Case Study Chapter 6 for Intro to Management Science

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Chapter 6 Network Optimization Problems

Review Questions

6.1-1 A supply node is a node where the net amount of flow generated is a fixed positive number. A demand node is a node where the net amount of flow generated is a fixed negative number. A transshipment node is a node where the net amount of flow generated is fixed at zero.

6.1-2 The maximum amount of flow allowed through an arc is referred to as the capacity of that arc.

6.1-3 The objective is to minimize the total cost of sending the available supply through the network to satisfy the given demand.

6.1-4 The feasible solutions property is necessary. It states that a minimum cost flow problem will have a feasible solution if and only if the sum of the supplies
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6.6 a) [pic]

b) [pic]

c) [pic]

d) [pic]

e) [pic]

f) $1,618,000 + $583,000 = $2,201,000 which is higher than the total in Problem 6.5 ($2,187,000).

6.7 [pic]

There are only two arcs into LA, with a combined capacity of 150 (80 + 70). Because of this bottleneck, it is not possible to ship any more than 150 from ST to LA. Since 150 actually are being shipped in this solution, it must be optimal.

6.8 Both Gassco and StatoilHydro use a management science tool called GassOpt to optimize the configuration of the offshore pipeline network on the Norwegian Continental Shelf and the routing of the natural gas through the network. The routing done by GassOpt is based on a model that is a generalization of the model for the maximum flow problem. Like the maximum flow problem, the objective is to maximize the flow of natural gas through the network. However, rather than a single source and a single sink, this model has multiple sources (separate natural gas fields) and multiple sinks (separate markets). In addition, the model has a number of extra constraints mentioned in the application vignette.

The use of GassOpt has had many important benefits.

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