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

## TL;DR

This paper introduces a polynomially scalable algorithm for generating minimal non-anticipativity constraints in multistage stochastic programming with incomplete scenario sets, accommodating gradual uncertainty realizations.

## Contribution

The paper presents SNAC, a novel algorithm that relaxes previous limitations, enabling efficient NAC generation for complex scenario structures in MSSPs.

## Key findings

- SNAC scales polynomially with the number of scenarios.
- It handles both endogenous and exogenous uncertainties.
- The approach relaxes the need for full scenario sets.

## Abstract

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.