Homework 8
Answers are in bold.
Part One
Answer the following questions using the answer report and sensitivity information from the
first part of the lab handout. Save the answer and sensitivity reports in your spreadsheet.
1) Report and Interpret the Reduced Cost (think of it as the objective penalty) of the
Evansville to Albuquerque route.
The reduced cost for the Evansville to Albuquerque route is 1. This means if
you were forced to send one unit from Evansville to Albuquerque it would
increase your objective or total costs by 1.
2) Do any routes have both a zero reduced cost (think of this as an objective penalty)
and a zero solution value? What does a zero reduced cost and a zero value for the
decision variable indicate?
None of the routes have both a zero reduced cost and a zero solution value. If
they did it would mean there are multiple optimal solutions to the problem.
3) Given the sensitivity information, which is the best route? (Hint: Which route is used
in the transportation plan and has the largest allowable increase.) Why might we
think of this route as the best (Recall that these problems depend on cost advantages
only and that allowable increases indicate a range over which costs could indicate for
a particular route without changing the advantage)?
Des Moines to Albuquerque is the best route because it is used in the solution
and has the largest allowable increase. If you look at the unit cost table you
can see that the Des Moines is the lowest cost source for Albuquerque.
Actually Des Moines is the lowest cost source for any of the destinations.
What makes the Des Moines to Albuquerque route better than the routes from
Des Moines to somewhere else is that there is a larger difference between the
most expensive source and least expensive source to Albuquerque. So by
using the least expensive source, Des Moines, to Albuquerque you save more
than if you were to use it else.
4) Given the shadow price information, which source is the most costly to ship from?
The most costly source to ship from is Ft. Lauderdale because if you had one
more unit you could ship from there it would not lower your costs at all.
Part 2
Answer the following questions using the answer and sensitivity reports generated in the
second part of the lab handout.
1) Which is the most desirable column person for any of the row persons?
Alex.
2) Which row person is assigned to this column person? Using the data in Table 3,
provide an explanation for this assignment.
3) Alex is assigned to Ellery. Similar to above, Alex is the most desirable guy.
The reason he is paired with Ellery is she would have the greatest decrease in
compatibility if she was not with Alex.
4) Which is the most desirable row person for any of the column persons?
Francis.
5) Which column person does this person get assigned to? Using the data in Table 3,
provide an explanation for this assignment.
Francis is assigned to Bo. It is all about maximizing the total number of
questions answered the same. While Francis has the most in common with Alex,
Ellery only has one less question in common with him. Francis has seven
questions in common with Bo, and if Bo were with anyone else he would only
have 4 questions in common. At the same time Francis is also the best girl for
Cameron however if Cameron is with any of the other girls his satisfaction only
decreases by 2. So we can see Bo will have the greatest decrease in satisfaction if
he is not with Francis.