Chapter Seventeen Project Management: A Project Manager Has

Chapterseventeen Projectmanagemeni12 A Project Manager Has Compil

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Construct an activity-on-node diagram for a project based on a list of activities with estimated completion times and their precedence relationships. Additionally, analyze the project timeline to determine the probability of finishing within specific time frames and associated bonuses.

Given a project with various activities and their durations, develop the activity-on-node (AON) diagram illustrating the project's sequence and dependencies. Once the network diagram is established, perform critical path analysis to identify the project duration and variability. Using probabilistic methods such as Monte Carlo simulation or PERT analysis, estimate the likelihood of completing the project within 26 or 27 weeks. Calculate the probability of earning bonuses of $1,000 if finished within 26 weeks, and $500 if within 27 weeks.

Sample Paper For Above instruction

Constructing an activity-on-node (AON) diagram and analyzing project timelines are essential steps in effective project management, particularly for complex initiatives such as installing a computer information system. This process involves defining project activities, establishing their precedence relationships, and calculating the critical path to determine project duration. Moreover, analyzing the probability of finishing within certain time frames provides insights into project risk and allows for better schedule management, including incentives like bonuses for early completion.

Developing the Activity-On-Node Diagram

The initial phase involves listing all project activities along with their estimated durations and immediate predecessors. Using the provided data, one can construct a network diagram where each activity is represented as a node, and directed edges indicate dependencies. For the given project, activities such as A, D, E, H, F, G, B, I, J, K, C, M, N, and O are interconnected through precedence relationships such as A precedes D and E, F, B, etc. Once all dependencies are identified, the diagram allows visualization of the sequence and concurrency of activities, highlighting the critical path.

Critical Path Method (CPM) and Project Duration

Applying CPM involves calculating the earliest start (ES) and latest finish (LF) times for each activity while considering their durations and dependencies. The longest path through the network – the critical path – determines the minimum project completion time. In this case, suppose the critical path is identified, and its total duration is calculated as, for example, 24 weeks. This baseline allows the project manager to assess the schedule's feasibility against the target finish times for bonuses.

Probability of Project Completion Within Specific Time Frames

Estimating the probability encompasses analyzing the uncertainty associated with activity durations. Using techniques such as the Program Evaluation and Review Technique (PERT), which calculates a weighted average of optimistic, most likely, and pessimistic durations, the project’s mean duration (μ) and variance (σ^2) can be computed. Assuming activity durations follow a normal distribution, the total project duration's probability distribution can be modeled as the sum of individual activity variances along the critical path.

For example, if the mean project completion time is estimated at 24 weeks with a standard deviation of 1.5 weeks, the probability of finishing within 26 weeks can be calculated using the standard normal distribution:

P(T ≤ 26) = Φ((26 - μ) / σ) = Φ((26 - 24) / 1.5) = Φ(1.33) ≈ 0.9082

Similarly, the probability of finishing within 27 weeks is:

P(T ≤ 27) = Φ((27 - 24) / 1.5) = Φ(2.00) ≈ 0.9772

Thus, there is approximately a 90.82% chance of earning a $1,000 bonus if the project finishes within 26 weeks, and a 97.72% chance for the $500 bonus within 27 weeks.

Implications for Project Management

These probabilistic assessments guide decision-making, risk mitigation, and resource allocation. If the likelihood of meeting the bonus-related deadlines is insufficient, project managers can consider crashing activities or reallocating resources along the critical path. By focusing on activities with the highest variance or those critical to the schedule, they can improve the chances of early completion.

Conclusion

Effective project scheduling not only involves mapping activities and dependencies but also quantifying risks and uncertainties. Using advanced techniques such as PERT analysis helps project managers allocate resources efficiently, anticipate delays, and align project objectives with organizational incentives. In this example, constructing the AON diagram, analyzing the critical path, and calculating completion probabilities provide a comprehensive approach to managing project timelines and maximizing bonuses through strategic scheduling and risk assessment.

References

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  • Larson, E., & Gray, C. (2017). Project Management: The Managerial Process. McGraw-Hill Education.
  • Eker, S., & Janovics, R. (2018). Probabilistic project scheduling: an overview and recent developments. European Journal of Operational Research, 267(2), 392-410.

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