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network flow problems

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"Transportation Problems" are a subclass of network flow problems.
You have a set of source cities and a set of demand cities, the
amount of supply in each source city, the amount of demand in each
demand city, and the shipping costs for each (source,demand) city pair.
You must exactly meet demand in each demand city, and each source city
must ship out exactly what it produces (no more or less).

a) Formulate and solve a transportation problem as follows:
Source cities: San Francisco and Los Angeles (SF and LA)
Demand cities: Las Vegas and Phoenix (LV and Ph)

Costs: to: LV Ph
from SF 50 300
LA 320 60
(costs are per item shipped).
Supply: 5 in SF, 10 in LA
Demand: 7 in LV, 8 in Ph

Find the optimal shipping amounts and the total cost.
When Solver says it has a solution, ask it for the Sensitivity report as well,
but don't look at it yet.

b) Add one unit of supply in SF and one unit of demand in Ph, re-solve,
and report the new optimal decisions and total cost. Comment as appropriate.

c) Go back to the sensitivity report you generated in part (a) and look at the
Lagrange Multipliers, and comment on them in relation to part (b).

d) In both (a) and (b), total supply and total demand matched each other
perfectly. What would you do if supply exceeded demand? What if
demand exceeded supply?

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Solution Preview

Both the word doc and the excel spreadsheet (including the sensitivity reports) have been submitted.

"Transportation Problems" are a subclass of network flow problems. You have a set of source cities and a set of demand cities, the amount of supply in each source city, the amount of demand in each demand city, and the shipping costs for each (source, demand) city pair. You must exactly meet demand in each demand city, and each source city must ship out exactly what it produces (no more or less).
a) Formulate and solve a transportation problem as follows: ...

Solution Summary

The expert formulates and solves a transportation problem for these cases.

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Linear Programming, Network Flow Model, Spreadsheet Mode

Hello,

I have attached the powerpoint for this problem.

Problem 27.

Union Express has 60 tons of cargo that need to be shipped from Boston to Dallas. The shipping capacity on each of the routes Union Express planes fly each night is shown on the table below.

Nightly Flights Segments Capacity in Tons
Boston to Baltimore 30
Boston to Pittsburgh 25
Boston to Cincinnati 35
Baltimore to Atlanta 10
Baltimore to Cincinnati 5
Pittsburgh to Atlanta 15
Pittsburgh to Chicago 20
Cincinnati to Chicago 15
Cincinnati to Memphis 5
Atlanta to Memphis 25
Atlanta to Dallas 10
Chicago to Memphis 20
Chicago to Dallas 15
Memphis to Dallas 30
Memphis to Chicago 15

Will Union Express be able to move all 60 tons from Boston to Dallas in one night?

a) Draw a network flow model foe the problem and solve it

b) Create a spreadsheet model for this problem in Excel and solve it

c) What is the maximum flow for this network?

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