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# lect25 - ISE 536Fall03 Linear Programming and Extensions...

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ISE 536–Fall03: Linear Programming and Extensions December 3, 2003 Lecture 25: LP in Research Lecturer: Fernando Ord´ o˜nez Robust Capacity Expansion of Transit Networks 1 Capacity expansion problem We consider the problem of deciding investment decisions on a given transit network. A standard solution approach for this problem is to formulate this as a network flow prob- lem with decision variables for possible capacity expansions. This leads to the following formulation: min x,y c t x s . t . Nx = b x u + y d t y I x 0 , y 0 , (1) where y are investment decisions, d t y is the total investment cost (bounded by a budget I ). Nx = b are the conservation of flow equations. c t x is the total (average) travel time. This is a classic network flow formulation for the network design problem. Some simple and extensions to this model: - Consider integer investment decision variables. 1

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- A more realistic representation of travel times.
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lect25 - ISE 536Fall03 Linear Programming and Extensions...

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