Linearized Robust Counterparts of Two-Stage Robust Optimization Problems 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 mainly relies on a linearization scheme employed in bilinear programming; therefore, we will say that it gives rise to the linearized robust counterpart models. We identify a close relation between this linearized robust counterpart model and the popular affinely adjustable robust counterpart model. We also describe methods of modifying both types of models to make these approximations less conservative. These methods are heavily inspired by the use of valid linear and conic inequalities in the linearization process for bilinear models. We finally demonstrate how to employ this new scheme in location-transportation and multi-item newsvendor problems to improve the numerical efficiency and performance guarantees of robust optimization.

Determining Flood Protection Strategy with Uncertain Parameter Using Adjustable Robust Counterpart Methodology

Flooding is a natural disaster that often occurs, it is not surprising that floods are one of the problems that must be resolved in various countries, one of which is Indonesia. Flood is very detrimental to the public because the impact could be the loss of material and non-material. A flood protection system is needed and must be managed properly. This aims in management of flood protection systems often requires efficient cost control strategies that are the lowest possible long-term costs, but still meets the flood protection standards imposed by regulators in all plans. In this paper a flood protection strategy is modeled using Adjustable Robust Optimization. In this approach, there are two kinds of variables that must be decided, i.e., adjustable and non-adjustable variables. A numerical simulation is presented using Scilab Software. Keywords: Flood Protection Strategy, Uncertainty, Adjustable Robust Optimization, Scilab Software.