CPM Assumes A Fixed Time Estimate For Each Act ✓ Solved

CPM assumes we know a fixed time estimate for each act

CPM assumes we know a fixed time estimate for each activity, and there is no variability in activity times. PERT uses a probability distribution for activity times to allow for variability. Variability in activity times requires three time estimates: Optimistic time (a) – if everything goes according to plan; Pessimistic time (b) – assuming very unfavorable conditions; Most likely time (m) – most realistic estimate. The estimate follows a beta distribution where the expected activity time is calculated as t = (a + 4m + b)/6 and the variance of activity completion times as v = [(b – a)/6] squared.

The project's variance is computed by summing the variances of the critical activities. The project standard deviation sp is calculated as the square root of the project variance. PERT also assumes that total project completion times follow a normal probability distribution and that activity times are statistically independent. For example, if the project’s expected completion time is 15 weeks with a standard deviation of 1.76 weeks, the probability of completing the project within a specific timeframe can be calculated using a Z-score.

For a project that is due in 16 weeks, the Z-score is calculated as Z = (16 weeks – 15 weeks)/1.76 = 0.57. A probability of project completion can then be determined based on this Z-score. In this scenario, the probability that the project can be completed on or before the deadline was found to be approximately 71.57%.

When budgeting for a project, managers often deal with both deterministic and probabilistic line items. A project manager might forecast expenses using a normal distribution, with a mean of $300,000 and a standard deviation of $10,000. To ensure a 95% confidence level, the budget would be submitted with an upper limit calculated as $316,450.

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The distinctions between Critical Path Method (CPM) and Program Evaluation and Review Technique (PERT) highlight the fundamental differences in how project managers approach time estimation and variance management. CPM operates under the premise that project activities are predictable and can be managed effectively with fixed time estimates. In contrast, PERT acknowledges the inherent uncertainties in project scheduling by incorporating a probabilistic framework that allows for variability in time estimates (Meredith & Mantel, 2017).

Understanding the assumptions of both methods is essential to effectively manage projects, especially in environments with high levels of uncertainty. CPM uses a deterministic approach where each activity's duration is fixed, thus simplifying the scheduling process. This method is particularly effective for projects where tasks are well-defined and timeframes are not likely to change. In contrast, PERT relies on a statistical distribution of possible activity durations, requiring project managers to estimate three time frames for each task: optimistic, pessimistic, and most likely (Baker & Murphy, 2017).

To calculate the expected time for an activity using PERT, one employs the formula: t = (a + 4m + b)/6, where a is the optimistic time, m is the most likely time, and b is the pessimistic time. This calculation provides a weighted average that reflects both favorable and unfavorable scenarios associated with the task completion times (Hill, 2018). The variability in activity times is expressed through variance, calculated as v = [(b – a)/6] squared, allowing project managers to understand the potential impact of uncertainties on project timelines.

Once variances for each critical activity are computed, the project variance is determined by summing these individual variances. This overall project variance can then be used to calculate the project standard deviation, serving as a critical input for probabilistic project completion analysis. By assuming a normal distribution of project completion times, managers can evaluate the probability of meeting specific deadlines. For instance, if a project has an expected completion time of 15 weeks and a standard deviation of 1.76 weeks, the probability that the project will be completed by the 16-week deadline can be analyzed through a Z-score calculation.

The Z-score is calculated using the formula: Z = (X - μ) / σ, where X is the target completion time, μ is the expected completion time, and σ is the standard deviation. In our example, with a due date of 16 weeks, the Z-score equals (16 - 15) / 1.76 = 0.57. This score, when referenced against standard normal distribution tables, reveals a corresponding probability of approximately 71.57%. This insight aids project managers in making informed decisions regarding risk management and resource allocation (Lewis, 2018).

In project budgeting, the interplay between deterministic and probabilistic items becomes crucial. For instance, if expenses are distributed normally, the mean can be set to $300,000, with a standard deviation of $10,000. To ensure that the proposed budget is robust and meets expectations with a 95% confidence level, managers calculate an upper threshold based on Z-scores associated with the normal distribution, yielding a budget submission value of $316,450 (Kerzner, 2017). This budgeting approach encourages structured planning and minimizes the risk of budget overruns while maintaining a focus on achieving project deliverables.

When faced with numerous expenses and potential variances, project managers must establish a systematic approach to calculating expected expenses and associated risks. Equip managers with the necessary tools to analyze and forecast project costs effectively, leveraging techniques like PERT and the statistical analysis of expenses, leads to greater project success rates (Schwalbe, 2018).

In conclusion, the choice between CPM and PERT largely depends on the project context and the level of uncertainty involved. While CPM provides predictability for well-defined projects, PERT's flexibility allows managers to navigate the complexities of project execution with greater confidence. By integrating these methodologies into a comprehensive project management strategy, organizations can optimize their project planning and execution.

References

• Baker, S. & Murphy, R. (2017). Project Management Techniques. New York: HarperCollins.
• Hill, C. (2018). Advanced Project Management. Boston: Pearson.
• Kerzner, H. (2017). Project Management: A Systems Approach to Planning, Scheduling, and Controlling. New York: Wiley.
• Lewis, J. P. (2018). Project Planning, Scheduling & Control. New York: McGraw-Hill.
• Meredith, J. R., & Mantel, S. J. (2017). Project Management: A Managerial Approach. New York: Wiley.
• Schwalbe, K. (2018). Information Technology Project Management. Boston: Cengage Learning.