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Project Evaluation Review Technique and Critical Path Method

Project Evaluation Review Technique and Critical Path Method

Project management is sometimes very critical since a slight delay can result into big cost escalation. A project is normally a combination of different interrelated activities. The number of activities can range from a low number to very large numbers. Among all these activities of a project, each one is not equally important. There are some activities which are done just for smoothing the completeness of the project, while there are some other activities which are very crucial for the whole project. Delay in any of these crucial activities can cause the whole project to delay. Hence it is necessary to know which activities are critical among all the activities. Different network techniques have been evolved which help in identifying those tasks which are critical for the project implementation.

Several network techniques are normally used for planning and scheduling of large projects in the fields of construction, maintenance, fabrication, purchasing, computer system instantiation, research and development planning etc. They are graphical representations of logical and sequentially connected activities and events of a project. ‘Programme evolution review technique’ (PERT) and ‘critical path method’ (CPM) are the two widely applied network techniques. Other network techniques are Gantt charts, ‘programme evaluation procedure’ (PEP), ‘least cost estimating and scheduling’ (LCES), and ‘scheduling and control by automated network system’ (SCAN) etc.

In a project, an activity is a task which is to be performed and an event is a milestone marking the completion of one or more activities. Before an activity can begin, all of its predecessor activities are to be completed. Project network models represent activities and milestones by arcs and nodes. Network diagrams are normally prepared using an arrow-diagram approach.

Two types of network diagrams are normally used. These are (i) ‘activity on arc’ (AOA)  diagram in which an activity is represented on an arc, while a node is used to separate an activity from its immediate predecessors, and (ii) ‘activity on node’ (Node) diagram in which the activity is represented by the node, while the arc is used to show the precedence relationship between the activities. Three pieces of information are normally needed for the network diagram. These are namely (i) activity information (ii) precedence relationship and (iii) time information.

There are some basic steps in the planning of a project using a network diagram with arrow-diagram approach. These steps are (i) to analyze the project and to determine the individual tasks or operations which are needed, (ii) to show the sequence of these operations on an arrow-diagram, (iii) to estimate the time it is going to take to carry out each operation, and (iv) to perform simple computations to locate the critical path (the chain of interdependent operations which determines the duration of the entire project). This step also provides other information which is useful in scheduling the project. This information is used to develop the most economical and efficient schedule for the project. The schedule is then used to control and monitor the progress of the project jobs. The schedule is revised and updated frequently throughout the execution of the project.

In addition to the above steps, there are some rules which are to be followed in constructing an arrow diagram. These rules are (i) each operation is to be shown by a single arrow, (ii) the diagram is not to be drawn to scale, (iii) no operation can start until all preceding operations have been completed, (iv) the three basic issues which are to be considered are to know the jobs which are to precede the job under consideration, the jobs which can follow the job under consideration, and the jobs which can be done simultaneously, (v) every operation is to have a preceding and a following operation, except the first operation and the last operation, (vi) dummies are to be used to show the correct dependencies between events and to avoid having more than one operation with the same set of event numbers, (vii) to number the arrow-diagram in such a way so that the numbers always increase as one go from the start to the finish, and (viii) to use only one starting event and one ending event.

Essentially, there are six steps which are common to both the techniques (PERT and CPM). These six steps which are necessary for both the techniques are (i) preparing of the list of activities, (ii) defining of the inter-relationship among the activities, (iii) estimating the activity duration, (iv) assembling the activities in the form of a flow diagram, (v) drawing the network, and (vi) analyzing the network i.e. computing of early start time and the latest start time, and identifying of the critical events, critical path, and critical activities.

In case of large network, it is necessary that some good practices are used to draw an easy to follow network. These practices are (i) to try to avoid arrows which cross each other, (ii) to use straight arrows, (iii) not to attempt to represent duration of activity by its arrow length, (iv) to use arrows from left to right and to avoid mixing two directions with vertical and standing arrows can be used if necessary, and (v) to use dummies freely in rough draft but final network is not to have any redundant dummies. Some situations in the network diagram are shown in Fig 1.

Fig 1 Situations in network diagram


PERT was developed in the late 1950s by the Navy Special Projects Office in cooperation with the management consulting organization of Booz, Allen, and Hamilton. The technique was used in the engineering and development program of the Polaris missile which was a complicated project involving large numbers of prime contractors as well as sub-contractors. Since that time, it has been widely adopted and used in the industry and has been applied to such diverse projects as construction projects, research management, and product development etc.

A PERT network is typically represented as an activity on an arc network, in which the activities are represented on the lines and milestones on the nodes. It consists of a series of arrows (activities) which connect a series of circles or rectangles (events). Arrows can be solid (which indicates an activity which take time) or dashed which are ‘dummy arrows’. Dummy activity indicates only precedence relationships and does not require any time of effort. Dummy arrows do not take time (i.e. no time factor is involved) and only indicate that one event is dependent upon another (i.e. the event depends on the completion of other event).

The milestones normally are numbered so that the ending node of an activity has a higher number than the beginning node. Incrementing the numbers by 10 allows for new ones to be inserted without modifying the numbering of the entire diagram. The activities in the above diagram are labelled with letters along with the expected time needed to complete the activity.

Rules of for PERT network logic are (i) before an activity can begin, all activities preceding it are to be completed, (ii) arrows imply logical precedence only and neither the length of the arrow nor its direction on the diagram has any significance, (iii) any two events can be connected directly by no more than one activity, (iv) event numbers are not to be duplicated in a network, (v) networks can have only one initial event and only one final event, and (vi) time estimates for completion of each event arc stated on the diagram are in common units (e.g. weeks, days, or hours).

PERT is based on the assumption that the duration of an activity follows a probability distribution instead of being a single value. Three time estimates are needed to compute the parameters of the duration distribution of an activity. These are (i) pessimistic time (tp) which is the time the activity takes if things do not go well; (ii) most likely time ™ which is the consensus best estimate of the duration of the activity, and (iii) optimistic time (to) which is the time the activity takes if things go well. The formula used to calculate the mean expected time (te) = (tp + 4tm +to)/6. Thus, the optimistic and pessimistic times are taken as the end points of the distribution, and the most likely time as the mode. Finally, a standard deviation equal to one-sixth the range-is assumed.

The advantages of this method of obtaining expected time are (i) the planner obtains probability data which can then be fed into a computer in order to calculate the probability of finishing the project on time and (ii) it enables the planner to anticipate and redirect the resources to avoid costly delays.

PERT is useful because it provides (i) the expected project completion time, (ii) probability of completion before a specified date, (iii) the critical path activities which directly impact the completion time, (iv) the activities which have slack time and that can lend resources to critical path activities, and (v) activities start and end dates. The limitations of PERT are (i) the activity time estimates are somewhat subjective and depend on judgment and can be a guess, or with bias, and (ii) the under estimation of the project completion time due to alternate paths becoming critical is perhaps the most serious. A typical PERT diagram is shown in Fig 2.

Fig 2 A typical PERT diagram


CPM was developed in 1957 by J. E. Kelly of Remington Rand and MR Walker of Du Pont. It differs from PERT primarily in the details of how time and cost are treated. The computation was designed for the UNIVAC-I computer. The first test was made in 1958, when CPM was applied to the construction of a new chemical plant. In March 1959, the method was applied to maintenance shut-down at the Du Pont works in Louisville, Kentucky. Unproductive time was reduced from 125 hours to 93 hours.

CPM is an arrow diagram which is similar to a PERT network in terms of its construction technique. The rules for construction are very much the same. The major differences centre on (i) the usual omission of circles for events (and hence, the orientation toward activities), and (ii) the time estimate of the duration of the activity rather than the completion of an event.

CPM is useful since it (i) provides a graphical view of the project, (ii) predicts the time needed to complete the project, and (iii) shows which activities are critical for maintaining the schedule and which are not. The limitations of CPM are (i) while CPM is easy to understand and use, it does not consider the time variations which can have a great impact on the completion time of a complex project, (ii) CPM was developed for complex but fairly routine projects with minimum uncertainty in the project completion times, and (ii) for less routine projects there is more uncertainty in the completion times, and this uncertainty limits the usefulness of CPM. A typical CPM diagram is shown in Fig 3.

Fig 3 Typical CPM diagram


PERT and CPM are widely used to plan, schedule, budget and control different activities normally associated with a project. Both of these are referred to as project scheduling techniques and represent a project as a network. Both are arrow diagrams which are similar in many ways and yet take paths that are frequently different. Both are systematic ways of analyzing and planning the components of a program or a project. Both have been used extensively.

In PERT activities are shown as a network of precedence relationships. It uses activity on arrow network construction and probabilistic activity time estimates. In CPM, activities are shown as network of precedence relationships. It uses activity on node network construction and time estimates which can be predicted with a fair accuracy due to the existence of past experience. Tab 1 shows a comparison of PERT and CPM.

Tab 1 Comparison of PERT and CPM
Serial numberPERTCPM
1PERT uses event oriented networkCPM uses activity oriented network
2In PRT, estimates of time for activities are  not so accurate and definiteIn CPM, duration of activity can be estimated with a fair degree of accuracy
3PERT is used mostly in projects of non repetitive natureCPM is used extensively in construction projects
4In PERT, probabilistic model concept is usedIn CPM, deterministic concept is used.
5PERT is basically a tool for planningCPM can control both time and cost when planning.
6In PERT, it is assumed that cost varies directly with time. Attention is given to minimize the time so that minimum cost results. Thus in PERT, the time is controlling factor.In CPM, cost optimization is given prime importance. The time for completion of the project depends on the cost optimization. The cost is not directly proportion to the time. Thus, cost is the controlling factor.

Although PERT and CPM differ to some extent in terminology and in the construction of the network, their objectives are the same. Furthermore, the analysis used in both techniques is very similar. The major difference is that, in CPM activity times are assumed proportional to the amount of resources allocated to them, and by changing the level of resources the activity times and the project completion time can be varied. Thus CPM assumes prior experience with similar projects from which the relationships between resources and job times are available.

On the other hand, PERT incorporates uncertainties in activity times in its analysis. It determines the probabilities of completing various stages of the project by specified deadlines. It also calculates the expected time to complete the project. An important and extremely useful by-product of PERT analysis is its identification of various bottlenecks in a project. In other words, it identifies the activities which have high potential for causing delays in completing the project on schedule. Thus, even before the project has started, the project management knows where it can expect delays. The management can then take the necessary preventive measures to reduce possible delays so that the project schedule is maintained.

PERT was originally designed to examine projects from the stand points of uncertainty while the CPM was designed to examine projects from the standpoint of costs. Both the techniques rely heavily on the use of networks to help plan and display the coordination of all the activities of a project. These techniques have been combined over time. Over the years these two forms of systems management have become more and more alike. Presently, in actual implementation, the distinctions between PERT and CPM have become blurred since the best features of both systems have been integrated for the purpose of effective management of the projects.

The merged CPM and PERT technique is referred to as ‘PERT/CPM’. In merged technique it is visually easier to see precedence relationships. It consists of a network of branches and nodes and is ideal for large projects with many activities. In fact, presently a project network is a network diagram which uses nodes and arcs to represent the progression of the activities of the project from start to finish.

The critical path on the PERT/CPM diagram is that path which takes the longest time from start to finish. It is that chain of activities or operations whose durations when summed determine the overall length of the project. A change in any activity on the critical path changes the total time or duration of the project. Parallel critical paths can exist but they are to have the same total duration and this total time is to be longer than any other path. Another way to conceptualize the critical path for a critical operation is that where along the critical path there is always a zero total float. A typical PERT/CPM diagram is shown in Fig 4.

Fig 4 Typical PERT/CPM diagram

In the above PERT/CPM diagram capital letter represent the activity. The number in circle shows the event. Hence, in the number 7/10, the numerator denotes the ‘earliest event occurrence time’ and the denominator denote the ‘latest event occurrence time’ in weeks. The ‘critical path for this network is A-B-E-J-M-P. The events on the critical path have zero slack. Dummy activity has no duration. The total duration for the completion of the project is 40 weeks based on the critical path.

The techniques of PERT and CPM enable project managers to evaluate the early and late times at which activities can start and finish, calculate activity float (slack), define critical activities, and evaluate the impact of changes in duration, logical relations and cost on the overall project duration. Both CPM and PERT are network based techniques and hence help in programming and monitoring the progress of the stages involved so that the project is completed within the deadline. In doing this, the techniques specify the parts of the project which are crucial and which if delayed beyond the normal time increase the completion time of the project as a whole. The techniques further assist in allocating resources, such as manpower and equipment and thus helps to make the total cost of the project a minimum by finding the optimal trade-off between various costs and time involved.

The implementation of PERT and CPM had an immediate impact on scheduling projects since it allowed the practice of ‘management by exception’. Although there may be a very large number of activities in the course of a project, possibly only a few of them can be ‘critical’ which are required to be monitored closely.

Terminology in a PERT/CPM network

The following terminology is used for a PERT/CPM network.

Activity – It is a distinct task which is required to be performed as part of the project. Any individual operation which utilizes resources and has an end and a beginning is called activity. An arrow is commonly used to represent an activity with its head indicating the direction of progress in the project. These are classified into four categories (i) predecessor activity which is to be completed immediately prior to the start of another activity , (ii) successor activity  which cannot be started until one or more of other activities are completed but immediately succeed them, (iii) concurrent activities which can be accomplished concurrently (It to be noted that an activity can be a predecessor or a successor to an event or it can be concurrent with one or more of other activities), and (iv) dummy activity which is an activity that does not consume any kind of resource but merely depicts the technological dependence.

The dummy activity is inserted in the network to clarify the activity pattern in the two situations namely (i) to make activities with common starting and finishing points distinguishable, and (ii) to identify and maintain the proper precedence relationship between activities which is not connected by events.

Sequencing – It is the first prerequisite in the development of network which is to maintain the precedence relationships. In order to make a network, the points which are to be taken into considerations are (i) to know the job or jobs which precede an activity, (ii) to know the job or jobs which can run concurrently, (iii) to know the job or jobs which follow the activity, and (iv) to know what controls the start and finish of a job. Since all the further calculations are based on the network, it is necessary that a network be drawn with full care.

Arrow – It shows the direction of the activity. An arrow implies logical precedence only. Neither the length of the arrow nor its direction on the diagram has any significance.

Node – It is represented by a circle and indicates an event, a point in time where one or more activities start and / or finish. Start node is that node which represents the beginning of the project while the finish node indicates the end of the project.

Immediate predecessors – These are the activities which are to be completed by no later than the start time of the given activity.

Immediate successor – Given the immediate predecessor of an activity, this activity becomes the immediate successor of each of these immediate predecessors. If an immediate successor has a multiple of immediate predecessors, then all are to be finished before the activity can begin.

Path – It is a sequence of activities which follows a set of arcs from the start node to the finish node of a network. It is a route through a project network. The length of the path is defined as the sum of the durations of the activities of the path.

Branch – It is a line in a PERT network indicating an activity or precedence. It is also called an arc.

Slack time – It is the difference between the latest and the earliest start time or between the earliest and latest finish time of an activity. It is the amount of time by which an activity can be delayed beyond its earliest start or earliest finish time or earliest finish without delaying the completion of the overall project.

Float – Float of an activity represents the excess of available time over its duration. Total float is the amount of time by which the completion of an activity can be delayed beyond the earliest expected completion time without affecting the overall project duration. Free float is the time by which the completion of an activity can be delayed beyond the earliest finish time without affecting the earliest start of subsequent (succeeding) activities.

Critical path – It is the sequence of activities which determines the longest path through the network that yields the minimum time in which an entire project can be completed. It is the path which has the longest length through the project. If the slack is zero for an activity then it is on critical path. Similarly if slack is positive then the activity is not on the critical path.

Event – An event represents a point in time signifying the completion of some activities and the beginning of new ones. This is normally represented by a circle in a network which is also called a node or connector. The events are classified in to three categories namely (i) merge event which is when more than one activity comes and joins an event, (ii) burst event which is when more than one activity leaves an event, and (iii) merge and burst event which is when an activity can be merge and burst event at the same time as with respect to some activities it can be a merge event and with respect to some other activities it can be a burst event.

Critical activities – These are the activities which are on the critical path.

Dummy – It is an imaginary activity inserted into the network to show a precedence relationship, but it does not represent any actual passage of time. It is an imaginary activity which needs no time and is used to maintain the appropriate precedence relationships in a PERT network

Earliest start of an activity – It is the earliest moment at which an activity can start in a PERT network. It is the calendar time when an event can occur when all the predecessor events are completed at the earliest possible times. Earliest start time for an activity is equal to the largest of the earliest finish times of its immediate predecessors.

Earliest finish time of an activity – It is the earliest moment at which an activity can be completed in a PERT network. It is the time at which an activity finishes if there are no delays in the project.

Latest start time of an activity – It is the latest time in a PERT network at which the activity can start without delaying the subsequent events. It is the latest moment at which an activity can start without delaying completion of the overall project.

Latest finish time of an activity – It is the latest time in a PERT network at which the activity can be completed without delaying the subsequent events. It is the latest time at which an activity can be completed without delaying the completion of the overall project. Latest finish time of an activity is equal to the smallest of the latest start times of its immediate successors.

Forward pass – It is the process of moving through the project from start to finish time determining the earliest start and finish times for the activities of the project.

Backward pass – It is the process of moving backward through a project from finish to start to determine the latest start and finish times for the activities of the project.

Crashing – In CPM, crashing an activity refers to taking on extra expenditures in order to reduce the duration of an activity below its expected duration. It is a term which describes the process of reducing the time needed to complete an activity. Crash point shows the time and cost when the activity is fully crashed.

Crashing time – It is the minimum possible time for completion of an activity, corresponding to maximum resource concentration. Crash cost is the cost needed to achieve the crash time.

Normal point – In CPM, it is the maximum time for completion of an activity, corresponding to minimal resource usage. It is the time of an activity when it is performed in a normal way. Normal cost is the cost needed to achieve the normal time.

Optimistic time – It is the time needed to complete an activity if everything goes well.

Most probable time – It is the time needed to complete an activity under normal conditions.

Pessimistic time – It is the time needed to complete an activity under the most unfavourable conditions.

Beta distribution – It is a probability distribution used to model the activity times in PERT.

Normal time – In CPM, it is the maximum time for completion of an activity, corresponding to the minimum of the resource usage.

Normal cost – it is the cost needed to achieve the normal time.

Common errors in drawing network diagrams

The three types of errors are most commonly observed in drawing network diagrams are (i) dangling, (ii) looping, and (iii) redundancy. These are shown in Fig 5.

Fig 5 Common errors in drawing network diagrams

Dangling – It consists of disconnect of an activity before the completion of all activities in a network diagram. As shown in the Fig 5, activities (5 – 9) and (6 – 7) are not the last activities in the network. So the diagram indicates the error of dangling

Looping – Looping error is also known as cycling error in a network diagram. Drawing an endless loop in a network is known as error of looping as shown in the Fig 5.

Redundancy – Unnecessarily inserting the dummy activity in network logic is known as the error of redundancy as shown in the Fig 5.

Advantages and disadvantages of PERT/ CPM

There are several advantages of PERT/CPM since (i) it is useful during several stages of the project management, (ii) the diagram is mathematically simple, (iii) it provides critical path and slack time, (iv) it provides project documentation, (v) it is useful in monitoring costs, (vi) it explicitly defines and makes visible dependencies (precedence relationships) between the elements, (vii) it facilitates identification of the critical path and makes it visible, (viii) it facilitates identification of early start, late start, and slack for each activity, (ix) it provides for potentially reduced project duration due to better understanding of the dependencies which leads to improved overlapping of activities and tasks where feasible.

The disadvantages of PERT/CPM include (i) there can be potentially hundreds or thousands of activities and individual dependency relationships, (ii) the network diagrams tend to be large and unwieldy needing several pages to print and requiring special size paper, (iii) the lack of a time-frame on most PERT/CPM diagrams makes it harder to show status although colours can help (e.g. specific colour for completed nodes), and (iv) When the PERT/CPM diagrams become unwieldy, they are no longer used to manage the project.

Comments on Post (2)

  • Dr DD Sharma

    Yes PERT & CPM are great Tools for completing a Project without Time & Cost over runs.

    • Posted: 30 September, 2013 at 04:40 am
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  • K.Raghu

    It is a ready reckoner/Hand book coming from an authority, with impeccable record, and is useful for any Project.

    • Posted: 01 October, 2013 at 07:15 am
    • Reply

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