A Node Formulation for Multistage Stochastic Programs with Endogenous Uncertainty

TL;DR

This paper presents a node formulation for multistage stochastic programs with decision-dependent uncertainty, simplifying the model structure and introducing an exact solution algorithm that outperforms commercial solvers on larger instances.

Contribution

It introduces a novel node formulation for endogenous uncertainty in multistage stochastic programming and an exact solution algorithm for a special case.

Findings

The node formulation avoids explicit non-anticipativity constraints.

The exact algorithm outperforms commercial solvers as problem size increases.

The approach is validated on a case study demonstrating scalability.

Abstract

This paper introduces a node formulation for multistage stochastic programs with endogenous (i.e., decision-dependent) uncertainty. Problems with such structure arise when the choices of the decision maker determine a change in the likelihood of future random events. The node formulation avoids an explicit statement of non-anticipativity constraints, and as such keeps the dimension of the model sizeable. An exact solution algorithm for a special case is introduced and tested on a case study. Results show that the algorithm outperforms a commercial solver as the size of the instances increases.