The L-Shaped Method for Stochastic Programs with Decision-Dependent Uncertainty

TL;DR

This paper extends the L-Shaped method to efficiently solve large-scale two-stage stochastic programming problems with decision-dependent uncertainty, using a new unified formulation and distribution-specific cuts.

Contribution

It introduces a novel, unified approach with distribution-specific cuts for linear and integer stochastic programs with decision-dependent uncertainty.

Findings

Effective on large-scale production planning problems

Significantly improves solution efficiency

Applicable to both linear and integer stochastic programs

Abstract

In this paper we extend the well-known L-Shaped method to solve two-stage stochastic programming problems with decision-dependent uncertainty. The method is based on a novel, unifying, formulation and on distribution-specific optimality and feasibility cuts for both linear and integer stochastic programs. Extensive tests on three production planning problems illustrate that the method is extremely effective on large-scale instances.