 we will discuss about network analysis by backward pass. These are the learning outcomes. At the end of the session students will be able to appraise let us start and the let us finish it for the project. Then second outcome evaluate the float value for each activity. And third outcome students will be able to estimate the duration along with the critical path. These are the contents of this video lecture. Then adding the time dimensions already knew that there are the two methods. The first is the forward pass method and the second is the backward pass method. So in the forward pass we have to calculate with the help of forward pass you have to calculate the earliest dates. And with the help of backward pass you have to calculate the let us dates that is the let us start date and the let us finish date. We see the definitions. So let us finish is nothing but it is the let us state that the activity can finish without causing a delay to the project completion date. And let us start means let us date that the activity can start without causing a delay to the project completion date. These are the let us dates. So let us start is calculated with the help of this formula. Let us finish minus duration and the let us finish is nothing but you have to write down as it is the let us start date. But if there are the two values of the let us start then you have to consider the minimum value from the immediate successor. Means if there are the two values 6 and 7 then you have to write down the six value for the let us finish date. This is the node with labeling convention. So this is activity level then this is duration and with the help of forward pass you have to calculate the earliest start and the earliest finish date. The next you have to calculate the let us start and the let us finish date with the help of backward pass. Then this is activity span and this is float. Now moving towards network analysis by backward pass you have to recall the procedure of the forward pass. Now pause the video for a minute and you have to recall procedure of the network analysis by forward pass. So already you have seen the example the project consists of the eight activities whose duration have been estimated okay. So first we see the stable. The stable is nothing but in this table these are the activities these are the activity descriptions. These are the duration then these are the precedents. Here a, b and f having no precedents they will start immediately. Already you knew that how to calculate the forward pass. This is the network after the forward pass. We see the network after the backward pass. So we see the calculation for backward pass. Here for the project completion we require the 13 weeks. So first write down the let us finish date. This is let us start date and this is let us finish date okay. So 13 is the maximum number for the completion of project. So you have to write down 13 as it is here okay. Then for h we have to calculate the let us start date. So how it is calculated let us start date. Let us finish minus duration we have to calculate the let us start. Means 13 minus 2 we get 11. Same here for the g activity it requires 3 weeks and 13 we are the let us finish date. So 13 minus 3 we get the 10 okay. Then c and d are the precedents of the h okay. So this 11 is write down as it is for the c and d. Then for c there is a 3 weeks is the duration okay. So for you have to calculate again let us start date for the c is what 11 minus 3 here we get 8. Then for d there is a 4 duration. Duration is 4 week. So 11 minus 4 here we get 7 okay. Then e and f are the precedents of the g activity. So let us start date of the activity g write down as it is for the activity e and f for the let us finish date. So 10 is written for the e and f as it is okay. Then c the let us start date of e how it is calculated again same 10 minus 3 we get 7. Here 10 minus 10 we get 0 okay. Then b, b is nothing but b is the precedent of c d and e activity. And here the let us start date of the d and e are same 7 here also 7. So write down 7 as it is. Then 7 minus 4 here we get 3. Then a is the precedent of activity c so we have to write down 8 as it is. And then 8 minus 6 we get the 2. So this is the let us start date of the activity a. So this is the net work after backward pass. Here we have to calculate the let us start date as well as let us finish date. Then we see the definitions of activity float and the delay span. So activity float is nothing but the difference between activity's earlier start date and its let us start date. So you have to take the difference between start dates or you have to take the difference between finished date. It is nothing but it is called the activity float. And the float means it is a major of how much you can delay in an individual project activity without delaying the overall project. So here we have to calculate the delay of independent activity each individual activity. So this is the formula let us start minus earlier start or let us finish minus earliest finish. In this way you have to calculate the float of that activity. Then activity span. Activity span is nothing but the difference between the earliest start date and the let us finish date. And it is a major of maximum time allowable for the activity. In this way you have to calculate the maximum time is required for that activity with the help of activity span. It is nothing but difference between let us finish and earliest start. And the free float is nothing but difference between the earliest completion date for the activity and the earliest start date of the succeeding activity. Then calculation of span and float. Here we have to calculate the span activity span and the float. So activate these are the earliest start date, earliest finish date. This is let us start date, let us finish date. So first we see the activity span. Activity span is nothing but let us finish minus earliest start. So 8 minus 0 here we get 8 and float is calculated with the help of you can take the difference between finished date or you can take the difference between start date. Both are same. So 8 minus 6 we get 2. Right? Here 7 minus 0 we get 7 and the 7 minus 4 we get 3. Again for this 10 minus 0 we get 10. Then 10 minus 10 here we get 0. For this 11 minus 6 5 then 11 minus 2 9 2. Then 11 minus 4 7 and the 11 minus 8 3. Then again 10 minus 4 here we get 6 and the 10 minus 7 here we getting 3. Then next for G 13 minus 10 here we are getting 3. Then 13 minus 13 we get 0. Here again 13 minus 9 is nothing but here we obtain 4 and the 13 minus 11 or 11 minus 9 we get 2. Okay? So in this way you have to calculate the activity span and float of the activity. Then identify the critical path. Critical path this is the largest path. At least one path through the network that defines the duration of the project. So here in this way you have to calculate the maximum duration of the project and it is shown with the help of bold line. And the project's duration is nothing but the sum of the activity durations in critical path and a delay to any critical activity will result in a delay to project completion date. So how to identify the critical path? If the float of activity is 0 and the two start dates and the two finish dates are the same then it is known as the critical path. So it is using identifying the task involved then time estimate of every activity, time taken to complete the whole project. In these points you have to use the CPM. So this is nothing but critical path method. It is shown in a red line bold line. Okay? Here we can see that finish date and the start dates are same. Here 0, 0 and this is also 10, 10. Here also start dates both start dates and the both finish dates are same and we get the float is 0 here also here also. So this is nothing but it is a critical path. One more any activities in the critical path are all the critical activities. If we delay in any activity then will occur the delay to the whole project. So in this way you have to identify the critical path method. Critical path. As the name implies this calculation step started at the last activity in the schedule. Here it starts from the backward pass and until the latest start value is computed for the schedule's beginning activity. Means we we can start from the latest finish date and end with the latest start date. These are the references. Thank you.