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# Quantitative Methods: Transportation Problem

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A logistics specialist for Wiethoff Inc. must distribute cases of parts from 3 factories to 3 assembly plants. The monthly supplies and demands, along with the per-case transportation costs are:

Destination Assembly Plant
1 2 3 Supply
Source A 5 9 16 200
Factory B 1 2 6 400
C 2 8 7 200
Demand 120 620 60

What are the total monthly transportation costs for the optimal solution?

B. Consider the following transportation problem:
1 2 Supply
1 5 6 100
2 4 2 200
3 3 6 150
4 9 7 50
Demand 250 250

How many supply-side constraints are there? Write the supply-side constraints.

C. Consider the following transportation problem:
1 2 Supply
1 5 6 100
2 4 2 200
3 3 6 150
4 9 7 50
Demand 250 250

How many demand-side constraints are there? Write the demand-side constraints
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#### Solution Preview

A logistics specialist for Wiethoff Inc. must distribute cases of parts from 3 factories to 3 assembly plants. The monthly supplies and demands, along with the per-case transportation costs are:

Destination Assembly Plant
1 2 3 Supply
Source A 5 9 16 200
Factory B 1 2 6 400
C 2 8 7 200
Demand 120 620 60

What are the total monthly transportation costs for the optimal solution?
Hints:
LP for the above model is
Decision variables:
xa1 be the quantity shipped from factory A to assembly plant 1. Similarly we have
xa2, xa3, xb1, xb2, xb3, xc1, xc2, and xc3

Objective function:
Min: 5 xa1+ 9xa2+ 16xa3+1 xb1+2xb2+6xb3+2xc1+8xc2+7xc3
As it is the case of balanced transportation problem, constraints are
Supply availability
xa1+ xa2+xa3=200
xb1+xb2+xb3=400
xc1+xc2+xc3=200

Demand requirements
xa1+ xb1+ xc1=120
xa2+ xb2+ ...

#### Solution Summary

The solutions for transportation problems are explained and the process is outlined.

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## Quantitative Methods

True and false

1. In a media selection problem, maximization of audience exposure may not result in maximization of total profit.

2. In an unbalanced transportation model, supply does not equal demand and supply constraints have signs.

3. Due to the unique characteristics of a transportation problem, the solution values of the decision variables are always integer values.

4. In a transportation problem, a demand constraint for a specific destination represents the amount of product demanded by a given destination (customer, retail outlet, store).

5. In maximization linear programming problem profit is maximized in the objective function by subtracting cost from revenue.

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