CPM Practice 1

 

Key Points:

1. Diagram Overview:

   • A network diagram with activities A, B, C, D, and E.
   • Durations: A = 3 days, B = 4 days, C = 6 days, D = 4 days, E = 3 days.
   • Goals:
     • Identify the Critical Path.
     • Perform Forward and Backward Pass.
     • Calculate Total Float and Free Float for activity D.

2. Critical Path Calculation:

   • Identify all paths:
     • Path 1: A → B → C → E = 3 + 4 + 6 + 3 = 16 days.
     • Path 2: A → B → D → E = 3 + 4 + 4 + 3 = 14 days.
   • Critical Path: Path 1 (A → B → C → E) with 16 days.

3. Forward Pass:

   • Start from Day 1 and calculate Early Start (ES) and Early Finish (EF) for each activity:
     • A: ES = 1, EF = 3 (1 + 3 - 1).
     • B: ES = 4, EF = 7 (4 + 4 - 1).
     • C: ES = 8, EF = 13 (8 + 6 - 1).
     • D: ES = 8, EF = 11 (8 + 4 - 1).
     • E: ES = 14 (max EF of C and D + 1), EF = 16 (14 + 3 - 1).

4. Backward Pass:

   • Start from the critical path duration (16 days) and calculate Late Finish (LF) and Late Start (LS):
     • E: LF = 16, LS = 14 (16 - 3 + 1).
     • C: LF = 13 (from E), LS = 8 (13 - 6 + 1).
     • D: LF = 13 (smallest LF from E), LS = 10 (13 - 4 + 1).
     • B: LF = 7 (smallest LF from C and D), LS = 4 (7 - 4 + 1).
     • A: LF = 3 (from B), LS = 1 (3 - 3 + 1).

5. Total Float Calculation:

   • Formula:
     Total Float = LF - EF or LS - ES.
   • Activity D:
     • LF = 13, EF = 11 → Total Float = 13 - 11 = 2.
     • LS = 10, ES = 8 → Total Float = 10 - 8 = 2.

6. Free Float Calculation:

   • Formula:
     Free Float = ES (Next Activity) - EF (Current Activity) - 1.
   • Activity D:
     • ES (E) = 14, EF (D) = 11 → Free Float = 14 - 11 - 1 = 2.
     • D can be delayed by 2 days without impacting E.

7. Exam Expectations:

   • Expect diagrams with:
     • Multiple paths and convergence points.
     • Questions requiring identification of the critical path, forward and backward pass, total float, and free float.
   • Mastery of these concepts ensures success in similar questions.

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Summary:

This exercise walks through the complete process of solving a network diagram, including identifying the critical path, performing a forward and backward pass, and calculating total float and free float. The critical path (A → B → C → E) spans 16 days, and Activity D has a total and free float of 2 days. By mastering the forward and backward pass techniques, along with float calculations, learners can confidently tackle more complex diagrams and related questions on exams.