Pert Vs. Monte Carlo

Question 3 вЂ" PERT Discussion

D) The Program Evaluation and Review Technique (PERT) was developed by Booz-Allen Hamilton, Lockheed Martin and the US Navy for the Navy’s Polaris project in 1958. Although the Polaris project was completed before its estimated completion date and under budget, we are not certain that this can be attributed solely to PERT, but PERT was used more widely on future projects after the success of the Polaris project. PERT became popular around the same time computers were progressing from the mainframe to mini-computers. During the evolution of computer technology, advanced programs were developed to provide further probabilistic estimates via simulations (Monte Carlo Analysis).

B) PERT assumes the Beta probability distribution to calculate the expected time of an activity within a network. PERT requires that for each activity, three duration estimates are needed (optimistic, most likely, pessimistic). This distribution is used for PERT since there was no set basis for selecting a specific distribution and was accepted in order to derive an equation. The Beta distribution is also used to calculate the variance and standard deviation of each task and ultimately the entire project via the critical path.

C) The Beta distribution constructs a smooth curve which places more emphasis on values around the most likely value while taking into account the pessimistic and optimistic values. The expected time calculated ideally would be close to the most likely time. Another distribution we could use other than Beta is the triangle distribution, which places even more emphasis on the most likely value than the Beta distribution.

E) The Central Limit Theorem (CLT) states that when using random samples from a population, the sampling distribution of the sample mean can be approximated by a normal distribution as the sample size becomes large (normally sample size of 30 or more). The CLT permits one to add the sum of the random sample means to approximate the population mean as well as add the random sample variances to approximate the population variance. PERT uses the CLT to sum the expected activity times and variances in order to obtain an expected project time and project variance (using the critical path). The square root of the project variance provides us with the total projects standard deviation which can be used to calculate the probability of a project finishing on a specified date.

I) PERT uses the following equation to approximate the standard deviation of a given

activity: (Pessimistic Time вЂ" Optimistic Time)/6. PERT uses the following equation to approximate the expected time of an activity: (Optimistic Time + 4(Most likely Time) + Pessimistic Time) / 6. In general, the most likely, pessimistic and optimistic times are estimated times that are guessed or based on past history (if this data exists). The probabilities used in the equations for standard deviation and expected times are the following: optimistic time = 1/6 (@ 16.7%), pessimistic time = 1/6 (@ 16.7%), most likely time = 4/6 (@ 66.7%). Per use of the above equations in the beta distribution, different probabilities can not be used for the PERT calculation, however different probabilities should be considered because each activity will not necessarily follow the beta distribution.

J) The Beta distribution is very sensitive to the three-point estimates used, especially when the pessimistic and optimistic time estimates (outside parameters) are changed. We compared the shape of the Beta Distribution of two sets of numbers below with approximately the same mean. The beta distribution below represents the distribution for the following durations in days: 3,4,7 (Optimistic, Most Likely , Pessimistic) which equate to an expected value of 4.3 days.

The resulting distribution is right-skewed. The beta distribution below is based upon the following durations: 1-4-8 (O,M,P) which equate to an expected value of 4.2.

The resulting beta distribution favors a normal distribution of the data. A small change in the outside parameters (while keeping the mean relatively the same) changed the shape of the beta distribution significantly which shows the sensitivity of the beta distribution.

H) In regards to the critical path, CPM uses a deterministic approach that establishes a unique critical path based on those activities that have zero slack. PERT takes the CPM approach one step further by calculating expected times using the optimistic, pessimistic and most likely activity durations of the unique critical path used in CPM. Although the PERT approach takes into account three various durations for each activity, only one unique critical path is established. Monte Carlo simulations build upon the PERT method by providing multiple critical paths based on the variances of the expected durations of the activities. Monte Carlo simulations take into account that activities not on the critical path in the deterministic approach can become critical.

F) Risk is when one can determine every outcome of any decision and can determine a probability for that outcome. Uncertainty is when information is not known and a guess has to be made.

G) In regards to a project, general risks occur throughout the course of a project and should be identified in the planning stage of a project. Scheduling risks are the risks that will directly affect the overall project schedule and include: estimates made on the durations of activities (normally optimistic estimates), estimates made on the amount of resources available for an activity and poor utilization of resources. PERT attempts to reduce the scheduling risks by using three estimates for the duration of activities vs. one deterministic estimate.

A) A Drawback from using PERT, occurs when there are activities that merge at one point. The PERT calculation underestimates the overall duration of a project and over estimates variance since these merging activities would not be included in the PERT calculation if they are not associated with the critical path. The merge bias worsens when the number of these merging activities as well as variance between the merging activities increases. The merge bias also worsens as the correlation among merging activities approaches zero and their expected completion time are closer together.

K) When comparing PERT to CPM the following Advantages and Disadvantages were determined:

Advantages

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