You have been asked to interview candidates for an open secretarial position. Each candidate's qualifications for the job can be modeled with a lognormal distribution with a mean of 10 and a standard deviation of 5. Unfortunately, you must decide whether to offer the job to each candidate in turn before being able to interview additional candidates. In other words, you will interview candidate 1 and decide to make an offer or not. If you do not make an offer to candidate 1 you will interview candidate 2 and again make an offer or not. If you pass on candidate 2 you will go on to candidate 3, and so on. If you get to the 10th candidate without having made an offer, you will be forced to accept that candidate regardless of his or her qualifications. Assume all offers are accepted.
Your objective is to hire the candidate with the highest possible qualifications. To achieve this you plan to set minimum acceptable scores (MAS) at each interview. For example, you might decide to accept the first candidate with a score over 8. Then your MAS would be 8 at each interview. An alternative policy would be to accept over 8 on the first interview, over 7 on the second, and so on. In general, you have 9 decision variables: one MAS for each interview.
a. What are the expected qualifications of the candidate hired if all MAS are set at 5?
b. What is the best choice for the MAS if you use the same MAS for all interviews?
c. Using Solver and 9 decision variables, determine the best policy. What are the optimal values for the 9 MAS and the resulting expected qualifications?
d. Using simulation sensitivity, determine which of the nine MAS have the biggest impact on the expected qualifications of the candidate hired.
e. Assume that a linear relationship applies among the 9 MAS. In other words, parameterize the decisions using the linear equation MAS (stage t) = α + bt, where t ranges from 1 for the first interview to 9 for the last. What is the optimal policy under this assumption and what are the resulting expected qualifications?