Question

Dr. Thomas has been given a budget of $10,000 to organize a conference at her university in 3 months’ time (12 weeks) via an educational grant. She has a team of 2 research assistants and after some deliberation, they identified the following activities that are required to be completed for hosting a successful conference.

Activity Description    Immediate Predecessor

A Planning Topics and Sessions    . .

B    Inviting presenters from various universities    A

C identifying potential venues in the city    . .   

D Selecting a venue for the conference C

E Finalizing presenters for each session B

F Completing registration for all presenters E

G Preparing agendas and inviting participants    D, E

H Last minute edits, replacements, and lists F, G

Thomas has approached you, her student, to help her figure this out, as a part of her Management Science class assignment. Please give your responses, with appropriate explanations, tables, and formulas, where relevant, to the following questions:Follow a PERT/CPM model to identify the project network, activity schedule, critical activities, and the expected time for completing the project successfully. The expected completion times for each of the listed activities is based on the experiences of all the people on the team and is as follows:

Activity    Optimistic    Most Probable Pessimistic

A    1.5 2    2.5

B    2 2.5 6

C    1 2 3

D 1.5 2 2.5

E 1.5 3    4.5

F 0.5    1 1.5

G 1    2    3

H    1 2 3

Dr.Thomas is worried about completing all the required activities before the 12-week deadline is up, because she has never hosted a conference before. She wants to know, based on her team’s estimates what is the probability of NOT completing the activities by the end of 12 weeks.In order to have some peace of mind, Dr. Ell decides that she is willing to pay her Research Assistants extra money, out of her own pocket, in order to complete the project within 10 weeks. She has identified the following crashing options for each activity.

Crashed Activity (cost ($)

Activity    Time Normal    Crashing

A    1 1,000    2,000

B 2 2,000 3,000

C 1.5    500 1,000

D    1.5 500 600

E 2    5,000 6,000

F 0.5 100    500

G    1    500 1,000

H 1    400 900

a. Write a Linear Program to help Dr. Thomas identify which, if any, activities should be crashed and how much that would cost her. Remember, since she is paying personally for the extra crashing time, she wants to minimize costs.

b. Provide a clear solution and present your case for her consideration by showing an updated activity schedule, and presenting the probability of getting the whole project completed within 12 weeks, if she decides to implement the crashing of activities. What is the probability of getting the whole project completed within 11 weeks? For the sake of simplicity, you can assume that the variances will not change for the crashed activities.

c. Perform a sensitivity analysis to identify if she can reduce her costs further by allowing an 11-week deadline instead of a 10-week deadline and explain if she should aim for 11-weeks instead of 10 weeks and why (or why not).

Answer 1

Using PERT, the expected project duration comes out to be 12 weeks. However, the standard variation for the same is 0.972 making the probability of completion within 12 weeks to be 0.5

Kindly refer the solution below for details. The activities are crashed and the new probabilities of project completion within 10 and 11 weeks are determined.