Project Scheduling 2 -Calculating variance and probabilities -PERT/CPM

Summary

This video provides a step-by-step guide to project scheduling under uncertainty. It explains how to calculate expected activity times and variances using optimistic, most likely, and pessimistic estimates. The presenter identifies the critical path, computes the overall project completion time, and demonstrates how to determine probabilities of finishing within or beyond specific deadlines using the normal distribution and Z-scores. Additionally, the video shows how to reverse-calculate the project completion time for a desired confidence level. Clear examples and formulas make it easy to understand probabilistic project scheduling, helping viewers plan projects more accurately and confidently.

Takeaways

• 📊 Project scheduling involves calculating expected times and variances for activities with uncertain durations.
• 🧮 The expected time for an activity is calculated using the formula: t = (a + 4m + b) / 6, where a, m, and b are optimistic, most likely, and pessimistic times.
• 📝 The critical path determines the project completion time and includes the activities that directly impact the overall schedule.
• ⏱️ Only critical activities’ expected times and variances are needed to calculate the project completion time and overall project variance.
• 📈 Variance for each activity is calculated using the formula: variance = ((b - a) / 6)².
• 🔢 The project standard deviation is the square root of the sum of variances of the critical activities.
• 📉 Project completion times can be approximated using a normal distribution, even if activity times are beta distributed.
• 🧮 Z-scores are used to calculate probabilities of completing the project within, beyond, or between specific time frames.
• 🎯 Reverse z-score calculations allow determining the completion time for a desired probability, such as 90% on-time completion.
• 🕒 For a 90% probability of on-time completion, the project should start earlier by the difference between the mean and the target completion time calculated via z-score.
• 📚 Understanding these calculations helps in effective project planning, risk assessment, and probability-based scheduling decisions.

Q & A

What is the formula used to calculate the expected time of an activity in PERT?

The expected time is calculated using 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.

Why is the most likely time weighted more heavily in the expected time formula?

The most likely time is multiplied by 4 to reflect its higher probability compared to the optimistic and pessimistic estimates.

How is the critical path of a project determined?

The critical path is determined by identifying the sequence of activities with the longest total expected duration, which directly affects the project completion time.

What was the critical path identified in the example?

The critical path identified in the example is B → D → E → F.

How is the total project completion time calculated?

The total project completion time is calculated by summing the expected times of all activities on the critical path.

What is the formula for calculating the variance of an activity?

The variance is calculated using the formula ((b - a) / 6)^2.

Why are only critical path activities used to calculate project variance?

Only critical path activities are used because delays in these activities directly affect the overall project completion time.

What is the relationship between project variance and standard deviation?

The standard deviation is the square root of the project variance.

Why is a normal distribution used to approximate project completion time?

Although individual activity times follow a beta distribution, the sum of these times can be approximated by a normal distribution due to the central limit theorem.

What is the purpose of calculating a Z-score in project scheduling?

The Z-score is used to determine the probability of completing the project within a specific time frame by comparing the desired completion time to the mean and standard deviation.

What is the probability of completing the project within 35 weeks in the example?

The probability of completing the project within 35 weeks is 0.8508.

How do you find the probability of completing a project after a certain time?

You calculate the Z-score for that time, find the corresponding cumulative probability, and subtract it from 1 to get the probability of exceeding that time.

How is the probability of completing the project between two time values calculated?

It is calculated by finding the Z-scores for both times, determining their cumulative probabilities, and subtracting the smaller probability from the larger one.

What does it mean to take the complement of a probability in this context?

Taking the complement means subtracting a probability from 1 to find the probability of the opposite event occurring.

How can you determine the required completion time for a desired probability?

You perform a reverse lookup to find the Z-score corresponding to the desired probability, then substitute it into the Z formula to calculate the required completion time.