Exam 8: Network Optimization Models

In finding the minimal spanning tree in a network using the algorithm in the text, if a tie occurs in the shortest arc from connected nodes to a node that is not connected, it may not be broken arbitrarily.

The labels used in the algorithm to find the shortest path have two numbers, the first of which refers to the node that immediately precedes the current node in the path.

Assume that you are a logistics manager for a firm in Toledo, Ohio. Your products should reach New York city. There are many ways to reach New York city from Toledo. If total time is strictly proportional to total distance, in order to send your products as quickly as possible, you would like to model your problem as

In the shortest route problem, the temporary label on the node closest to the destination is converted to a permanent label.

Find the maximal flow in the network given in Figure 7a.

What is the maximum flow possible from source to sink in the network given in Figure 4a?

In the spanning tree problem, one is trying to find the longest tree from the origin to the destination.

Consider a path 1-2-4-6, in a network where 1 is the source and 6 is the sink. Suppose that the capacity in this direction from 1-2 is 5, 2-4 is 7, and 4-6 is 3 , then the flow capacity of this path in the direction given above will be

In the iterations of the maximal flow algorithm, the sum of the capacity/flow values of at each end of an arc is always equal to the sum of the original capacity values at each end of the arc.

The solution to a minimum spanning tree problem over a network of pipes gives you the total amount of material that can be piped from the origin to the destination.

Which is not a reason for the importance of network models as a problem solving tool of management science?

Suppose that you are applying the minimal spanning tree algorithm. At some point during the application, you have a connected component. Which one of the following is true?

Find the shortest route from node 1 to all other nodes of the graph using the shortest route algorithm given in the book. List all the shortest routes in a table.

-In Figure 2a, using the shortest route algorithm presented in the text book, the label and the node that would get the permanent label next, will be

In the shortest path algorithm given in the text, all nodes will have a label either temporary or permanent, even at the starting point.

What is the maximum flow possible from source to sink in the network given in Figure 4b?

In the shortest route problem, backtracking is used as a feasibility check on a network solution.

Suppose that you are applying the maximal flow algorithm. At some point during the application, you have an arc with the numbers 6 and 3 as shown above in Figure 3d. Which of the following is incorrect?

In the shortest route problem, the length of the shortest path will depend on the origin destination pair used in the algorithm.

In the spanning tree algorithm, we try to find the shortest arc from the connected nodes to any nodes of the rest of the graph.