CHAPTER 5
TRANSPORTATION, ASSIGNMENT, AND NETWORK MODELS
SOLUTIONS TO DISCUSSION QUESTIONS
51.
The transportation model is an example of decision making under certainty since the costs of each
shipping route, the demand at each destination, and the supply at each source are all assumed to be known
with certainty.
52.
A balanced transportation problem is one in which total demand (from all destinations) is exactly
equal to total supply (from all sources). If a problem is unbalanced, either the demand or the supply
constraints must be inequalities.
53.
The enumeration method is not a practical means of solving 5 x 5 or 7 x 7 problems because of the
number of possible assignments to be considered. In the 5 x 5 case, there are 5! = (5 x 4 x 3 x 2 x 1) = 120
alternatives that need to be evaluated. In the 7 x 7 case, there are 7! = 5,040 alternatives.
54.
The minimalspanning model is one that will find the best way to connect all the nodes in a network
together while minimizing the total distance between nodes or the total cost of connecting the nodes
together. A number of decision modeling problems can be solved using this model: an example was given
connecting water and power to a real estate development project. This model can also be used to
determine the best way to deliver cable TV to households, connect computers on a computer network,
install an oil pipeline, develop a natural gas network, and more.
55.
The maximalflow model can be used to determine the maximum number of cars that can flow
through a road system, the number of gallons of chemicals that can flow through a chemical processing
plant, the barrels of oil that can go through a pipeline network, the number of people that can use public
transportation to get to work, the number of pieces of mail that can go through a mail service, and more.
Any time that material or items flow through a network, the maximalflow model can be used.
56.
The shortestpath model can be used to find the best way to install a phone cable between two major
cities. Any time items must be moved from one place to another or something, like a cable, must be used
to connect two points, the shortestpath model can be used.
57.
A flow balance constraint calculates the net flow at a node (that is, the difference between the total
flow on all arcs entering the node and the total flow on all arcs leaving the node). At each source node, the
net flow is expressed as a negative quantity, and represents the amount of flow created at the node. At
each destination node, the net flow is expressed as a positive quantity, and represents the amount of flow
consumed at the node. At each pure transshipment node, the net flow is zero.
58.
To set up a maximalflow problem as an LP problem, we create a unidirectional dummy arc going
from the destination node to the source node, and set the capacity of this arc at infinity.
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 Spring '10
 Bryan

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