Multi-Stage Decisions under Uncertainty



In real world problems, we often have parameters that are not exactly known due to measurement, implementation, or prediction errors and uncertainty. When solving optimization problems, we want to find a solution that will be feasible and work well in practice despite these uncertainties. Finding such a solution becomes harder when dealing with a multi-stage problem, in which we need to devise a strategy to make the best decision at each stage, without knowing the future realization of the uncertainty. These problems arise in real-world applications such as inventory control, energy systems, portfolio management and many others.

In this talk, we will review existing robust and adaptive optimization approaches for solving two-stage and multi-stage optimization problems with uncertain parameters. Specifically, we look at the case of two-stage linear problems where some decisions may be infeasible for some realization of the uncertainty (no complete recourse). We look at this problem in a robust setting and a stochastic setting. In the robust setting, we are interested in the best adaptive decision which minimizes the worst-case performance. We develop a generalization of the column and constraint generation (CCG) method for problems without complete recourse, and show its benefits in terms of tractability and performance. In the stochastic setting, we are interested in finding an adaptive decision that optimizes the average performance; however, we do not know the true distribution and only have i.i.d. generated data. We develop the sample-robust optimization (SRO) data-driven model and show that it can be tractably approximated by local affine decision rules. Moreover, we show that this approximation converges to the true solution of the underlying stochastic optimization problem as the number of data points increase.

Registration to Remy Spliet, is required for availability of lunch.