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Exam 7: Network Flow Models

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Question 51

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In networks with fewer than five nodes, the minimal spanning tree algorithm will yield answers identical to the maximal flow solution approach.

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B) False

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Question 52

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The maximal flow algorithm may end with capacity remaining at the source.

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Question 53

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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 -What is the distance for the shortest route from the carpet plant in Valparaiso to retail outlet in Lansing, Illinois. State the total completion time in minutes.

-Which of these is the shortest route through the network?

Pro-Carpet company manufactures carpets in Northwest Indiana and delivers them to warehouses and retail outlets. The network diagram given in the figure below shows the possible routes and travel times (in minutes) from the carpet plant to the various warehouses or retail outlets. V = Valparaiso, P=Portage, G=Gary, Ha=Hammond, Hi=Highland, M = Merillville, L = Lansing -Write the constraint associated with the Lansing (destination) node for the 0-1 integer linear programming formulation of the shortest route problem.

Once a decision maker has determined the shortest route to any node in the network, that node becomes a member of the ________.

To determine the maximum possible flow of railroad cars through the rail system, they should first select the longest path from origin to destination and ship as much as possible on that path.

If we wanted to represent water resources as a network flow problem, which of the following would be represented as nodes?

In a network flow model, a directed branch

Branches connect nodes and show flow from one point to another.

Determining where capacity needs to be added within a series of one-way roads within a park represents a ________ model.

Draw the network associated with the following constraints for a shortest route problem. X12 + X13 = 1 X12 - X24 = 0 X13 - X34 = 0 X24 + X34 - X45 = 0 X45 = 1

The maximal flow solution algorithm allows the user to choose a path through the network from the origin to the destination by any criteria.

Pro-Carpet company manufactures carpets in Northwest Indiana and delivers them to warehouses and retail outlets. The network diagram given in the figure below shows the possible routes and travel times (in minutes) from the carpet plant to the various warehouses or retail outlets. V = Valparaiso, P=Portage, G=Gary, Ha=Hammond, Hi=Highland, M = Merillville, L = Lansing -Write the constraint associated with the Valparasio (source) node for the 0-1 integer linear programming formulation of the shortest route 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. What is the objective function for the 0-1 integer linear programming formulation of the maximal flow problem?

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 second node (node 2) for the 0-1 integer linear programming formulation of the shortest route problem.

Regardless of the number of nodes in a network, the minimal spanning tree never contains the two nodes with the greatest distance between them.

-If the origin node for this network is node number 1 and flow proceeds from node 1 to node 6, what is the shortest route through the network?

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 fifth node of the network diagram for the 0-1 integer linear programming formulation of the maximal flow problem?

Figure 4 -Determine the minimum distance required to connect all nodes in Figure 4.