CPM-PERT

Critical Activity : An activity is said to be critical if a delay in its start will cause further delay in completion of the entire project .

Critical Path : The sequence of critical activities in a network is called the critical path . It is the longest path in the network from the starting event to the ending event and defines the minimum time required to complete the project . In the network it is denoted by double line.

Critical Path Method (CPM)Critical Path Method (CPM) is the technique to determine the duration of a project with great accuracy .What is Critical Path ?The critical path is defined as the largest duration path between the first and the last nodes of a project .Different paths are possible between these first and last nodes .While tracing a path from the first node to the last node , one should always move along the direction of the arrows .The duration of a path is simply the sum of the duration of all the activities on the path .Duration of a project is always the same as the duration of its Critical Path .

Critical Path Schwalbe

Problem-1

Tasks/ActivitiesTime (Days)Required PredecessorsA2-B3-C4-D1AE2BF5BG7CH2D,EI3F,GJ1H,I

Problem-2

Draw the Network Diagram . (b) Find the Critical Path and longest duration of the project .

Tasks/ActivitiesTime (Months)Required PredecessorsA5-B1-C2BD4A,CE6AF3D,E

We are interested in knowing when can an individual activity (activities) start and finish at the earliest if no delay occurs .

Having no delay means :The actual duration of each activity is the same as its estimated duration .Each activity begins as soon as all its immediate predecessors are finished .

Early Start Time / Early Finish TimeEarliest Starting Time (ES) : The starting time of each activity if no delay occur anywhere is called earliest start time . Earliest Finish Time (EF) : The finishing time of each activity if no delay occur anywhere is called earliest finish time .

EF=ES + Estimated duration of the activity .ES=Largest EF of its immediate predecessors .

Schedule Trade-offsFree slack or free float is the amount of time an activity can be delayed without delaying the early start of any immediately following activities.Total slack or total float is the amount of time an activity can be delayed from its early start without delaying the planned project finish date.A forward pass through the network diagram determines the early start and finish dates.A backward pass determines the late start and finish dates.

Program Evaluation and Review Technique (PERT)PERT is a network analysis technique used to estimate project duration when there is a high degree of uncertainty about the individual activity duration estimates.PERT uses probabilistic time estimates:Duration estimates based on using optimistic, most likely, and pessimistic estimates of activity durations, or a three-point estimate.

Uncertain Activity DurationsProject activity durations are not known with certainty . It is very rare that the actual duration will be equal to the estimated duration . Duration of each activity is a variable having a probability distribution .

PERT assumes this distribution to be a beta distribution and allows three estimates .

Most likely estimate : (M ) This is the time estimate that has the highest probability of occurrence .Optimistic Estimate :(O) This is the shortest possible time estimate of an activity .This is the estimate of duration under most favorable conditions .Pessimistic Estimate :(P) This is the longest possible time estimate of an activity .This is the estimate of duration under most unfavorable conditions .

PERT Formula and ExamplePERT weighted average =

optimistic time + 4X most likely time + pessimistic time6Example:

PERT weighted average = 8 workdays + 4 X 10 workdays + 24 workdays = 12 days6where: optimistic time= 8 daysmost likely time = 10 dayspessimistic time = 24 days Therefore, youd use 12 days on the network diagram instead of 10 when using PERT for the above example.

Problem on PERTThe following table gives details about the various activities of a project . Find (a) The Critical path of the project and its expected duration . (b) the probability that the project will be completed within 50 days .

ActivityNodeOMPA1-2101112B2-361014C2-45811D2-5159E3-6375F4-64914G5-7123H6-73711I7-891215J7-9357

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