slack) and does not mean "delay" at all.

There are four types of scrolling:

  • total float: total scrolling
  • free float: Free scrolling
  • dipendent float: Chained or constrained scrolling
  • indipendent float: Independent scrolling

Total scrolling

The total scrolling of an activity represents the maximum end-of-activity sliding with respect to the minimum end date which does not delay the total time of the end of the project; it can be calculated alternatively as the difference between the maximum end date and the minimum end date or as the difference between the maximum start date and the minimum start date

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Total scrolling can be further broken down into two subcomponents: free scrolling and constrained scrolling.

Free scrolling

Free scrolling is the maximum delay of the end of activity with respect to its minimum end date which, if used, has no effect on the minimum dates of the next start. It is present only when there is an activity connected to a critical activity or milestone on the path. 

The free scroll corresponds to the difference between the minimum of the minimum start date of the subsequent activities and the minimum end date of the activity in question.

In some cases (most), total scrolling may instead be shared in whole or in part with other project activities that lie on the same path-sequence. So, if scrolling is used by the considered activity, it subtracts available scrolling to a subsequent activity that shares the amount.

Constrained scrolling

Shared share comes defi“constrained scrolling” and is calculated as the difference between total scrolling and free scrolling.

The "independent scrolling" represents the result of a sort of pessimistic simulation carried out on the lattice and measures the amplitude of the time interval within which the minimum start (or end) date of the activity can vary, if the following hypotheses are valid : all previous activities end on their maximum end date and all the following start at their minimum start date.

If in this situation there are independent slips, some form of guarantee is still assured. 

It is calculated as the difference between the minimum of the minimum dates for the start of the following activities and the maximum between the maximum dates of the previous activities and the duration of the activity in question.

If the result is negative, the scroll is null.

Project Plan: the Critical Path

Si defiThe critical activity is the end of that activity which has zero total flow. In fact, this activity cannot be delayed without causing an effective delay in the entire duration of the project (it is also possible definish "quasi-critical activity" if the slip is below a certain threshold).

Si definishes critical path or critical path the sequence of critical activities from the origin node to the end-of-lattice node. Critical paths can be multiple.

All the activities of a critical path are critical. But critical activities can also be linked by non-critical paths.

Ercole Palmeri

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