# Question

Brent Bonnin begins his senior year of college filled with excitement and a twinge of fear. The excitement stems from his anticipation of being done with it all—professors, exams, problem sets, grades, group meetings, all-nighters. The list could go on and on. The fear stems from the fact that he is graduating in December and has only 4 months to find a job. Brent is a little unsure about how he should approach the job search. During his sophomore and junior years, he had certainly heard seniors talking about their strategies for finding the perfect job, and he knows that he should first visit the Campus Career Planning Center to devise a search plan. On Sept. 1, the fist day of school, he walks through the doors of the Campus Career Planning Center and meets Elizabeth Merryweather, a recent graduate overflowing with energy and comforting smiles. Brent explains to Elizabeth that since he is graduating in December and plans to begin work in January, he wants to leave all of November and December open for interviews. Such a plan means that he has to have all his preliminary materials, such as cover letters and résumés, submitted to the companies where he wants to work by Oct. 31. Elizabeth recognizes that Brent has to follow a very tight schedule, if he wants to meet his goal within the next 60 days. She suggests that the two of them sit down together and decide the major milestones that need to be completed in the job search process. Elizabeth and Brent list the 19 major milestones. For each of the 19 milestones, they identify the other milestones that must be accomplished directly before Brent can begin this next milestone. They also estimate the time needed to complete each milestone. The list is shown below.

In the evening after his meeting with Elizabeth, Brent meets with his buddies at the college coffeehouse to chat about their summer endeavors. Brent also tells his friends about the meeting he had earlier with Elizabeth. He describes the long to-do list he and Elizabeth developed and says that he is really worried about keeping track of all the major milestones and getting his job search organized. One of his friends reminds him of the cool OR class they all took together in the first semester of Brent’s junior year, and how they had learned about some techniques to organize large projects. Brent remembers this class fondly, since he was able to use a number of the methods he studied in that class in his last summer job.

(a) Draw the project network for completing all milestones before the interview process. If everything stays on schedule, how long will it take Brent until he can start with the interviews? What are the critical steps in the process?

(b) Brent realizes that there is a lot of uncertainty in the times it will take him to complete some of the milestones. He expects to get really busy during his senior year, in particular since he is taking a demanding course load. Also, students sometimes have to wait quite a while before they get appointments with the counselors at the career center. In addition to the list estimating the most likely times that he and Elizabeth wrote down, he makes a list of optimistic and pessimistic estimates of how long the various milestones might take.

How long will it take Brent to get done under the worst-case scenario? How long will it take if all his optimistic estimates are correct?

(c) Determine the mean critical path for Brent’s job search process. What is the variance of the project duration?

(d) Give a rough estimate of the probability that Brent will be done within 60 days.

(e) Brent realizes that he has made a serious mistake in his calculations so far. He cannot schedule the career fair to fit his schedule. Brent read in the campus newspaper that the fair has been set 24 days from today on Sept. 25. Draw a revised project network that takes into account this complicating fact.

(f) What is the mean critical path for the new network? What is the probability that Brent will complete his project within 60 days?

In the evening after his meeting with Elizabeth, Brent meets with his buddies at the college coffeehouse to chat about their summer endeavors. Brent also tells his friends about the meeting he had earlier with Elizabeth. He describes the long to-do list he and Elizabeth developed and says that he is really worried about keeping track of all the major milestones and getting his job search organized. One of his friends reminds him of the cool OR class they all took together in the first semester of Brent’s junior year, and how they had learned about some techniques to organize large projects. Brent remembers this class fondly, since he was able to use a number of the methods he studied in that class in his last summer job.

(a) Draw the project network for completing all milestones before the interview process. If everything stays on schedule, how long will it take Brent until he can start with the interviews? What are the critical steps in the process?

(b) Brent realizes that there is a lot of uncertainty in the times it will take him to complete some of the milestones. He expects to get really busy during his senior year, in particular since he is taking a demanding course load. Also, students sometimes have to wait quite a while before they get appointments with the counselors at the career center. In addition to the list estimating the most likely times that he and Elizabeth wrote down, he makes a list of optimistic and pessimistic estimates of how long the various milestones might take.

How long will it take Brent to get done under the worst-case scenario? How long will it take if all his optimistic estimates are correct?

(c) Determine the mean critical path for Brent’s job search process. What is the variance of the project duration?

(d) Give a rough estimate of the probability that Brent will be done within 60 days.

(e) Brent realizes that he has made a serious mistake in his calculations so far. He cannot schedule the career fair to fit his schedule. Brent read in the campus newspaper that the fair has been set 24 days from today on Sept. 25. Draw a revised project network that takes into account this complicating fact.

(f) What is the mean critical path for the new network? What is the probability that Brent will complete his project within 60 days?

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