Robust Decision Making as a Decision Making Aid Under Uncertainty

Abstract

We present a general modeling framework for robust optimization of linear programs with uncertainty in the values of the objective function coefficients and the values of the right-hand-side. The methodology presented here is straightforward applicable to the uncertainty in the constraints matrix coefficients as well. In contrast to traditional mathematical programming approaches, we model uncertainty by using scenarios to characterize the objective function and right-hand-side coefficients. Solutions are obtained for each scenario and, then, these individual scenario solutions are aggregated to yield a non-anticipative or implement able policy that minimizes the regret of wrong decisions. Such approach makes it possible a variety of recourse decision types. A given solution is termed robust if it minimizes the expected difference over the set of scenarios between the objective function value of the solution and the objective function value of the optimal solution for each scenario, while satisfying certain non-anticipativity constraints. This approach results in a huge model with a submodel per scenario group at each period. Different Augmented Lagrangian strategies are proposed. Our approach allows the parallel solution of the decomposed submodels. Some ideas for problem solving are explored.