Critical Path Method

3.4.5 Network Diagrams

For a project involving a large number of activities, the project scheduling becomes very complex and use of the conventional method of scheduling like bar charts will not be effective. Complex projects, if not correctly scheduled, will probably result in either under estimation or over estimation of the project implementation period, both of which will have serious consequences. Network diagrams are one of the modern tools of project management. There are two popular network based scheduling techniques.

Critical Path Method (CPM) - Critical Path Method (CPM) is a graphical network- based scheduling technique that evolved in late 60’s. US Government agencies insisted on their use by contractors on major government projects.

Project Evaluation and Review Technique (PERT) – In 1958 US Navy developed project management tool known as PERT for scheduling Polaris Missile Project.

3.4.5a) Terminologies to understand how a network is drawn for a project:

a. Activity (Task): An activity is any identifiable job which requires time, manpower, material and other resources to complete. The arrow in a network diagram represents activity.

Relationship between activities:

b. Concurrent (parallel) activities: Those activities which can be performed simultaneously and independently to each other are known as concurrent activities. In the figure, A and B are concurrent activities.

c. Serial Activities: Those activities which are to be performed one after the other, in succession are known as serial activities. In the figure below A and B are serial activities.

d. Activity duration: An activity’s duration is estimated the time required for its completion. Time unit may be hours, days, weeks or months.

Activity duration= Work quantity/Production rate

e. Event (Node): The beginning or end of the activity is known as event. It represent specific time and does not consume time manpower, material, and other resources.

Two convention can be used for developing networks are:

Activity on Arrow (AOA) and Activity on Node (AON).

f.Dummy Activity: It is the activity, which doesn’t consume resources like time, cost, manpower, equipment etc. but is only used to show relationships. It is represented by Dashed Arrow. Dummies serve two purposes in network:

1. Grammatical purpose: It is used to prevent two arrows having the common beginning and end nodes for two or more activities.
2. Logical purpose: Dummies are also used to give logical clear representation in the network having an activity common to two sets of operations running parallel to each other.

g.Earliest Start time (EST): It is the earliest possible time an activity or operation can be started. It is equal to the earliest occurrence time of the tail event of that activity.

h.Earliest Finish Time (EFT): It is the earliest possible time for completion of an activity without delaying the project completion time.

EFT= EST + duration

i. Latest Finish Time (LFT): It is the latest time the activity must be completed without delaying project duration. It is equal to the latest occurrence time of the head event.

j. Latest Start time (LST): It is the latest possible time; an activity can be started without delaying the project.

LST= LFT – duration

3.4.5b) Rules of Drawing Network diagram

i. The flow of network shall be from the left to right.

ii. There must be the only single initial node as well as the end node in a network.

iii. An event cannot occur twice.

iv. There shall not be any crisscrossing of arrows.

v. There should be only one arrow for an activity.

vi. There shall not be unnecessary dummy activities in the network.

3.4.5c) Numbering the Events

For any activity, the number on the Tail Event should not be greater than that on the Head Event. In other words, the number on Head Event must always be greater than that on Tail Event. - Fulkerson’s Rule

3.4.6 Critical Path Method (CPM)

Developed by Du-pont chemical works-USA in 1956/57 and used for preparing maintenance shutdown schedule of chemical plant for the first time.

Unlike bar chart, it uses arrows to represent activities and length of arrows ha no relation with activity duration.

Start or end of an activity is called event and it is shown by circles with the special designation.

Starting event is called tail event and ending event is called head event. Some event plays dual both the role of head and tail such events are called dual role events.

Activity which must be completed before start of another activity is predecessor.

Activity which starts after completion of an activity is its successor.

In above figure,

Activity B is successor of activity A and activity A is predecessor of activity B.

Critical path: The longest path in a CPM network is called critical path. There may be more than one critical path in a network.

Project duration: The time required to travel critical path is called project duration.

Critical activities: The activities lying on critical path are called critical activities.

For example, the CPM network is-

There are three paths:

Hence from above definition,

Critical path= 1-3-4-5

Project duration= 12 days

Critical activities= B, D, and F.

Characteristics of critical path:

i. It is the longest path of activities.

ii. It determines the total project duration.

iii. There may be more than one Critical Path in a network.

iv. A Critical Path may consist of less no. of activities than Non-critical Path.

v. t is the starting point for project planning.

vi. The Critical Activities demand the requirement of resources prior to other activities to complete the project in time.

3.4.6a) Significance of critical path:

If there is any delay in either starting or if the time taken to complete critical activity exceeds the estimated time, project implementation period will get extended. Thus any delay in critical activities leads to time overrun of the project which ultimately results in cost overrun.

3.4.6b) Floats

Float means the available free time for an activity, which is useful for managers to manage the limited resources. An activity has four types of floats.

i. Total Float (TF): It is the total free time for an activity i.e. maximum time by which completion of an activity can be delayed without affecting project completion time.

TF= LFT-EFT or LST-EST

ii. Free Float (FF): It is the spare time allowable for an activity so that the start time of succeeding activities are not affected.

FF of an activity= EST of succeeding activity-EFT of that activity

iii. Independent Float (IF or Ind. Float): It is the maximum delay allowable for an activity so that the start time of succeeding activities are not affected. It may come negative but should be taken as zero.

IF of an activity= EST of succeeding activity - LFT of that activity

iv. Interfering Float (Int. Float): It is name given to head event slack. It is the difference between TF & FF.

Int. Float= TF – FF

3.4.6c) Advantages of Critical Path Method

i. Makes dependencies visible.

ii. Organizes large and complex project.

iii. Enables the calculation of float of each activity.

iv. Encourages the project manager to reduce project duration.

v. Increases visibility of the impact of schedule revisions.

vi. Provides opportunities to respond to the negative risk going over-schedule.

3.4.6d) Disadvantages of Critical Path Method

i. In large and complex projects, there will be thousands of activities and dependency relationships.

ii. This method doesn’t account for resource and resource allocation.

Bibliography:

IshwarAdhikari and Santosh Kr. Shrestha, “A text book of Project Engineering” 2011, Chandeshwori Publication, First Edition.

K. Nagarajan, “Project Management”, ISBN: 81-224-1340-4, New Age International (P) Limited, New Delhi, India, 2001.

E.R. Yescombe, “Principles of Project Finance” 2002, Yescombe-Consulting Limited.