Distributionally Robust Single Machine Scheduling Cost Problem Under Wasserstein Metric

Distributionally robust optimization is one of the hot issues in optimization in recent years.Distributionally robust optimization model with decision dependent are widely used in finance,industry and other fields,such as random single-machine scheduling problems,large-scale asset allocation problems,bank cash flow problems,and so on.In this thesis,we firstly consider three decision dependent Wasserstein uncertainty sets.They are decision dependent random variables,Wasserstein uncertainty set with decision dependent center and Wasserstein uncertainty set with decision dependent radius.Accordingly,we consider three corresponding decision dependent distributionally robust chance constrained optimization models.We obtain the equivalent reformulations of these three cases by duality theory.By using the outer and CVaR approximation,we extend the single decision depent robust chance constrainted optimization model to joint distributionally robust chance constrianted optimization and obtain the equivalent expression.Then we study a numerical experiment.We consider the models with parameter dimensions of 10,20 and 30.We also obtain the optimal values of these models under different ?.Finally,the related model is applied to the random single machine scheduling cost problem.