Davison Construction Company is building a luxury lakefront

Davison Construction Company is building a luxury lakefront home in the Finger Lakes region of New York. Coordination of the architect and subcontractors will require a major effort to meet the 44-week (approximately 10-month) completion date requested by the owner. The Davison project manager prepared the following project network: 14. Start Finish

Solution

a. In order to find the critical path , we are requiredto first calculate expected time for each activity by using the formula (a+4*m+b)/6 weighted mean of optimistic (a), most likely (m) and pessimistic (b) times. The following table gives the expected time for actvities:

a. Critical path is the longest path an the network diagram from Start to Finish which is:

Start --A---C----E----G---H---Finish having maximum duration = 52 (8+12+10+15+7)

b. Expected duration of completion of project = 52 weeks

c. Probability of project being completed in 44 weeks is less than .5 as mean time mentioned above is 52 weeks. In order to calculate probability we first find out the standard deviation(sd) of the critical path which is combined sd of critical activities namely A, C, E, G and H = Sqrt ( 16/9 + 4 + 4 + 25/9 + 16/9 ) = SQRT(129/9) = 3.79 approx.

Standard deviation of activity = (b-a)/6 and Variance is square of standard deviation, variance of project duration is sum of variances of critical activities on the critical path.

Project duration follows normal distribution with mean 52 weeks and standard deviation 3.79

Therefore Probability that project get completed in 44 weeks = Probability Z <= z1 where Z is standard normal variable and z1 = (44-52)/3.79 = -2.11 From the Standard Normal table it is .5 - .4826 = .0174

To conclude , chances of project getting completed within 44 weeks is less than 18%

d. For probability of project taking more than 3 months or 57 weeks, the value of Z is (57-52)/3.79 = 1.32 approx

and Probability Z taking more than 1.32 from the table is =.5 - .4066 = .0934

Therefore chances that project takes more than 57 weeks is less than 10% more precisely 9.34%

e. The construction company can tell that the expected time to finish the project is 52 weeks with sd of 3.79 weeks

Activity	Expected duration
A	8
B	7
C	12
D	5
E	10
F	9
G	15
H	7