Distributionally robust optimization under endogenous uncertainty with an application in retrofitting planning

Abstract

Endogenous uncertainty concerns uncertainty which is dependent of decisions such as link failure in the retrofitting planning application. We propose a marginal-based distributionally robust optimization framework for integer stochastic optimization with decision-dependent discrete distributions that can be applied for the retrofitting planning application. We show that the resulting model can be formulated as a mixed-integer linear optimization problem. In order to solve the problem, we develop a constraint generation algorithm given the exponentially large number of constraints. Numerical results for the retrofitting planning application show that the proposed algorithm once tailored can solve the problem efficiently.