Robust Linear Programming with Right-Hand-Side Uncertainty, Duality and Applications

Introduction

Various models for handling robustness objectives with respect to uncertainties on some specified coefficients in linear programming (LP) models have been proposed in the literature. We can mention Soyster [9], Ben-Tal and Nemirovski [1,2] and Bertsimas and Sim [3,4].

The various approaches proposed can roughly be divided into two distinct categories, depending on whether the underlying uncertainty model refers to possible fluctuations on the row vectors of the constraint matrix (we call this ‘rowwise uncertainty’), or on the column vectors (we call this ‘columnwise uncertainty’).

Columnwise uncertainty was first considered by Soyster [9]. In this model each column A _j of the ${ m\times n }$ constraint matrix is either supposed to be exactly known, or is only known to belong to a given subset ${ K_j \subset \mathbb{R}^m }$(‘uncertainty set’). The cost vector and the right hand side (RHS) are supposed to be certain. A robust solution is a solution which is...