# What is the Critical Path Method in Project Management?

## Critical Path Method (CPM):

A **path** in the activity network graph is any set of consecutive nodes and edges in this graph from the starting node to the last node. A **critical path** consists of a set of dependent tasks that need to be performed in a sequence and which together take the longest time to complete.

A critical task is one with zero slack time. A path from the start node to the finish node containing only critical tasks is called a **critical path**. **CPM** is an algorithmic approach to determine the critical paths and slack times for tasks.

### Quantities of Critical Path Method (CPM):

**Minimum time (MT):** It is the minimum time required to complete the project. It is computed by determining the maximum of all paths from start to finish.

**Earliest start (ES):** It is the time of a task is the maximum of all paths from the start to this task. The ES for a task is the ES of the previous task plus the duration of the preceding task.

**Latest start time (LST):** It is the difference between MT and the maximum of all paths from this task to the finish. The LST can be computed by subtracting the duration of the subsequent task from the LST of the subsequent task.

**Earliest finish time (EF):** The EF for a task is the sum of the earliest start time of the task and the duration of the task.

**Latest finish (LF):** LF indicates the latest time by which a task can finish without affecting the completion time of the project. A task completed beyond its LF would cause a project delay. LF of a task can be obtained by subtracting the maximum of all paths from this task to finish from MT.

**Slack time (ST):** The slack time (or float time) is the total time that a task may be delayed before it will affect the end time of the project. The slack time indicates the ”**flexibility**” in the starting and completion of tasks. ST for a task is LS-ES and can equivalently be written as LF-EF.