PERT and CPM are network techniques for project planning and programming. Let us understand each technique in detail.

Index

**PERT**

PERT stands for ‘Program Evaluation and Review Techniques’. In this technique, a network diagram consisting of events is used to plan a project. An event is a specific moment at which some specific part of a plan is achieved. It represents a point in time and does not consume any resource. In this type of network diagram, the events are joined by arrows. The example of PERT network is, suppose a road is to be constructed. Then different events like excavation done, subgrade prepared, drains and parapets constructed, bitumen layers laid and crush barriers and other road furniture installed are joined by arrows forming a network.

PERT system is preferred for the projects or operations which are of non- repetitive nature or for the projects for which precise time for different activities cannot be determined. For e.g. launching a spacecraft is a unique kind of project which involves the works never done before. The risks and technical problems in these kind of projects are of high magnitude. PER network is suitable for research and development projects.

**CPM**

CPM stands for **‘Critical Path Method’.** In these type of networks, the whole project is divided into small, clearly defined jobs or operations called activities. The activities are the operations which consume both time and resource. Junctions between the activities are called events. These are often referred to as activity oriented diagrams in which, each activity is connected by an arrow. If we take the example of road construction as above, the various activities of road construction, such as excavation, laying of subgrade layer, construction of drains and parapets, laying of bituminous layers, installation of crush barrier and road furniture, etc. are connected through arrows, forming a network diagram. Please note that all of these activities consume time and resources.

CPM networks are mainly used for repetitive nature of projects, or we can say that for the projects where fairly accurate estimates for completion of each activity as well as cost estimates can be made. An example of this type of project is construction of building, where the activities performed are of repetitive nature and fairly accurate estimates of completion time and cost of each activity can be made.

**Difference Between PERT and CPM**

Feature | PERT network | CPM network |

Type of network | Event oriented | Activity oriented |

Nature of project/ job | Non repetitive/ Uncertain | repetitive |

Time estimate for completion | Not accurate and defined | Accurate and defined |

Relationship between cost and time | Cost varies directly with time | Cost is not directly proportional to time |

Controlling factor | Time is the direct controlling factor or control over time overweighs control over cost | Cost is the controlling factor |

Degree of uncertainty | extreme | Mild |

Technology Employed | New technology, experimental | Stable and well established |

Model | Probabilistic Model | Deterministic Model |

Accuracy | Appropriate for high precision time | Suitable for reasonable time estimation |

Crashing of Activities | No crashing is possible because there is no certainty of time | Crashing is possible because time of estimation is definite |

Dummy Activities | No use of dummy activities | Dummy activities are used to show the sequence of activities |

Let us learn in more details about PERT and CPM methods of network analysis.

**PERT: Time Estimates**

As said earlier also, PERT uses a network of events connected by arrows to plan and program the projects. It’s a tool for defining and coordinating various operations involved in it. It may also be defined as a technique that provides statistical information regarding the uncertainties about computation time of various activities associated with the project. It is a method of scheduling and budgeting resources to accomplish the defined task and minimizes delays and conflicts.

PERT uses probabilistic or non- deterministic approach for assessment of duration of completion of an activity. In this approach a limit is fixed within which it is virtually certain that the activity duration will lie. The probability of executing the activity within these limits can be determined.

*Estimating Time in PERT System*

Time is the most essential and basic variable in PERT system. Time is the controlling factor in PERT analysis because PERT is used in the projects which are of uncertain nature and the time and cost estimates of activities or operations cannot be accurately determined in such projects. Therefore, controlling the time in such projects means cost controlling. In projects, there is uncertainity about the time required for the completion of various activities. Thus, to take the uncertainties into account, PERT has three kinds of time estimates:

- The optimistic time estimate
- The pessimistic time estimate
- The most likely time estimate

*The Optimistic Time Estimates*

This is the shortest possible time to complete and activity in an ideal condition. This time estimates are denoted by t_{O.}

*The Pessimistic Time Estimates*

It is the estimation for time required to complete an activity if everything went wrong and adverse conditions prevailed. It does not include the natural calamities such as earthquakes, floods, fires, etc. This is denoted by t_{P.}

*The Most Likely Time Estimate*

This is the most probable time required to complete an activity if normal conditions prevail. This time estimate lies between optimistic and pessimistic time estimates and is denoted by t_{L.}

**Applicability of Frequency Distribution Concept in PERT**

Frequency distribution curve is used to determine the three time estimates, i.e. the most optimistic time (t_{O}), most pessimistic time (t_{P}) and the most likely time (t_{L}), used in PERT network analysis. Let us take an activity ‘A’ under different conditions. The time required to complete the activity in most favorable conditions will be less than the time required in most adverse conditions. If we plot a curve between the ‘time of completion’ and the number of activities completed in that time, then a frequency distribution curve as shown in Fig 1.1 below will be obtained.

From the above curve, it is clear that large number of activities completed in the most likely time (t_{L}). Point A in the curve shows most optimistic time (t_{O}), point B denotes the most pessimistic time (t_{P}) and the point C demonstrates the most likely time of completion of activities (t_{L}).

You can observe that the curve is symmetrical about the vertical line passing through C. This type of curve is called the *‘normal distribution curve’*. A frequency distribution curve may also be asymmetrical about the central axis, i.e. it may be skew to either side of the curve. This type of curve is known as *‘beta distribution curve’*.

Fig 1.2 (a) below shows the frequency distribution curve for activity A, which is skew to the left. The difference between t_{L }and t_{O }is 2 days while the difference between t_{p }and t_{L }is 4 days. Similarly, in Fig 1.2 (b), which is skewed to the right, the difference between t_{L }and t_{O }is 5 days while the difference between t_{p }and t_{L }is 1 day. If we see Fig 1.2 (c) and Fig 1.2 (d), then we can observe that both the curves are symmetrical about their vertical axis, therefore they are normal distribution curves. However, the variation between t_{P} and t_{L} is more in case of curve (c) which means there is more uncertainity in time estimates while it is smaller in case of curve (d) which shows that more reliable time estimates are expected in case of curve (d).

In a nutshell we can conclude that a wide range of time estimates represents greater uncertainity in estimating correct time the said activity will require for completion.

The statistical data for completion time of a particular type of activity in different circumstances is used to plot a frequency distribution curve. Let us take an example, how to prepare a frequency distribution curve by using given data.

*Example:*

Time required for casting columns of similar dimensions in a construction project are recorded below. Plot the frequency distribution curve:

*Time of completion for casting the columns (days)*

5 | 6 | 5 | 3 | 7 |

7 | 4 | 8 | 6 | 3 |

5 | 5 | 7 | 4 | 10 |

6 | 5 | 6 | 5 | 6 |

9 | 7 | 4 | 7 | 8 |

8 | 8 | 5 | 8 | 7 |

10 | 9 | 6 | 7 | 9 |

6 | 11 | 8 | 9 | 12 |

7 | 6 | 11 | 4 | 6 |

10 |

*Solution*

By seeing above table we can observe that minimum number of days for casting the column are 3 while the maximum days required for casting similar columns are 12. Now we will segregate the number of activities by the days of completion using the table mentioned below.

Days of completion | No. of activities |

3 | 2 |

4 | 4 |

5 | 7 |

6 | 9 |

7 | 8 |

8 | 6 |

9 | 4 |

10 | 3 |

11 | 2 |

12 | 1 |

Using the above data, a frequency distribution curve can be plotted between ‘No. of days’ in X- axis and No. of columns in Y- axis which is shown below.

From the above curve a conclusion can be drawn that the *‘most pessimistic time t _{P}= 12’, ‘the most optimistic time t_{O}= 2*’, while

*‘the most likely time t*’.

_{L}= 6So, in PERT networks, a probability distribution chart can be used in the above manner to determine the three time estimates t_{O}, t_{L }and t_{P} for an activity. Also the frequency distribution curve is skewed to the left.

**Critical Path Method: Time Estimates**

The critical path method is commonly used in for the repetitive type of projects or for the projects comprising of the activities which are common in nature and many similar activities has been done earlier also. The CPM technique is widely used in construction projects.

CPM networks are activity oriented which means the arrows represent activities and the sequence in which the activities are performed is shown by the sequence of the arrows. The main focus of CPM networks is to determine the critical activities. Critical activities are the activities if delayed then the whole project will be delayed. Therefore, the focus is to control the critical activities.

In CPM technique, first of all a network of activities is prepared. The placement of an activity is mainly done by answering the three basic questions:

- Which activity or activities immediately precede this activity?
- Which activity or activities cannot be started until after the completion of this activity?
- Which activity or activities can be performed concurrently with this activity?

After preparing the networks, the time estimate of different activities is determined. As discussed earlier also, there are two approaches to determine the time estimate. One is called the probabilistic approach and another is deterministic approach. Probabilistic approach is used in PERT network, where the activities are new and mainly related to research and development. We do not have much know- how of these type of activities and accurate estimation of completion time is not possible for these type of activities. Uncertainties are taken into account for this analysis and hence three time estimates are calculated in this approach. Deterministic approach is used in CPM network analysis. The activities in CPM are of repetitive nature and we have enough know- how about these kind of activities. Therefore, fairly accurate time estimation is possible for these kind of activities. No uncertainties are taken into account in this approach.

Figure 1.3 (a) and 1.3 (b) shows probabilistic and deterministic type of frequency distribution curves. Fig 1.3 (a) has wider range and hence greater uncertainty while Fig 1.3 (b) has narrow range and therefore more predictability.

In PERT the expected time in completion of an activity is calculated on the basis of three time estimates while in CPM no calculation for time estimate is required. The estimated time which is denoted by ‘t’ is directly used for network analysis.

**Key Takeaways**

(a) PERT and CPM are network techniques for project planning and programming.

(b) PERT system is preferred for the projects or operations which are of non- repetitive nature or for the projects for which precise time for different activities cannot be determined.

(c) CPM networks are mainly used for repetitive nature of projects, or we can say that for the projects where fairly accurate estimates for completion of each activity as well as cost estimates can be made.

(d) PERT uses probabilistic or non- deterministic approach for assessment of duration of completion of an activity while CPM uses deterministic approach.

(e) In PERT control over time overweighs control over cost while in CPM, cost in the controlling factor.

Also read: Checking the Health of the Project using Earned Value Management Analysis