a. Given the bids, you need to assign one senior scientist to each of the five projects to maximize the preferences of the scientists. What are the assignments?

b. Dr. Rollins is being courted by Harvard Medical School to accept a teaching position. You are fighting desperately to keep her at Tazer, but the prestige of Harvard may lure her away. If this were to happen, the company would give up the project with the least enthusiasm. Which project would not be done?

c. You do not want to sacrifice any project since researching only four projects decreases the probability of finding a breakthrough new drug. You decide that either Dr. Zuner or Dr. Mickey could lead two projects. Under these new conditions with just four senior scientists, which scientists will lead which projects to maximize preferences?

d. After Dr. Zuner was informed that she and Dr. Mickey are being considered for two projects, she decided to change her bids. Dr. Zuner's new bids for each of the projects are shown next.

Project Up: 20

Project Stable: 450

Project Choice: 451

Project Hope: 39

Project Release: 40

Under these new conditions with just four senior scientists, which scientists will lead which projects to maximize preferences?

e. Do you support the assignments found in part d? Why or why not?

f. Now you again consider all five scientists. You decide, however, that several scientists cannot lead certain projects. In particular, Dr. Mickey does not have experience with research on the immune system, so he cannot lead Project Hope. His family also has a history of manic-depression, and you feel that he would be too personally involved in Project Stable to serve as an effective project leader. Dr. Mickey therefore cannot lead Project Stable. Dr. Kvaal also does not have experience with research on the immune system and cannot lead Project Hope. In addition, Dr. Kvaal cannot lead Project Release because he does not have experience with research on the cardiovascular system. Finally, Dr. Rollins cannot lead Project Up because her family has a history of depression and you feel she would be too personally involved in the project to serve as an effective leader. Because Dr. Mickey and Dr. Kvaal cannot lead two of the five projects, they each have only 600 bid points.

Dr. Rollins has only 800 bid points because she cannot lead one of the five projects. The following table provides the new bids of Dr. Mickey, Dr. Kvaal, and Dr. Rollins.

Which scientists should lead which projects to maximize preferences?
g. You decide that Project Hope and Project Release are too complex to be led by only one scientist. Therefore, each of these projects will be assigned two scientists as project leaders. You decide to hire two more scientists in order to staff all projects: Dr. Arriaga and Dr. Santos. Because of religious reasons, neither of them want to lead Project Choice and so they assign 0 bid points to this project. The next table lists all projects, scientists, and their bids.

Which scientists should lead which projects to maximize preferences?
h. Do you think it is wise to base your decision in part g only on an optimal solution for a variant of an assignment problem?
Tazer, a pharmaceutical manufacturing company, entered the pharmaceutical market 15 years ago with the introduction of six new drugs. Five of the six drugs were simply permutations of existing drugs and therefore did not sell very heavily. The sixth drug, however, addressed hypertension and was a huge success.
Since Tazer had a patent on the hypertension drug, it experienced no competition, and profits from the hypertension drug alone kept Tazer in business. Pharmaceutical patents remain in force for 20 years, so this one has five more years before it expires.
During the past 15 years, Tazer continued a moderate amount of research and development, but it never stumbled upon a drug as successful as the hypertension drug. One reason is that the company never had the motivation to invest heavily in innovative research and development. The company was riding the profit wave generated by its hypertension drug and did not feel the need to commit significant resources to finding new drug breakthroughs.
Now Tazer is beginning to fear the pressure of competition.
Tazer knows that once the patent expires in five years, generic drug manufacturing companies will swarm into the market like vultures. Historical trends show that generic drugs decrease sales of branded drugs by 75 percent.
Tazer is therefore looking to invest significant amounts of money in research and development this year to begin the search for a new breakthrough drug that will offer the company the same success as the hypertension drug. Tazer believes that if the company begins extensive research and development now, the probability of finding a successful drug shortly after the expiration of the hypertension patent will be high.
As head of research and development at Tazer, you are responsible for choosing potential projects and assigning project directors to lead each of the projects. After researching the needs of the market, analyzing the shortcomings of current drugs, and interviewing numerous scientists concerning the promising areas of medical research, you have decided that your department will pursue five separate projects, which are listed below:
Project Up: Develop a more effective antidepressant that does not cause serious mood swings.
Project Stable: Develop a drug that addresses manic-depression.
Project Choice: Develop a less intrusive birth control method for women.
Project Hope: Develop a vaccine to prevent HIV infection.
Project Release: Develop a more effective drug to lower blood pressure.
For each of the five projects, you are only able to specify the medical ailment the research should address since you do not know what compounds will exist and be effective without research.
You also have five senior scientists to lead the five projects.
You know that scientists are very temperamental people and will only work well if they are challenged and motivated by the project. To ensure that the senior scientists are assigned to projects they find motivating, you have established a bidding system for the projects. You have given each of the five scientists 1,000 bid points. They assign bids to each project, giving a higher number of bid points to projects they most prefer to lead.
The following table provides the bids from the five senior scientists for the five individual projects.

You decide to evaluate a variety of scenarios you think are likely.

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Dr. Mickey Dr. Kvaal Dr. Rollins Project Project Up Project Stable Project Choice Project Hope Project Release Can't lead 50 50 100 600 300 Can't lead 125 Can't lead 175 86 343 171 Can't lead Can't lead Project Dr. Mickey Dr. Rollins Dr. Arriaga Dr. Santos Dr. Kvaal Dr. Zuner Dr. Tsai Project Up Project Stable Project Choice Project Hope Project Release 86 343 171 Can't lead Can't lead 100 100 100 100 Can't lead 50 50 100 600 250 250 111 300 Can't lead 125 Can't lead 175 200 800 250 250 333 555 600