Linearized Robust Counterparts of Two-stage Robust Optimization Problem with Applications in Operations Management

In this article, we discuss an alternative method for deriving conservative approximation models for two-stage robust optimization problems. The method extends in a natural way a linearization scheme that was recently proposed to construct tractable reformulations for robust static problems that involve profit functions that decompose as a sum of piecewise linear concave expressions. Given that this generalized method mainly relies on a linearization scheme employed in bilinear optimization problems, we will say that it gives rise to the “linearized robust counterpart” model. We identify an intimate relation between this linearized robust counterpart model and the popular affinely adjustable robust counterpart model. We also describe a simple way of modifying both types of models in order to make these approximations less conservative. We finally demonstrate how to employ this new scheme in a set of operations management problems in order to improve the performance and guarantees of robust optimization.