Assignment 7
Due October 19, 2012
Answers are in bold.
1) Solve for the optimal transportation solution and answer the following questions
about the results.
a)
What is the minimum total cost?
$121,450
b)
Which shipping routes are used? How many motors are shipped for each of
these?
Amsterdam to Tillburg= 300
Amsterdam to Liege = 200
Antwerp to Nancy = 700
Le Havre to Leipzig = 400
Le Havre to Nancy = 200
Le Havre to Tillburg = 200
c)
Which constraints bind?
All of the constraints are binding.
d)
Given total demand (requirements at assembly plants) and supply (motors
available from ports) is it possible for any constraints to be slack?
No, it is not possible for any of the constraints to be slack because this
is a balanced transportation problem. Total Demand=Total Supply
e)
Report and Interpret the Reduced Cost/Objective Penalty of the Amsterdam
to Nancy route.
The Reduced Cost for the Amsterdam to Nancy route is 22.5. If we
had to ship one unit from Amsterdam to Nancy it would increase our
cost by 22.5.
Why does the Amsterdam to Leipzig route have both a zero solution value
and a zero reduced cost?
The Amsterdam to Leipzig route having both a zero solution value and
a zero reduced cost indicates there are multiple optimal solutions to
the problem.
f)
g)
Interpret the Shadow Prices on the constraints. (Be sure and use the
Allowable Increase and Decrease Information since these shadow prices are
only valid in one direction i.e. either having one more unit available to ship
or requiring one less unit at an assembly plant).
Amsterdam has a shadow price of 0 with an allowable increase of
infinity. This means having one more unit to ship from Amsterdam
would not change costs.
Antwerp has a shadow price of -67.5. This means for each additional
unit we had available to ship from Antwerp our costs would decrease
by 67.5. This shadow price is valid for an additional 200 units.
AGEC 352
Assignment 7
Due October 19, 2012
Le Havre has a shadow price of -17.5. This means for each additional
unit we had available to ship from Le Havre our costs would decrease
by 17.5. This shadow price is valid for an additional 300 units.
The shadow price for Leipzig is 120 with an allowable decrease of 300.
This means if we could decrease the number of motors needed at
Leipzig by 1 unit our total cost would decrease by 120. This shadow
price is valid for a decrease of up to 300 units.
The shadow price for Nancy is 107.5 with an allowable decrease of 200.
This means if we could decrease the number of motors needed at
Nancy by 1 unit our total cost would decrease by 107.5. This shadow
price is valid for a decrease of up to 200 units.
The shadow price for Liege is 41 with an allowable decrease of 200.
This means if we could decrease the number of motors needed at
Liege by 1 unit our total cost would decrease by 41. This shadow price
is valid for a decrease of up to 200 units.
The shadow price for Tillburg is 59.5 with an allowable decrease of
300. This means if we could decrease the number of motors needed at
Tillburg by 1 unit our total cost would decrease by 59.5. This shadow
price is valid for a decrease of up to 300 units.
h)
Given the Reduced Cost/Objective Penalty information, which route is the
worst?
Antwerp to Liege is the worst route with a Reduced Cost of 126.5.
i)
Given the shadow price information, which source is the most costly to ship
from?
Amsterdam
The decision maker would like to know if it is possible to transport the motors at minimum
cost while also minimizing the cost attributable to shipments from Le Havre.
2) Report the optimal solution given the second objective of minimizing costs from Le
Havre while holding fixed the Total Cost level at $121,450.
a)
What activities (routes) decreased?
Amsterdam to Tillburg decreased from 300 to 0, and Le Havre to
Leipzig decreased from 400 to 100.
b)
What activities (routes) increased?
Amsterdam to Leipzig increased from 0 to 300 and Le Havre to
Tillburg increased from 200 to 500.
c)
How much is shipping cost from Le Havre reduced?
The shipping cost from Le Havre decreased $18,150.
d)
Which destination costs changed (sum of total costs to a particular plant
location)?
AGEC 352
Assignment 7
Due October 19, 2012
Costs to Leipzig increased and costs to Tillburg decreased.
e)
Why did these change?
Destination costs for Leipzig increased because some of the motors
which were shipped from Le Havre were shifted to the more expensive
route from Amsterdam. Tillburg decreased because it is the least
expensive source for motors shipped from Le Havre so originally some
motors were shipped from the more expensive route from Amsterdam
to Tillburg, but when minimizing costs from Le Havre all the motors
shipped to Tillburg come from Le Havre.
AGEC 352