Probability

Questions to be answered in Excel QM using project management various and project crash.

11-22 A project was planned using PERT with three time estimates. The expected completion time of the project was determined to be 40 weeks. The variance of the critical path is 9.

What is the probability that the project will be finished in 40 weeks or less?

What is the probability that the project will take longer than 40 weeks?

What is the probability that the project will be finished in 46 weeks or less?

What is the probability that the project will take longer than 46 weeks?

The project manager wishes to set the due date for the completion of the project so that there is a 90% chance of finishing on schedule. Thus, there would only be a 10% chance the project would take longer than this due date. What should this due date be?

11-24 Using PERT, Ed Rose was able to determine that the expected project completion time for the construction of a pleasure yacht is 21 months and the project variance is 4.

What is the probability that the project will be completed in 17 months or less?

What is the probability that the project will be completed in 20 months or less?

What is the probability that the project will be completed in 23 months or less?

What is the probability that the project will be completed in 25 months or less?

11-28 Bowman Builders manufactures steel storage sheds for commercial use. Joe Bowman, president of Bowman Builders, is contemplating producing sheds for home use. The activities necessary to build an experimental model and related data are given in the following table:

ACTIVITY NORMAL TIME CRASH TIME NORMAL COST ($) CRASH COST ($) IMMEDIATE PREDECESSORS

A 3 2 1,000 1,600 —

B 2 1 2,000 2,700 —

C 1 1 300 300 —

D 7 3 1,300 1,600 A

E 6 3 850 1,000 B

F 2 1 4,000 5,000 C

G 4 2 1,500 2,000 D, E

What is the project completion date?

Formulate an LP problem to crash this project to 10 weeks.

11-32 The estimated times (in weeks) and immediate predecessors for the activities in a project are given in the following table. Assume that the activity times are independent.

a m b

A — 9 10 11

B — 4 10 16

C A 9 10 11

D B 5 8 11

Calculate the expected time and variance for each activity.

What is the expected completion time of the critical path? What is the expected completion time of the other path in the network?

What is the variance of the critical path? What is the variance of the other path in the network?

If the time to complete path A–C is normally distributed, what is the probability that this path will be finished in 22 weeks or less?

If the time to complete path B–D is normally distributed, what is the probability that this path will be finished in 22 weeks or less?

Explain why the probability that the critical path will be finished in 22 weeks or less is not necessarily the probability that the project will be finished in 22 weeks or less.