Calculation of Time Estimates in CPM
In the project network given in figure below, activities and their durations are specified at the activities. Find the critical path and the project duration.
Calculations in Network Analysis
The following calculations are required in network analysis in order to prepare a schedule of the project.
The symbols used in the calculations are shown in table below.
The computations are made in following steps.
(a) Forward Pass Computations :
(b) Backward Pass Computations :
(c) Calculation of Slack:
The calculations for the above taken example network are summarised below in the table.
(d) Determination of Critical Path:
The sequance of critical activities in a network is called the critical path. The activities with zero slack of head event and zero slack for tail event, are called as crititcal activities. In the taken network, the following activities are critical activities: 5 - 10, 10 - 20, 20 - 30, 30 - 35, 35 - 45.
Calculation of Expected Time and Variance of a Path in PERT
The Expected Time of a chain of activities in series, is the sum of their expected times. Similarly the variance of the path, is the sum of variances of activities on the path. In Figure below, three activities A,B and C are connected in series, (i.e. form a path). Their time estimates to-tm-tpare given along the activity arrows. The expected time of the path 1-2-3-4 is calculated as:
As the length of the path ,that is the number of activies connected in series increases,the variance of the path and hence the uncertainty of meeting the expected time also increases.
In the network of figure below, the PERT time estimates of the activities are written along the activity arrows in the order to-tm-tp. Compute the expected time and variance for each activity. Also compute the expected duration and standard deviation for the following paths of the network.
The computation of expected times and variances for different activities are carried in a table given below.