  We propose an algorithm for generating a minimum-cardinality set of
non-anticipativity constraints (NAC) for scenario-based multistage-stochastic
programming (MSSP) problems with both endogenous and exogenous uncertainties
which allow for gradual realizations. Recently several authors have considered
approaches to generate the minimum cardinality NAC set for MSSPs for various
scenario set structures. However, these approaches have been limited to
uncertain parameters where the realizations occur instantaneously or the full
set of scenarios is required. The proposed algorithm, referred to as Sample
Non-Anticipativity Constraint algorithm (SNAC) relaxes this requirement. We
show that as long as the number of uncertain parameters and parameter values
are kept constant, the algorithm scales polynomially in the number of
scenarios.
