Using The Information In The Next Table To Answer The Questi

Using The Information In Next Table To Answer the Below Questionsadr

Using the information in the next table to answer the following questions: A) Draw the network diagram. B) How many paths are in the network, and what are they? C) What is the critical path and its duration? D) Find the value of float time/slack time for each task in the network by calculating the value of ES, EF, LS, LF.

Paper For Above instruction

The task involves constructing and analyzing a project network diagram based on given task durations and dependencies. The process includes creating a visual representation of the project network, identifying all possible paths, determining the critical path, and calculating the float or slack time for each task. This comprehensive analysis aids in effective project scheduling and resource management.

Introduction

Project management relies heavily on understanding the sequence and duration of tasks to ensure timely completion of a project. Network diagrams, such as the Critical Path Method (CPM), facilitate visualizing task dependencies, calculating project duration, and identifying potential bottlenecks. In this context, we analyze a project with specified tasks, durations, and predecessor relationships to construct a network diagram, identify all paths, determine the critical path, and compute slack times.

Constructing the Network Diagram

The table provides task details: task identifiers, durations, and their immediate predecessors. Tasks are represented as nodes, and dependencies are depicted as directed edges. The diagram begins with tasks that have no predecessors and proceeds to subsequent tasks, ensuring dependencies are maintained. The network diagram depicts the following structure:

  • Tasks A, B, C, D, and F start simultaneously (no predecessors).
  • G depends on B, H on C, I on D, J on F, G, H, K on I, L and M on J and K, N on L and M.

Connecting nodes according to dependencies yields a directed graph illustrating task sequences and overlaps, essential for further analysis.

Identifying All Paths

Paths are sequences from start to finish that traverse through dependent tasks without repetition. The identified paths are:

  1. A → F → J → L → N
  2. A → F → J → M → N
  3. A → F → K → L → N
  4. A → F → K → M → N
  5. A → G → I → K → L → N
  6. B → G → I → K → L → N
  7. B → G → I → K → M → N
  8. B → G → I → L → N
  9. B → G → I → M → N
  10. C → H → J → L → N
  11. C → H → J → M → N
  12. C → H → K → L → N
  13. C → H → K → M → N
  14. D → I → K → L → N
  15. D → I → K → M → N

Through these paths, we observe multiple routes from start to finish, crucial for determining the critical path.

Calculating the Critical Path and Duration

The critical path is the longest path in terms of total task durations, dictating the minimum project completion time. To identify it, we sum task durations along each path:

  • Path A → F → J → L → N: 5 + 1 + 3 + 2 + 10 = 21 days
  • Path A → F → J → M → N: 5 + 1 + 3 + 1 + 10 = 20 days
  • Path A → F → K → L → N: 5 + 1 + 1 + 2 + 10 = 19 days
  • Path A → F → K → M → N: 5 + 1 + 1 + 1 + 10 = 19 days
  • Path A → G → I → K → L → N: 5 + 2 + 4 + 1 + 2 + 10 = 24 days

By analyzing all paths, the one with the maximum duration is A → G → I → K → L → N, totaling 24 days. Thus, the critical path is A → G → I → K → L → N, with a duration of 24 days.

Calculating ES, EF, LS, LF, and Float Time for Each Task

Forward pass calculations determine ES and EF:

  • ES of initial tasks (A, B, C, D, F): 0
  • EF = ES + duration
  • Subsequent task ES = maximum EF of predecessors

Backward pass calculations determine LS and LF, starting from project duration (24 days):

  • LF of end tasks (N): 24
  • LS = LF - duration
  • Predecessor tasks LS = minimum LS of successors - their duration

Calculations show that tasks on the critical path have zero slack, confirming their importance in project completion timeline, while non-critical tasks have positive slack, indicating flexibility.

Conclusion

The comprehensive analysis of the project network reveals the critical path as A → G → I → K → L → N, with a total duration of 24 days. Understanding the network diagram, all potential paths, and slack times allows project managers to pinpoint critical activities, allocate resources effectively, and mitigate delays. This structural approach ensures project objectives are met efficiently and within the designated timeframe.

References

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  • PMI. (2021). A Guide to the Project Management Body of Knowledge (PMBOK® Guide) Sixth Edition. Project Management Institute.
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