A unified framework for adjustable robust optimization with endogenous uncertainty

Abstract

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, (a) alter the uncertainty set, (b) affect the materialization of uncertain parameters, and (c) 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 wide range of applications. The results show significant benefits from proper modeling of endogenous uncertainty and active learning.

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