Consider the TGA situation in problem 39. When TGA attempted to schedule pilots using the new policy, it found that there can be many options for the total minimal ranked schedule. Furthermore, sometimes the most senior pilots are relegated to routes they truly do not prefer, while more junior pilots receive their first choice. Another problem is that such a ranking procedure does not show the depth of displeasure between one route and the next. For example, Captain Smith may be relatively indifferent to the London and Paris routes but certainly prefers either to Hawaii (his third choice).
In an effort to take seniority into account, a young management consultant has suggested another method. Each pilot would receive 10 points for each year of service attempted to schedule pilots using the new policy, it found that there can be many options for the total minimal ranked schedule. Furthermore, sometimes the most senior pilots are relegated to routes they truly do not prefer, while more junior pilots receive their first choice. Another problem is that such a ranking procedure does not show the depth of displeasure between one route and the next. For example, Captain Smith may be relatively indifferent to the London and Paris routes but certainly prefers either to Hawaii (his third choice). In an effort to take seniority into account, a young management consultant has suggested another method. Each pilot would receive 10 points for each year of service
to distribute in any manner among the five routes, standby, and vacation. Suppose this method yielded the point scores for this period shown in the table for problem 40.
a. Construct a lost opportunity matrix from these points by replacing the numbers in each column by the difference between the numbers and the maximum number in the column.
b. Solve the optimal assignment using this approach.
c. Why is Captain Smith still unhappy? How could Captain Smith be assured of always getting his first preference using this approach?
d. List some other potential pitfalls that might occur using this approach. Suggest other approaches that might be fairer.