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Unformatted text preview: CHAPTER 5 TRANSPORTATION, ASSIGNMENT, AND NETWORK MODELS SOLUTIONS TO DISCUSSION QUESTIONS 5-1. 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. 5-2. 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. 5-3. 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. 5-4. The minimal-spanning 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. 5-5. The maximal-flow 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 maximal-flow model can be used. 5-6. The shortest-path 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 shortest-path model can be used. 5-7. 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....
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