  Multistage Stochastic Programming (MSP) is a class of models for sequential
decision-making under uncertainty. MSP problems are known for their
computational intractability due to the sequential nature of the
decision-making structure and the uncertainty in the problem data due to the
so-called curse of dimensionality. A common approach to tackle MSP problems
with a large number of stages is a rolling-horizon (RH) procedure, where one
solves a sequence of MSP problems with a smaller number of stages. This leads
to a delicate issue of how many stages to include in the smaller problems used
in the RH procedure. This paper addresses this question for, both, finite and
infinite horizon MSP problems. For the infinite horizon case with discounted
costs, we derive a bound which can be used to prescribe an epsilon-sufficient
number of stages. For the finite horizon case, we propose a heuristic approach
from the perspective of approximate dynamic programming to provide a sufficient
number of stages for each roll in the RH procedure. Our numerical experiments
on a hydrothermal power generation planning problem show the effectiveness of
the proposed approaches.
