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We propose an algorithm for generating a minimum-cardinality set ofnon-anticipativity constraints (NAC) for scenario-based multistage-stochasticprogramming (MSSP) problems with both endogenous and exogenous uncertaintieswhich allow for gradual realizations. Recently several authors have consideredapproaches to generate the minimum cardinality NAC set for MSSPs for variousscenario set structures. However, these approaches have been limited touncertain parameters where the realizations occur instantaneously or the fullset of scenarios is required. The proposed algorithm, referred to as SampleNon-Anticipativity Constraint algorithm (SNAC) relaxes this requirement. Weshow that as long as the number of uncertain parameters and parameter valuesare kept constant, the algorithm scales polynomially in the number ofscenarios.

A Graph Theoretic Approach to Non-Anticipativity Constraint Generation in Multistage Stochastic Programs with Incomplete Scenario Sets