The VP of marketing of an electronic toy company is about to begin a project to

Question

The VP of marketing of an electronic toy company is about to begin a project to design an advertising campaign for a new line of toys. She wants the project to be completed within 57 days in time to launch the campaign for the holiday season. The VP has identified six activities (labelled A, B, C, D, E and F) needed to execute this project. Activities A and B can start immediately in parallel. Once B is completed, D would start. Also, once A is completed, it would be followed by activities C, E and F in series. When both D and F are completed, the project would end. Thus there are two paths from start to finish: A-C-E-F and B-D. The following are estimates (in days) for the duration of each activity. Find the estimate of the mean and variance of the duration of each activity. Find the critical path. Using the critical path, find the approximate probability that the advertising campaign will be ready to launch in 57 days.

Explanation / Answer

In order to find the mean estimated and variace of the duration of each activity we use below formula

mean = (to + 4tm + tp)/6

variance = ((tp - to)/6)^2

Below is the table gives value for each activity

Hence Critical path is ACEF with completion time of 51 days

Variance of the critical path = 9 hence std. dev. = 3

Probability that the project will complete within 57 days P(X<57)

P(X<57) = P(z < (57 - 51)/3) = P(z <2) = 0.9772

Activity to tm tp estimated time Variance A 12 12 12 12 0 B 15 21 39 23 16 C 12 15 18 15 1 D 18 27 36 27 9 E 12 18 24 18 4 F 2 5 14 6 4

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