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    Quantitative Methods: Transportation Problem

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    (See attached file for full problem description)

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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.

    $2.19

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