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Exam 7: Network Flow Models

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Question 31

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The local Internet provider wants to develop a network that will connect its server at its satellite center in Valparaiso with the main city computer centers in Northwest Indiana to improve the Internet service and to minimize the amount of cable used to connect network nodes. If we represent this problem with a network,

A) the cities are branches and cables are nodes.
B) the cables are the branches and the cities are the nodes.
C) the length of cables in miles are the branches, and the cities are the nodes.
D) the cities are the branches and the length of cables in miles are the nodes.

E) A) and B)
F) A) and C)

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Question 32

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The shortest route network problem could help identify the best route for pizza delivery drivers from the pizza parlor to a specific customer.

A) True
B) False

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Question 33

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The last step of the minimal spanning tree solution method is to make sure all nodes have joined the spanning tree.

The shipping company manager wants to determine the best routes for the trucks to take to reach their destinations. This problem can be solved using the

A network is an arrangement of paths connected at various points through which items move.

The objective of the maximal flow solution approach is to

Refer to the figure below to answer the following questions. Figure 3 -Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. What is the capacity constraint associated with the branch from node 7 to node 9 of the network diagram for the 0-1 integer linear programming formulation of the maximal flow problem?

The shipping company manager wants to determine the best routes for the trucks to take to reach their destinations. This problem can be solved using the minimal spanning tree.

The first step of the maximal flow solution method is to

Figure 1. Delivery Routes -Consider the network diagram given in Figure 1. Assume that the amount on each branch is the distance in miles between the respective nodes. Also assume that it is not possible to travel from a node with a higher number to a node with a lower number. Write the constraint associated with the fifth node (node 5) for the 0-1 integer linear programming formulation of the shortest route problem.

The minimal spanning tree allows the visitation of each node without backtracking.

The source node is the input node in a maximal flow problem.

Refer to the figure below to answer the following questions. Figure 3 -Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. Determine the maximal flow on the following path: node 1 to node 2 to node 7 to destination node 9.

Refer to the figure below to answer the following questions. Figure 3 -Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. Determine the maximal flow on the following path: node 1 to node 4 to node 3 to node 5 to node 8 to destination node 9.

Refer to the figure below to answer the following questions. Figure 3 -Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. What is the input- output constraint associated with the first node of the network diagram for the 0-1 integer linear programming formulation of the maximal flow problem?

Regardless of the number of nodes in a network, the minimal spanning tree always contains the two nodes with the shortest distance between them.

Pro-Carpet company manufactures carpets in Northwest Indiana and delivers them to warehouses and retail outlets. The network diagram given in figure below shows the possible routes and distances from the carpet plant in Valparaiso to the various warehouses or retail outlets. V = Valparaiso, P=Portage, G=Gary, Ha=Hammond, Hi=Highland, M = Merillville, L = Lansing -Determine the shortest route for a carpet delivery truck from the carpet plant in Valparaiso to retail outlet in Hammond.

Figure 2 -Consider the network diagram given in Figure 2. Assume that the amount on each branch is the distance in miles between the respective nodes. What is the distance for the shortest route from the source node (node 1) to node 5?

A company plans to use an automatic guided vehicle for delivering mail to ten departments. The vehicle will begin from its docking area, visit each department, and return to the docking area. Cost is proportional to distance traveled. The type of network model that best represent this situation is ________.

Once the shortest route to a particular node has been determined, that node becomes part of the permanent set.