Project scheduling is the process of determining start and end dates for project activities, allocating resources, and establishing dependencies among tasks to achieve project objectives within defined constraints such as time, cost, and resources. Effective scheduling helps in organizing and managing project activities, optimizing resource utilization, and ensuring timely project completion.

Two widely used methods for project scheduling are Critical Path Method (CPM) and Program Evaluation and Review Technique (PERT).

Critical Path Method (CPM):

**Definition**: CPM is a deterministic scheduling technique used to determine the longest sequence of dependent activities (critical path) in a project, which dictates the minimum duration required to complete the project.**Key Features**:**Activity-Based**: Breaks down the project into a network of activities and their dependencies.**Deterministic**: Relies on known activity durations and dependencies to calculate project duration.**Focus on Critical Path**: Identifies the sequence of activities that collectively determine the shortest project duration.**Float Analysis**: Identifies non-critical paths and activities with slack or float time, which can be delayed without impacting project completion.

**Steps**:- Identify project activities and their dependencies.
- Estimate activity durations.
- Construct a network diagram (Activity-on-Node or Activity-on-Arrow).
- Calculate earliest start and finish times, and latest start and finish times for each activity.
- Identify the critical path (activities with zero float) and total project duration.

Program Evaluation and Review Technique (PERT):

**Definition**: PERT is a probabilistic scheduling technique used to analyze and represent the uncertainty in project duration by considering three time estimates for each activity: optimistic (O), most likely (M), and pessimistic (P).**Key Features**:**Probabilistic Approach**: Incorporates uncertainty by using three time estimates for each activity.**Activity Duration Calculation**: Calculates activity durations using weighted averages of the three time estimates (PERT formula).**Focus on Variability**: Identifies activities with the highest variability and potential impact on project duration.**Probability Analysis**: Estimates the probability of completing the project within a specified duration.

**Steps**:- Identify project activities and their dependencies.
- Determine optimistic (O), most likely (M), and pessimistic (P) time estimates for each activity.
- Calculate activity durations using the PERT formula:
`(O + 4M + P) / 6`

. - Construct a network diagram (similar to CPM).
- Perform forward and backward pass calculations to determine earliest start and finish times, latest start and finish times, and float.
- Analyze the critical path and project duration uncertainty.