10:30 AM - 10:55 AM
Robust Coordination of Large-Scale, Static LQ Problems in Presence of Uncertainties
We propose a price driven decomposition / co-ordination algorithm for distributed, worst case LQ optimization problems. We do so by: 1) rewriting the dual problem associated with the centralized robust optimization problem; and then 2) modifying the co-ordination problem to incorporate determination of the worst case scenario.
10:55 AM - 11:20 AM
Analysis of Single Class Queueing Networks - A Robust Optimization Approach
We propose and explore an alternate way to model the uncertain arrival and service processes. Instead of assuming a stochastic process as characterizing the arrival and service processes, we assume that the arrival and service processes are characterized by appropriately constructed uncertainty sets. These uncertainty sets are constructed based on the various limit laws of probability theory. In this framework, we obtain a Burke's theorem like result that relates the arrival and departure process of a queue, using which we are able to exactly analyze a fairly general class of queueing networks. This framework has multiple advantages: (a) ability to exactly analyze generalized queueing networks, and (b) ability to adapt the primitive uncertainty sets to various scenarios. This adaptability allows us to construct uncertainty sets that help us in approximating key performance measures in a queuing network. In this regard, we provide supporting empirical evidence when we compute waiting times in the network.
11:20 AM - 11:45 AM
Adaptive Robust Optimization for Security Constrained Unit Commitment Problems
Unit commitment, one of the most critical operations of an electric power system, faces new challenges as the supply and demand uncertainty increases dramatically due to the integration of variable generation resources such as wind power and price responsive demand. To meet this challenge, we propose a two-stage adaptive robust unit commitment model and a practical solution methodology. We present extensive numerical study on the real-world large scale power system operated by the ISO New England. Computational results demonstrate the economic and operational advantages of our model over the traditional reserve adjustment approach.
11:45 AM - 12:10 PM
On the Value of Stochastic Modeling in a Two-Stage Stochastic Linear Program
Decisions often need to be made in situations where key parameters are uncertain : e.g., information about future demand. While developing an accurate Stochastic Program is effective, it can be costly compared to a deterministic model. We show that, when the uncertainty is limited to the objective function, the solution of a deterministic model can in fact be robust with respect to the choice of distribution in a SP. We also propose tractable methods for bounding how much can be gained by designing a stochastic model. Our framework is applied to an airline fleet composition problem.