Project management and critical path analysis

What network analysis is for

It answers three questions: how long will the project take at minimum, which activities cannot be delayed without delaying the whole project, and where is there spare time that can be reallocated.

Building the network

Nodes are events (a moment in time); arrows are activities with a duration. Each node carries the earliest start time (EST) and the latest finish time (LFT). EST is calculated by a forward pass — take the largest total arriving at each node. LFT is calculated by a backward pass — take the smallest value working back. Taking the largest on the way forward and the smallest on the way back is where most errors happen.

Float and the critical path

$\text{Thời gian dự trữ}=\text{LFT}-\text{thời lượng}-\text{EST}$

The critical path is the chain of activities with zero float. Any delay to a critical activity delays the entire project by the same amount; a delay to a non-critical activity is absorbed by its float until the float runs out.

What it is genuinely useful for

It shows where to concentrate management attention, allows resources to be moved from activities with float to critical ones, and supports just-in-time ordering because it says when each input is actually needed.

Its limitations

Durations are estimates, and a network built on optimistic estimates gives a confident-looking answer that is wrong. It assumes resources are available when the plan says so. It does not by itself manage the project — a critical path drawn once and never updated is decoration. And a complex project produces a network too large to read, which is why software is used in practice.