Activity networks, forward and backward passes to find earliest and latest times, the critical path, float, and resource scheduling with Gantt charts.

What this dot point is asking

AQA wants you to draw an activity network from a precedence table, carry out a forward pass for earliest event times and a backward pass for latest event times, identify the critical path and the minimum project duration, calculate float, and schedule activities with a Gantt chart and a given number of workers.

Activity networks and the two passes

You draw the network from a precedence (dependence) table, in which each activity lists its immediate predecessors. AQA uses an activity-on-arc convention: arcs are activities and nodes are events, with each node split into the earliest and latest event times. Sometimes a dummy activity (a dotted arc of zero duration) is needed to preserve the correct logic when two activities share a predecessor but not all dependencies, or to give two activities distinct start and end events. Once the network is drawn, you sweep through it twice.

The critical path and float

Resource scheduling

A Gantt chart (cascade chart) plots each activity against time as a horizontal bar, with critical activities fixed in place and non-critical activities drawn at their earliest start with a trailing block showing their float. Stacking the bars by time lets you read off the number of workers required at each instant, the resource histogram. If the peak demand exceeds the workforce available, you slide non-critical activities later within their float to flatten the peaks, a process called resource levelling. Because critical activities have no float, they cannot be moved, so levelling only ever shifts the non-critical work, and the project duration is unchanged provided no float is exceeded.

Besides total float, two finer measures sometimes appear. Independent float is the spare time available even if every other activity is as late as possible, and interfering float is the difference between total and independent float, the part shared with neighbouring activities. The key exam discipline is to apply the maximum rule on the forward pass and the minimum rule on the backward pass without mixing them, to read the critical path as the longest route through the network, and to remember that using an activity's float can consume the float of others further along the same chain.