  In stochastic optimisation, the large number of scenarios required to
faithfully represent the underlying uncertainty is often a barrier to finding
efficient numerical solutions. This motivates the scenario reduction problem:
by find a smaller subset of scenarios, reduce the numerical complexity while
keeping the error at an acceptable level.
  In this paper we propose a novel and computationally efficient methodology to
tackle the scenario reduction problem when the error to be minimised is the
implementation error, i.e. the error incurred by implementing the solution of
the reduced problem in the original problem. Specifically, we develop a
problem-driven scenario clustering method that produces a partition of the
scenario set. Each cluster contains a representative scenario that best
reflects the conditional objective values in each cluster of the partition to
be identified.
  We demonstrate the efficiency of our method by applying it to two challenging
stochastic combinatorial optimization problems: the two-stage stochastic
network design problem and the two-stage facility location problem. When
compared to alternative clustering methods and Monte Carlo sampling, our method
is shown to clearly outperform all other methods.
