Project Libre Lab tasks -2,3

 Lab Problem-2

Problem: Calculating Earliest Start and Finish Times

Scenario:

Continuing from Lab Problem-1, where you've modeled the e-commerce website project as a Directed Acyclic Graph (DAG), you now need to perform a forward pass analysis. This analysis is crucial for determining the earliest possible start and finish times for each task, given their durations and dependencies. Understanding these times helps in scheduling resources and identifying potential bottlenecks.

Your Goal:

For each task in the project, calculate its Earliest Start Time (ES) and Earliest Finish Time (EF). The ES for a task is the earliest a task can begin once all its prerequisites are completed. The EF for a task is its ES plus its duration. Assume the project starts at day 0.

Task List (same as Lab Problem-1 for reference):

  • T1: Setup Cloud Infrastructure

    • Duration: 3 days

    • Prerequisites: None

  • T2: Design Database Schema

    • Duration: 5 days

    • Prerequisites: T1

  • T3: Develop Backend API

    • Duration: 10 days

    • Prerequisites: T2

  • T4: Design Frontend UI/UX

    • Duration: 7 days

    • Prerequisites: T1

  • T5: Build Frontend Components

    • Duration: 12 days

    • Prerequisites: T4

  • T6: Implement Payment Gateway

    • Duration: 8 days

    • Prerequisites: T3, T5

  • T7: Write User Documentation

    • Duration: 4 days

    • Prerequisites: T5

  • T8: Deploy to Production

    • Duration: 2 days

    • Prerequisites: T6, T7

Lab Problem-3

Problem: Identifying the Critical Path and Project Completion Time

Scenario:

Having constructed the project dependency graph and calculated the earliest start/finish times, your final step is to identify the critical path and the minimum project completion time. The critical path is the longest sequence of dependent tasks, and any delay in a task on this path will directly delay the entire project. Identifying it is crucial for effective project management and resource allocation.

Your Goal:

  1. Determine the minimum total time required to complete the entire e-commerce website project.

  2. Identify all tasks that lie on the critical path(s). A critical path is a sequence of tasks from the start of the project to the end, where the float (or slack) for each task is zero. You may need to calculate Latest Start (LS) and Latest Finish (LF) times for each task in a backward pass to determine the float.

    • Latest Finish (LF): The latest a task can finish without delaying the project completion.

    • Latest Start (LS): The latest a task can start without delaying the project completion (LF - Duration).

    • Float/Slack: The amount of time a task can be delayed without affecting the project completion date (LS - ES or LF - EF).

Task List (same as Lab Problem-1 and 2 for reference):

  • T1: Setup Cloud Infrastructure

    • Duration: 3 days

    • Prerequisites: None

  • T2: Design Database Schema

    • Duration: 5 days

    • Prerequisites: T1

  • T3: Develop Backend API

    • Duration: 10 days

    • Prerequisites: T2

  • T4: Design Frontend UI/UX

    • Duration: 7 days

    • Prerequisites: T1

  • T5: Build Frontend Components

    • Duration: 12 days

    • Prerequisites: T4

  • T6: Implement Payment Gateway

    • Duration: 8 days

    • Prerequisites: T3, T5

  • T7: Write User Documentation

    • Duration: 4 days

    • Prerequisites: T5

  • T8: Deploy to Production

    • Duration: 2 days

    • Prerequisites: T6, T7

Expected Output:

  1. The minimum total project completion time.

  2. A clear listing of the tasks that form the critical path(s). If there are multiple critical paths, list all of them.

  3. (Optional but Recommended for clarity): A table showing ES, EF, LS, LF, and Float for each task.

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