  We show that the multistage linear problem (MSLP) with an arbitrary cost
distribution is equivalent to a MSLP on a finite scenario tree. We establish
this exact quantization result by analyzing the polyhedral structure of MSLPs.
In particular, we show that the expected cost-to-go functions are polyhedral
and affine on the cells of a chamber complex, which is independent of the cost
distribution. This leads to new complexity results, showing that MSLP is
fixed-parameter tractable.
