Imagine a bus serving a line with N stations (one direction). Each station, i, i=1,…N, has s_ij passengers that want to board the bus to go to j, for all j not equal to i. . So there are sum(sij) passengers waiting at station i to board the bus. Now, suppose that station m, is a very important station and we want to make sure there will be enough room on the bus to board waiting passengers. Assume the bus can choose how many people to board at each station, regardless of their destination. We now want to determine how many people at each of the stations (prior to station m) can board the train to ensure everyone at station m can board the bus.

What type of optimization problem is this? Typical network optimization problems involve maximizing flow or capacity, but not this sort of problem. How would one go about modeling this? Are there any examples of problems similar to this?

asked 16 Nov '16, 20:07

Pep's gravatar image

Pep
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Hint: define a network with a node for each station, arc \((i,j)\) (with \(i < j\)) for each pair of stations, and flow variable \(x_{ij}\) with bounds \([0,s_{i,j}]\).

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answered 17 Nov '16, 17:45

Rob%20Pratt's gravatar image

Rob Pratt
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accept rate: 28%

edited 17 Nov '16, 17:46

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Asked: 16 Nov '16, 20:07

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Last updated: 17 Nov '16, 17:46

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