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I am trying to learn how to study uncertainty in supply in a network flow problem. Specifically, I am using network simplex method on an undirected graph with a bunch of nodes with source/supply and a bunch of other nodes as sink/demand nodes. I would like to study the solution when there is some uncertainty in supply, how would the network flow change.

a) Can this by studied by using interval/fuzzy/affine arithmetic? b) If so, wouldn't it be possible that part of the interval might give rise to an infeasible solution? Part of the interval might even change the path (new arcs could become active in which there are zero flow)

How does one study uncertainties in linear programming/network flows? How is the feasibility or change of solution handles by these fancy arithmetic? Any pointers along these lines would be appreciated. Thanks.

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