Robust Optimization Under Controllable Uncertainty

We call an optimization problem an optimization problem with controllable uncertainty if a) it contains uncertain input data and b) prior to deciding the optimization variables, the optimizer can for a certain cost reduce the scenario set of this uncertain data. In particular, we are interested in situations where each uncertain parameter is a priori known to lie in a closed, bounded interval and the optimizer has a fractional choice to shrink each interval. We study this setting for optimization problems with uncertain non-negative linear cost functions and non-negative decision variables. Moreover, we assume the scenario set to be restricted by so-called budgeted uncertainty, i.e. the sum over all intervals of relative deviations from the lower boundary cannot exceed a given budget. In particular, we show that the resulting three-stage problem can be solved efficiently as a single linear program, if the underlying optimization problem is a linear program given by a TDI description.



View Robust Optimization Under Controllable Uncertainty