## The backward pass

The second stage is to carry out a backward pass to calculate the latest date at which each event may be achieved, and each activity started and finished, without delaying the end date of the project. The latest date for an event is the latest date by which all immediately following activities must be started for the project to be completed on time. In calculating the latest dates, we assume that the latest finish date for the project is the same as the earliest finish date - that is, we wish to complete the project as early as possible.

Figure 6.19 illustrates our network and Table 6.3 the activity table after carrying out the backward pass - as with the forward pass, event dates are recorded on the diagram and activity dates on the activity table.

The backward pass rule: the latest date for an event is the latest start date for all the activities that may commence from that event. Where more than one activity commences at a common event we take the earliest of the latest start dates for those activities.

Figure 6.19 The CPM network after the backward pass.

 Activity Duration Earliest Latest Earliest Latest Total (weeks) start date start date finish fate finish date float A 6 0 2 6 8 B 4 0 3 4 7 C 3 6 8 9 11 D 4 4 7 8 11 E 3 4 7 7 10 F 10 0 0 10 10 G 3 10 10 13 13 H 2 9 11 11 13

The latest event dates are calculated as follows.

• The latest date for node 6 is assumed to be week 13, the same as the earliest date.

• The latest date for event 5 is week 10, since activity G will take 3 weeks and must be completed by week 13 if the project end date is not to be exceeded.

• The latest date for event 4 is week 11 since activity H does not need to be started until week 11 if it takes 2 weeks and does not need to be completed until week 13.

• The latest date for event 3 is the latest date by which we must be in a position to start both activities D and E. Activity E need not finish until week 10 and

Figure 6.19 The CPM network after the backward pass.

need not therefore start until week 7. Activity D need not finish until week 11 and, having a duration of 4 weeks, need not start until week 7. The latest date for event 3 is therefore week 7.

• The latest date for event 2 is week 8 since C, which takes 3 weeks, need not be finished until week 11.

• The earliest and latest dates for the start event must always be the same unless an arithmetic error has occurred.

• The latest date for event 1 is the latest by which we must be in a position to start activity A (which must start by week 2), activity B (which must start by week 3) and activity F (which must start by week 0). This event's latest date is therefore zero. This is, of course, not very surprising since it tells us that if the project does not start on time it won't finish on time.