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Dr. Maddah
ENMG 500 Engineering Management I
12/20/05
The Transportation Problem (1)
•
Definition
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The transportation problem (TP) is concerned with shipping a
commodity between a set of sources (e.g. manufacturers) and
a set of destinations (e.g. retailers).
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Each source has a capacity dictating the amount it supplies.
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Each destination has a demand dictating the amount it
receives.
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For
now
, we assume that the system is
balanced
.
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That is, the total amount demanded at all destinations is equal
to the total supply available at all sources.
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The objective is to determine the amounts to be shipped
between each source and destination in a way as to minimize
shipping cost while meeting demand and supply constraints.
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The shipping cost is proportional to the amount shipped.
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TP Network Representation
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•
Overview
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The TP has many practical applications. (The one I like the
most is about snow moving in Montreal.)
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The transportation problem can be modeled and solved as a
linear program.
¾
However, this problem has a special
structure
, which allows
for specialist solution techniques that are more efficient than
the usual simplex algorithm.
¾
In particular, we will see that starting basic feasible solutions
of high quality can be obtained with ease.
¾
We will then customize the simplex method to produce an
efficient
transportation simplex method
.
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 Fall '09
 DrBacelMaddah
 Optimization, Supply And Demand, Simplex algorithm, Vogel, prototype example, NW Corner

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