Vaccine Development Project

Developing a vaccine is an expensive, lengthy process that involves a rigorous series of steps to first identify a potential vaccine "candidate" and then going through phases of development, assessment, and approvals.

Under normal circumstances, the entire process typically takes $10$ to $15$ years $-$ but steps are being taken now to accelerate it$.$ More than $65\%$ of vaccine candidates fail, according to an MIT study. As of May $15,2020,$ there were more than $110$ COVID$-19$ vaccines in development globally.

Imagine $10$ years from now, a pharmaceutical company wants to develop a vaccine for new virus called COVID$-$XI$!$ Consider the following project tasks and their identified best, most likely, and worst$-$case estimates of task duration. Time estimates are in month.

Activity

Description

Predecessors

Optimistic

$($a$)$

Most Likely $($m$)$

Pessimistic $($b$)$

A

Identify and produce antigens $($exploratory$)$

$--$

$6$

$12$

$36$

B

Animal test

$($pre$-$clinical$)$

A

$3$

$9$

$24$

C

Phase I of clinical trials

B

$3$

$12$

$24$

D

Phase II of clinical trials

C

$3$

$12$

$24$

E

Phase III of clinical trials

D

$6$

$12$

$24$

F

Approval and licensing

E

$3$

$9$

$12$

G

Manufacturing development

C

$6$

$9$

$12$

H

Manufacturing

Scale up

D$,$ G

$6$

$9$

$12$

I

Large scale production

F$,$ H

$4$

$10$

$16$

Assume this company calculates the expected duration times based on the standard beta distribution formula. Answer the following questions, based on the above information.

$1.$ Complete the following table for the expected duration and variance of activities $($Keep up to two decimal places$).$

Activity

Predecessors

Estimated Duration

Variance

A

$--$

B

A

C

B

D

C

E

D

F

E

G

C

H

D$,$ G

I

F$,$ H