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From: Ray Vickson on 12 Feb 2010 20:03
On Feb 12, 12:23 pm, Konstantin Smirnov
<konstantin.e.smir...(a)gmail.com> wrote:
> And does it have sense to minimize transportation cost if some data
> are subdetermined (in [a,b]), for ex., distances/fuel prices from
> vendors to buyers are not exactly known because of possible traffic
> jams etc.?
> Do you see sense in a matrix of interval supply numbers for each
> vendors?
> For ex.
>
>         Buyer 1 -- Buyer 2
> Vendor 1   5         (11,15)
> Vendor 2   0            20
> Vendor 3   (100,110)   10
>
> Something like this - we have minimized the total cost and found
> interval supply data. In this manner, is this task usually encountered?

This is the type of situation dealt with by the older tools of "chance-
constrained programming" or "stochastic programming with recourse", or
by the newer (and seemingly much more successful) "robust
optimization" (RO). See
http://web.mit.edu/dbertsim/www/papers/Robust%20Optimization/Robust%20and%20data-driven%20optimization-%20modern%20decision-making%20under%20uncertainty.pdf
or
http://users.ece.utexas.edu/~cmcaram/pubs/RobustOptimizationPaper.pdf
.. See also
http://www2.staff.fh-vorarlberg.ac.at/~hgb/New-Papers/CMAME07_BS07b.pdf
for a survey as of 2007.

In the case you cite, the dual problem would have uncertainty in the
right-hand-sides, and that is the type of situation RO can handle.

R.G. Vickson
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