  To model combinatorial decision problems involving uncertainty and
probability, we introduce scenario based stochastic constraint programming.
Stochastic constraint programs contain both decision variables, which we can
set, and stochastic variables, which follow a discrete probability
distribution. We provide a semantics for stochastic constraint programs based
on scenario trees. Using this semantics, we can compile stochastic constraint
programs down into conventional (non-stochastic) constraint programs. This
allows us to exploit the full power of existing constraint solvers. We have
implemented this framework for decision making under uncertainty in stochastic
OPL, a language which is based on the OPL constraint modelling language
[Hentenryck et al., 1999]. To illustrate the potential of this framework, we
model a wide range of problems in areas as diverse as portfolio
diversification, agricultural planning and production/inventory management.
