Project Planning and Scheduling Using Critical Path Analysis (CPA) Assessment

Project planning and scheduling using critical path analysis (CPA)

• Construct a network to represent the durations and interdependencies of activities that must be completed during the project
• Use forward and backward scanning to determine the earliest starting time (EST) and latest starting times (LST) for each activity in the project
• Use ESTs and LSTs to locate the critical path(s) for the project
• use the critical path to determine the minimum time for a project to be completed
• Calculate float times for non-critical activities

You need to choose one of the following scenarios:

• You have been designated the task by the Junior School staff to plan and coordinate the next Junior School Production.
•  You have been designated the task by your best friend to plan and coordinate their 18^th Birthday Party.
•  You have been designated the task by your parents to plan and coordinate the next family holiday to Bali.
•  Choose your own task. This needs to be approved by the 2025 Year 12 Applications teaching team before 3:15pm Tuesday 19 August.

Please Note:

The creativity, complexity and quality of your solution, along with attention to mathematical detail, will be assessed in this task. Ensure that your project network is complex enough to display your complete understanding of this topic.

To best show your understanding, consider which tasks might have delays, and what effect this will have on the critical path and/or the minimum completion time.

The project network should not include the event itself.

Mathematical Thinking Process

Your investigation should make use: 

• clarifying the task and the key information
• choosing the mathematics which could help to complete the task
• applying existing mathematical knowledge and strategies to obtain a solution
• interpreting the results in relation to the context
• communicating the solution to the problem as required.

You will need a comprehensive report to accompany your project network. As you write your report, take care to clearly identify the underlying mathematics used throughout the process.

Your report should include the following:

• An introduction, that clearly defines the purpose of the task, identifies key information, any assumptions made.
• An outline of your strategy, including draft designs.
• Evidence of the application of mathematical knowledge and strategies, including calculations, tables and diagrams/graphs etc as you develop your project network.
• Analysis of the project in the context of the problem and consideration of the reasonableness and limitations of the results.
• Your final design communicated to your employer in a systematic and concise manner.

Use of correct mathematical conventions, symbols and terminology.

Assessment Summary and Guided Approach

Assessment Requirements – Brief Summary

The assessment focused on Project Planning and Scheduling using Critical Path Analysis (CPA). Students were required to:

• Construct a network diagram to represent durations and interdependencies of activities.
• Use forward and backward scanning to determine earliest start time (EST) and latest start time (LST) for each activity.
• Identify the critical path(s) in the project network.
• Calculate the minimum completion time for the project.
• Determine float times for non-critical activities.
• Choose a scenario (e.g., school production, birthday party, holiday plan, or an approved custom task).
• Present findings in a comprehensive report including:
  • Introduction & purpose of the task
  • Strategy and draft designs
  • Application of mathematical knowledge (calculations, tables, diagrams)
  • Analysis and interpretation of results
  • Final design and conclusions
  • Correct use of mathematical conventions and terminology

The report had to demonstrate both creativity and mathematical accuracy, with attention to how delays affect critical paths and project completion time.

Mentor’s Step-by-Step Guidance

The academic mentor guided the student systematically to ensure each section of the assessment was completed effectively:

Step 1: Clarifying the Task

• Mentor helped the student choose a practical scenario (e.g., planning a family holiday).
• Together, they listed all activities required, along with their estimated durations and dependencies.
• Assumptions were noted, such as fixed travel dates or venue availability.

Step 2: Drafting the Project Strategy

• The mentor encouraged creating a draft activity list and sequencing the tasks.
• A preliminary network sketch was developed to visualize how tasks connect.
• The importance of identifying dependencies (which task must be finished before another starts) was emphasized.

Step 3: Applying Mathematical Knowledge

• Mentor guided the student in constructing the network diagram using nodes and arrows.
• Forward scanning was explained and applied to calculate the earliest start and finish times.
• Backward scanning was demonstrated to determine the latest start and finish times.
• The mentor reinforced correct use of CPA symbols, notations, and conventions.

Step 4: Identifying the Critical Path & Float

• The student learned how to trace the critical path (the longest sequence of dependent tasks with no slack).
• Mentor showed how to calculate total float and free float for non-critical activities.
• Scenarios of potential delays were tested to see their impact on the overall timeline.

Step 5: Analysis and Interpretation

• Mentor guided the student to interpret results in relation to the chosen scenario (e.g., if flight booking is delayed, the whole holiday plan shifts).
• Limitations and assumptions (e.g., estimated times, availability of resources) were clearly documented.

Step 6: Communicating the Solution

• The mentor stressed the importance of professional report structure:
  • Title page, introduction, clear headings, diagrams, and references.
• The student was guided on presenting calculations, tables, and the final CPA network diagram neatly and systematically.

Outcome and Learning Achievements

By the end of the guided process, the student successfully:

• Produced a comprehensive CPA network diagram showing interdependencies, EST, LST, floats, and critical path.
• Determined the minimum project duration accurately.
• Demonstrated clear application of mathematical strategies in project scheduling.
• Communicated the findings in a professional, well-structured business report.

Learning Objectives Achieved:

• Understanding of critical path analysis and project scheduling.
• Ability to apply forward and backward scanning techniques.
• Skills in identifying and interpreting critical and non-critical activities.
• Application of mathematical problem-solving in real-life contexts.
• Development of professional report-writing and analytical skills.

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