Exam 7: Network Flow Models

The minimal spanning tree problem is to connect all nodes in a network so that the total branch lengths are minimized.

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 ________ solution technique.

Consider the following network, which shows the location of various facilities within a youth camp and the distances (in tens of yards) between each facility. -The camp nurse is stationed at Facility B. What is the shortest route from B to C?

The first step in the shortest route solution method is to

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 -Determine the shortest route for a carpet delivery truck from the carpet plant in Valparaiso, Indiana, to warehouses in Hammond, Gary, and Merillville. State the total completion time in minutes or each route

In a network flow problem, the values assigned to ________ typically represent distance, time, or cost.

A branch where flow is permissible in either direction is a(n)

Consider the following network, which shows the location of various facilities within a youth camp and the distances (in tens of yards) between each facility. There is a swampy area between facilities A and E. -Walking trails will be constructed to connect all the facilities. In order to preserve the natural beauty of the camp (and to minimize the construction time and cost), the directors want to determine which paths should be constructed. What is the minimum number of paths (in tens of yards) that must be built to connect each facility?

-This network has been targeted for the innovative new "Redundancy Elimination" program that offers a compromise between two competing factions. The plan is to remove paths one at a time until all of the nodes are interconnected without any loops in the network while minimizing the sum of all of the path lengths. Which of these paths is part of the new network?

Nodes represent junction points connecting branches.

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

Consider the following network, which shows the location of various facilities within a youth camp and the distances (in tens of yards) between each facility. -Walking trails will be constructed to connect all the facilities. In order to preserve the natural beauty of the camp (and to minimize the construction time and cost), the directors want to determine which paths should be constructed. Use this network to determine which paths should be built.

The ________ connects all nodes in a network so that the total branch lengths are minimized.

Consider the following network, which shows the location of various facilities within a youth camp and the distances (in tens of yards) between each facility. There is a swampy area between facilities A and E. -Walking trails will be constructed to connect all the facilities. In order to preserve the natural beauty of the camp (and to minimize the construction time and cost), the directors want to determine which paths should be constructed. Use this network to determine which paths should be built.

In a typical network flow problem, the branches show flow from one node to the next. The nodes themselves are ________ points.

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 -Determine the shortest route for a carpet delivery truck from the carpet plant in Valparaiso, Indiana, to retail outlets in Portage, Highland, and Lansing. State the total completion time in minutes or each route

Consider the following network, which shows the location of various facilities within a youth camp and the distances (in tens of yards) between each facility. There is a swampy area between facilities A and E. -A clean-up crew is stationed at facility D and wants to take the shortest route to each site. They usually clean up facilities C, E, A and F on the same day and therefore want the shortest route from D to each facility. Recommend a route for the crew to leave from D, clean up each facility one after the other, and return to facility D. (Assume all paths are accessible.)

The goal of the ________ problem is to maximize the amount of flow of items from an origin to a destination.

A traffic system could be represented as a network in order to determine bottlenecks using the maximal flow network algorithm.

Networks are popular because they provide a picture of a system and because a large number of systems can be easily modeled as networks.