Exam 4: Network Models

A map of the United States can be drawn as a network with each state represented by a node and arcs connecting each pair of states that share a boundary.

A city needs to design and build a completely new storm drainage system.The excess rainwater runoff in each neighborhood is to be channeled to a suburban reservoir.The appropriate network model would most likely be:

In a maximal flow problem:

Network flow models are integer linear programming models.Why, then, would we prefer using a linear programming model? Does the linear programming model give an optimal solution?

Describe two Greedy algorithms for solving the minimal spanning tree problem.

You can solve the traveling salesman problem by selecting a cycle with the lowest cost.

A transportation model has been selected to represent the production schedule of a product to meet demand over a twelve month planning horizon with 12 production nodes, on each of which is defined the production capacity for each month, and 12 demand nodes, on each of which is defined the demand for each month.If goods can be stored a maximum of 3 months, which of the following statements is not true?

Minimal spanning tree problems do not lend themselves to a convenient linear programming formulation.

The Department of Defense (DOD) is conducting weapons tests in an isolated part of the Nevada desert.At one particular site, the DOD has six structures that are in proximity to the blast area and must be evacuated to an observation area at times when testing is done.The blast area lies in a combination of flat and mountainous terrain, and the actual blast site, the DOD sites, and the observation area are connected by various dirt paths over which only 4-wheel drive vehicles are permitted.The network below shows these paths and the approximate driving times in minutes on these paths using 4-wheel drive vehicles.

A car dealership uses its van to drive its service customers to their jobs.If the dealership van has five people who need to be taken to work, what network algorithm should be used in order to minimize the distance the van must travel in order to accomplish this task?

The optimal solution to a standard linear programming problem need have no more non-zero-valued decision variables than there are linear constraints.The standard balanced transportation model, in which total supply equals total demand, has one linear constraint restricting the amount shipped from each of the m source nodes and one linear constraint restricting shipments into each of the n demand nodes.For this model, which is simply a special case of linear programming, the number of non-zero-valued decision variables in the optimal solution need be no more than one less than the total number of linear constraints.Why?

The Greedy algorithms for solving the minimal spanning tree problem require selecting the remaining arc with the smallest cost unless what is true?

In the standard assignment problem where, for example, workers are being assigned tasks, which of the following situations would preclude the application of the assignment approach (the Hungarian algorithm)?

In network flow models, all arcs are generally assumed to be directed.In connectivity models, all arcs are generally assumed to be undirected.

A minimal spanning tree connects all nodes in a minimal total distance or cost.

Name the two types of nodes in a network flow model.

An environmental impact report for a proposed new industrial center complex must include the total amount of sewage that can be pumped through existing pipes.Which network model would be the most appropriate representation?

In a standard transportation model, each objective function coefficient represents the:

Suppose in problem 3 that over the 15 week semester each of the five interns must spend 12 dates each at Winslow Graphics with no two interns being at Winslow on the same day.Assume that student availability will not change from week to week over the semester.

The assumptions underlying the application of the basic transportation model do not include: