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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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