PERT and CPM - Free MCQ Practice Test with solutions, GATE Civil Construction

There are three phases of project management. These are project planning, project scheduling and project controlling. Project management refers to a highly specialised job to achieve the objectives of a project.

In CPM:
The standard deviation of critical path:

Where, σ₁, σ₂, ...., σ₈, σ₉ are the standard deviation of each activity on the critical path   
Calculation:
Given:
σ₁, σ₂, ...., σ₈, σ₉ = 3

∴ the standard deviation of the critical path is 9.

Henry Gantt introduced the bar charts around 1900 A.D. They give pictorial representation in two dimensions of a project by breaking it down into numerous manageable units.

Optimistic time (t_o), Pessimistic time (t_p), Most likely time (t_m):

The variance is given by:

Calculation:
Given:
t_o = 4, t_E = 7, t_p = 11

There are various network techniques that are called by various names like PERT, CPM, TOPS and LESS. Network technique is one of the major advancements in management science. The full form of PERT is Program Evaluation and Review Technique.

PERT is almost identical to the critical path method (CPM) technique except it assumes each activity duration has a range that follows a statistical distribution.

• In PERT the Normal distribution is used for the completion time of Project.
• PERT uses three-time estimates for each activity. Basically, this means each activity duration can range from an optimistic time to a pessimistic time, and a weighted avenge can be computed for each activity. 
• Because project activities usually represent work, and because work tends to stay behind once it gets behind, the PERT developers chose an approximation of the beta distribution to represent activity durations.
• The activity durations can be skewed more toward the high or low end of the data range. 

• Figure A depicts a beta distribution for activity duration that is skewed toward the right and is representative of work that tends to stay late once it is behind. 
• The distribution for the project duration is represented by a normal (symmetrical) distribution shown in Figure B. 
• The project distribution represents the sum of the weighted avenges of the activities on the critical path.

The full form of CPM is the Critical Path Method. CPM networks are mainly used for those projects for which a fairly accurate estimate of time of completion can be made for each activity.

Resources smoothing:

• It is the first approach of solving the resources allocation problem, in which the resources are considered to be unlimited. The original project duration (i.e. duration along the critical path) is however maintained.
• The start times of some of the activities are shifted within their available floats so that uniform demand is created for the resources.
• The smoothing or adjustment of resources resulting in least variation of resource demand is known as resource smoothing.

In bar charts, different colours are sometimes filled in the bars for showing various control information. For actual progress, green colour is used. For anticipated progress, black colour is used and for progress behind schedule, red colour is used.

Project Crashing

• Project crashing is an exercise carried out to reduce the time of a project by investing more money.
• This becomes necessary when the deadline has to be met.
• For crashing only the critical activities are considered since the duration of the project could be reduced by crashing these activities only.
• It is possible that when a project is crashed another non-critical activity may become critical and in the next cycle, this has to be considered for further crushing.
• Crashing is done on the critical activities which have lower cost slopes to the maximum possible extent. The activities lying on the critical path have the minimum cost slope.

• Crash time is the minimum activity duration to which an activity can be compressed by increasing the resource and hence by increasing the direct cost of a project.
• The objective of crashing is a network is to determine the optimum project duration corresponding to the minimum cost of the project.

Additional Information
Steps involved in crashing a project Network.

• Draw a network diagram and find the critical path and expected project completion time.
• Select the critical activity having a minimum cost slope.
• Reduce the duration of the selected activity by a one-time unit.
• Revise the network diagram by adjusting the time and cost of crashed activity, again finding a critical path, project duration, and total cost of the project.
• if optimum project duration is obtained, then stop otherwise repeat from starting.