## CPM/PERT network for Moore Housing Contractors for determining the probability that the contractors can complete a house within 45 days

The CPM/PERT network for Moore Housing Contractors is supposed to determine whether the Contractors of the Moore Housing would be able to finish the work on the house within agreed forty-five days. In order to do that, we need to estimate the expected time of the construction, according to the following formula (Russell & Taylor, 2009).

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*(a* + 4*m* + *b) / *6

In this equation *a* stands for optimistic time estimation, *b* is pessimistic time estimation, and *m* is for most likely time estimation. For example, for the activity a (excavation, pouring footers) the optimistic time estimation is 3, the most likely time estimation is 4, and the pessimistic time estimation is 6.

*(3 + 4*4 + 6) / 6*

Thus, the estimated time (*t*) is 4,14. The next step in the CPM/PERT network is to define the variance of the time from the estimated indication. The formula for defining variance is the following:

*б*^{2} = ((*b-a*)/6)^{2}

Thus, for the activity a (excavation, pouring footers), if we use the formula, the variance will be:

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*б*^{2} = ((*6-3*)/6)^{2}= 0,25.

The cases in which the mean (expected) time plus the variance would exceed the pessimistic expectation of the time need for the construction would be considered critical cases (Moosa, 2007). The following table represents the way the time will be distributed for the activities by the construction team.

## Project activities Moore Contractors should be particularly diligent to keep on schedule

The Constructors should pay attention to the activities a, b, e, g, k, m, q, s, t, and v because the time planned to spend on the building is less than the estimated mean time. They can do it by making sure workers and materials are always available. As the need arises, the company might shift workers from activities such as c, f, and j because the variance plus the expected time does not exceed the most likely time estimate for those cases.

## References

Moosa, I. (2007). *Operational risk management*. New York, NY: Palgrave Macmillan.

Russell, R., & Taylor, B. (2009). *Operations management*. Hoboken, NJ: John Wiley & Sons.