Abstract
We present decision/optimization problems driven by uncertain and online data, and show how analytical models and computational algorithms can be used to achieve solution efficiency and near optimality. We first describe the so-called Distributionally or Likelihood Robust optimization models and their algorithms in dealing stochastic decision problems when the exact uncertainty distribution is unknown but certain statistical moments and samples can be estimated. Then we describe an online combinatorial auction problem using online linear programming technologies. We discuss near-optimal algorithms for solving this surprisingly general class of online problems under the assumption of random order of arrivals and some conditions on the data and size of the problem. These algorithms have a feature of "learning while doing" by dynamically updating a threshold price vector at certain time intervals, where the dual prices learned from revealed data from the previous periods are used to determine the sequential decision making in the current period.