A Unified Framework for Adjustable Robust Optimization with Endogenous Uncertainty

TL;DR

This paper introduces a comprehensive framework for multistage adjustable robust optimization that models three types of endogenous uncertainty, linking optimization with active learning, and demonstrates its effectiveness across various practical applications.

Contribution

It unifies the treatment of different endogenous uncertainties in robust optimization and proposes a decision rule approach with decision-dependent uncertainty sets.

Findings

Significant improvements in optimization performance with endogenous uncertainty modeling

Effective application to plant redesign and maintenance planning

Tractable reformulation enabling practical implementation

Abstract

This work proposes a framework for multistage adjustable robust optimization that unifies the treatment of three different types of endogenous uncertainty, where decisions, respectively, (i) alter the uncertainty set, (ii) affect the materialization of uncertain parameters, and (iii) determine the time when the true values of uncertain parameters are observed. We provide a systematic analysis of the different types of endogenous uncertainty and highlight the connection between optimization under endogenous uncertainty and active learning. We consider decision-dependent polyhedral uncertainty sets and propose a decision rule approach that incorporates both continuous and binary recourse, including recourse decisions that affect the uncertainty set. The proposed method enables the modeling of decision-dependent nonanticipativity and results in a tractable reformulation of the problem. We demonstrate the effectiveness of the approach in computational experiments that cover a range of applications, including plant redesign, maintenance planning with inspections, optimizing revision points in capacity planning, and production scheduling with active parameter estimation. The results show significant benefits from the proper modeling of endogenous uncertainty and active learning.