PERT and CPM

PERT and CPM

Introduction

Network scheduling is a technique used for planning and scheduling large projects in the fields of construction,maintenance, fabrication,purchasing,computer system installation,research and development designs ,etc.The technique is a method of minimizing trouble spots,such as,production bottlenecks,delays and interruptions,by determining critical factors and coordinating various parts of overall job.

There are two basic planning and control techniques that utilize a network to complete a pre-determined project or schedule.These are: Program Evaluation and Review Technique(PERT); and the Critical Path Method (CPM).

Network: Basic components

A network is a graphic representation of a project's operations and is composed of activities and events that must be completed to reach the end objective of a project.The basic components of a network are:

• Activity:  An activity is a task,or item of work to be done,that consumes time,effort, money or other resources.It lies between two events, called the 'preceding' and 'succeeding' ones.It is represented by an arrow with its head indicating the sequence in which the events are to occur.
• Event: An event represent the start or completion of some activity and as such it consumes no time.An event is nothing but a node and is generally represented on the network by a circle.An event is not complete until all the activities flowing into it are completed.

An event representing the joint completion of more than one activity is called a merge event.

If an event represents the joint initiation of more than one activity, it is called a burst event.

The activities can be further classified into three categories:

1. Predecessor activity: An activity which must be completed before one or more other activities start is known as predecessor activity.
2. Successor activity: An activity which started immediately after one or more of the activities are completed is known as a successor activity.
3. Dummy activity: An activity which does not consume either any resource or time is known as a dummy activity. A dummy activity is depicted by dotted line in the network diagram.

Errors to be avoided in constructing a network

1. Looping: If an activity were represented as going back in time, a closed loop would occur which will result in an endless cycle.This situation can be avoided by checking the precedence relationship of the activities.
2. Dangling: No activity should end without being joined to the end event..Suck end-events other than the end of the project as a whole are called dangling events.

Network representation

Each activity of the project is represented by an arc pointing in the direction of progress in project..For the construction of a network,generally,the following rules are followed:

1. Each activity is represented by one and only one arrow.
2. Each activity must be identified by two distinct nodes i.e.  its starting and end node .
3. Nodes are numbered to identify an activity uniquely.
4. Between any pair of nodes, there should be one and only one activity,however more than one activity may emanate from and terminate to a node.
5. Arrows should be kept straight and not curved or bent.
6. The logical sequence between activities must follow the following rules:

• An event cannot occur until all the incoming activities into it have been completed.
• An activity cannot start unless all the preceding activities on which it depends,have been completed.
• Dummy activities should only be introduced if absolutely necessary.

Critical Path(CPM) Computations

The purpose of analysis or computation is to find the critical path, i.e.,the sequence of activities with the longest duration,and to find the float associated with each non-critical activity.This helps in checking actual progress against the scheduled duration of the project.

To achieve this objective we carry out special computations that produce the following information:

• Total duration needed for the completion of the project.
• Categorization of the activities of the project as being critical or non-critical.

An activity is said to be critical,if the delay in its start will further delay the project completion time.

A non-critical activity allows some scheduling slack ,so that the start time of the activity may be delayed within limits without affecting the completion time of entire project.

To carry out the special computations, the following terms shall be used in critical path calculations:

• Earliest occurrence time of event  'i'.
• Latest occurrence time of event 'j'.
• Duration of activity(i,j)

The critical path calculations are done in two ways:

1. Forward pass calculations
2. Backward pass calculations

Critical path: The critical activities of a network that constitute an uninterrupted path which spans the entire network from start to finish is known as critical path.

Float (or Slack) of an activity and event

The float of an activity is the amount of time by which it is possible to delay its completion time without affecting the total project completion time.

1. Event float : The float is the difference between its latest time and earliest time.
2. Activity float: It is the float in the activity time estimates.There are mainly three types of activity float:

 (i)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.It is the positive difference between the earliest finish time and the latest finish time. or the positive difference between the earliest start time and the latest start time of an activity depending upon which is defined.

(ii)Free float: It is that portion of total float within which an activity can be manipulated without affecting the float of subsequent activities.It is computed for an activity by subtracting the head event slack from its total float.

(iii)Independent float: It is that portion of total float within which an activity can be delayed for start without affecting floats of the preceding activities.It is computed by subtracting the tail event slack from the free float of the activity.If the result is negative,it is taken as zero.

 which causes a reduction in the float of the successor activities.

(iv)Interfering float:Interfering float can be defined as that part of the total float It is the difference between the latest finish time of the activity under consideration and the earliest start time of the following activity,or zero, whichever is larger.

    

PERT Networks

Under the conditions of uncertainty,the estimated time for each activity for PERT network is represented by a probability distribution.The probability distribution of activity time is based upon three different estimates made for each activity.These are:

1. Optimistic time,' a',is the shortest possible time  which occurs when execution goes extremely well.
2.  Most likely time, 'm', is the estimate of the normal time an activity would take,which occurs when execution is done under normal conditions.
3.  Pessimistic time,' b',is the longest time that an activity could take which occurs when execution goes extremely poorly.

The range (a, b) encloses all possible estimates of the duration of an activity. The estimate

m lies somewhere in the range (a, b). Based on the estimates, the average duration

time, D, and variance, v, are approximated as:

                           D= (a+4m+b) / 6

                           v= (b-a / 6)²  

Distinction between PERT and CPM

1. CPM is used for repetitive jobs. On the other hand, PERT is used for non-repetitive jobs.
2. PERT is a probabilistic model with uncertainty in activity duration.On the contrary, CPM is a deterministic model with well known activity times based on experience.It therefore doesn't deal with uncertainty in project duration.
3. PERT is said to be event oriented as the results of analysis are expressed in terms of events or distinct points in time indicative of progress. CPM is , on the other hand, activity oriented as the results of calculations are considered in terms of activities of the project.
4. PERT is applied mainly for planning and scheduling research programmes. On the other hand,CPM is employed in construction and business problems.
5. PERT incorporates statistical analysis and thereby enables determination of probabilities concerning the time by which each activity and the entire project would be completed.On the other hand,CPM doesn't incorporate statistical analysis in determining time estimates because time is precise and known.