Exam 4: Network Models

A model which matches salespeople to retail customers based on estimated profit potential of each salesperson-retail customer match, where each salesperson is to be matched with at most 25 retail customers, could be modeled as which network models?

What is the term for a path from a node that returns to the same node without including any arc more than once?

In addressing and solving a maximal flow problem, flow capacities between adjacent nodes must be equal in both directions.

The sensitivity report from problem 9 is given below.The "Reduced Gradient" column contains reduced costs, and the "Lagrange Multiplier" column contains shadow prices.

A tree cannot contain a cycle.

In which of the following network models is it not possible to "ship" both in and out of a given node?

Which statement is not true?

As part of a work-study program, Winslow Graphics has agreed to have 5 internship students from the Communications Department of the local university spend one day each during the next week in its labs participating in the development of magazine layouts for a variety of products.Since these internship students are in their final year of a master's degree program, they possess significant skills, and Winslow feels it would benefit by having the maximum total number of student hours during the week.Each student was asked for his availability in terms of maximum number of continuous hours for each day during the coming week.

The objective function of a transportation model is to minimize the total shipping costs.

In a problem formulated as a standard transportation model, where there are m sources and n destinations, the number of arcs (routes) in an optimal solution need be:

An optimal maximum flow solution will involve positive flow on every arc.

SnowDevil produces snowboards at its factories in Reno and Tahoe with weekly outputs of 30 and 20 units, respectively.This commodity is to be transported to three regional warehouse locations, Warehouses 1, 2, and 3, which have weekly requirements of 10, 15, and 25 units, respectively.Unit shipping costs are:

For a network of n nodes, a spanning tree contains n - 1 arcs.

In a transportation model, how are shadow prices interpreted for supply nodes? For demand nodes?

Identify the four parts of a maximal flow problem.

If a general linear programming problem can also be formulated as a network problem, the network formulation is generally preferable because of easier model input and a quicker solution technique.

Cajun Oil Company operates pipelines for transporting oil from its source in the Gulf of Mexico to storage facilities located on the mainland in Louisiana.Before reaching the storage facilities, the oil must pass through one or more pumping stations.The network below gives the maximum amount that can be transported in pipes between sites in thousands of gallons per hour.

Transshipment, assignment, shortest path, and traveling salesman problems are network flow models.

In formulating a transportation model using a balanced format in which total supply must equal total demand, indicate how to model each of the following unusual circumstances:

In a problem formulated as a standard transportation model, if all the source/destination quantities are integer-valued, the set of solution variables is guaranteed to be integer-valued as well.