Exam 6: Network Optimization Problems

A minimum cost flow problem will have feasible solutions as long as there is a balance between the total supply from the supply nodes and the total demand at the demand nodes.

The figure below shows the nodes (A - I) and capacities (labelled on arcs in packages/day) of a shipping network. The firm would like to know how many packages per day can flow from node A to node I. Note: This question requires Solver. Formulate the problem in Solver and find the optimal solution. What is the maximum amount of data that can be transmitted from node A to node I?

When reformulating a shortest path problem as a minimum cost flow problem, each link should be replaced by a pair of arcs pointing in opposite directions.

A transportation problem is just a minimum cost flow problem without any transshipment nodes and without any capacity constraints on the arcs.

A manufacturing firm has three plants and wants to find the most efficient means of meeting the requirements of its four customers. The relevant information for the plants and customers, along with shipping costs in dollars per unit, are shown in the table below: \text{Customer (requirement)}\\ \begin{array} { l c c c c } &&&Customer ~3 &Customer ~4\\ \text { Factory (capacity) } & \text { Custcmer } 1 ( 25 ) & \text { Customer } 2 ( 50 ) & ( 125 ) & ( 75 ) \\ \text { A (100) } & \$ 15 & \$ 10 & \$ 20 & \$ 17 \\ B ( 75 ) & \$ 20 & \$ 12 & \$ 19 & \$ 20 \\ \text { C (100) } & \$ 22 & \$ 20 & \$ 25 & \$ 14 \end{array} Note: This question requires Solver. Formulate the problem in Solver and find the optimal solution. What is the optimal quantity to ship from Factory A to Customer 2?

Which of the following is not an assumption of a shortest path problem?

The amount of flow that is eventually sent through an arc is called the capacity of that arc.

Which of the following is an example of a transshipment node?

The figure below shows the nodes (A-I) and capacities (labelled on arcs in packages/day) of a shipping network. The firm would like to know how many packages per day can flow from node A to node I. Note: This question requires Solver. Formulate the problem in Solver and find the optimal solution. At maximum capacity, what will be the flow between nodes B and E?

The network simplex method can aid managers in conducting what-if analysis.

The figure below shows the nodes (A-I) and capacities (labelled on arcs in packages/day) of a shipping network. The firm would like to know how many packages per day can flow from node A to node I. How many transshipment nodes are present in this problem?

Conservation of flow is achieved when the flow through a node is minimized.

In a minimum cost flow problem, the cost of the flow through each arc is proportional to the amount of that flow.

In a minimum cost flow problem there can be only one supply node and only one demand node.

The figure below shows the possible routes from city A to city M as well as the cost (in dollars) of a trip between each pair of cities (note that if no arc joins two cities it is not possible to travel non-stop between those two cities). A traveler wishes to find the lowest cost option to travel from city A to city M. Note: This question requires Solver. Formulate the problem in Solver and find the optimal solution. What is the minimum cost for the traveler to move from node A to node M?

The source and sink of a maximum flow problem have conservation of flow.

The figure below shows the nodes (A-I) and capacities (labelled on arcs in packages/day) of a shipping network. The firm would like to know how many packages per day can flow from node A to node I. Which type of network optimization problem is used to solve this problem?

Network representations can be used for the following problems:

The figure below shows the nodes (A-I) and capacities (labelled on arcs in TB/s) of a computer network. The firm would like to know how much information can flow from node A to node I. Which nodes are the sink and source for this problem?

In a shortest path problem, when "real travel" through a network can end at more than one node: I. An arc with length 0 is inserted. II. The problem cannot be solved. III. A dummy destination is needed.