robust optimization

From CVaR to Uncertainty Set: Implications in Joint Chance Constrained Optimization

  • Wenqing Chen
  • Jie Sun
  • Chung-Piaw Teo
  • Melvyn Sim
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    In this paper we review the different tractable approximations of individual chance constraint problems using robust optimization on a varieties of uncertainty set, and show their interesting connections with bounds on the condition-value-at-risk CVaR measure popularized by Rockafellar and Uryasev. We also propose a new formulation for approximating joint chance constrained problems that improves upon … Read more

    A New Cone Programming Approach for Robust Portfolio Selection

  • Zhaosong Lu
    • Categories Applications - Science and Engineering, Finance and Economics, Robust Optimization Tags ,

    The robust portfolio selection problems have recently been studied by several researchers (e.g., see \cite{GoIy03,ErGoIy04,HaTu04,TuKo04}). In their work, the “separable” uncertainty sets of the problem parameters (e.g., mean and covariance of the random returns) were considered. These uncertainty sets share two common drawbacks: i) the actual confidence level of the uncertainty set is unknown, and … Read more

    Selected Topics in Robust Convex Optimization

  • Aharon Ben-Tal
  • Arkadi Nemirovski
    • Categories Control Applications, Robust Optimization, Stochastic Programming Tags , , ,

    Robust Optimization is a rapidly developing methodology for handling optimization problems affected by non-stochastic “uncertain-but-bounded” data perturbations. In this paper, we overview several selected topics in this popular area, specifically, (1) recent extensions of the basic concept of {\sl robust counterpart} of an optimization problem with uncertain data, (2) tractability of robust counterparts, (3) links … Read more

    Step decision rules for multistage stochastic programming: a heuristic approach

  • Julien Thénié
  • Jean-Philippe Vial
    • Categories Stochastic Programming, Supply Chain Management Tags , , ,

    Stochastic programming with step decision rules, SPSDR, is an attempt to overcome the curse of computational complexity of multistage stochastic programming problems. SPSDR combines several techniques. The first idea is to work with independent experts. Each expert is confronted with a sample of scenarios drawn at random from the original stochastic process. The second idea … Read more

    Goal Driven Optimization

  • Wenqing Chen
  • Melvyn Sim
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    Achieving a targeted objective, goal or aspiration level are relevant aspects of decision making under uncertainties. We develop a goal driven stochastic optimization model that takes into account an aspiration level. Our model maximizes the shortfall aspiration level criterion}, which encompasses the probability of success in achieving the goal and an expected level of under-performance … Read more

    A Tractable Approximation of Stochastic Programming via Robust Optimization

  • Xin Chen
  • Peng Sun
  • Jiawei Zhang
  • Melvyn Sim
    • Categories Robust Optimization, Second-Order Cone Programming, Stochastic Programming Tags , , ,

    Stochastic programming, despite its immense modeling capabilities, is well known to be computationally excruciating. In this paper, we introduce a unified framework of approximating multiperiod stochastic programming from the perspective of robust optimization. Specifically, we propose a framework that integrates multistage modeling with safeguarding constraints. The framework is computationally tractable in the form of second … Read more

    A Robust Optimization Framework for Analyzing Distribution Systems with Transshipment

  • Mabel C. Chou
  • Melvyn Sim
  • Rick So
    • Categories Robust Optimization, Stochastic Programming, Supply Chain Management Tags , , ,

    This paper studies a distribution system consisting of multiple retail locations with transshipment operations among the retailers. Due to the difficulty in computing the optimal solution imposed by the transshipment operations and in estimating shortage cost from a practical perspective, we propose a robust optimization framework for analyzing the impact of transshipment operations on such … Read more

    Single-Product Pricing via Robust Optimization

  • Aurelie Thiele
    • Categories Robust Optimization, Yield Management Tags , ,

    We present a robust optimization approach to the problem of pricing a capacitated product over a finite time horizon in the presence of demand uncertainty. This technique does not require the knowledge of the underlying probability distributions, which in practice are difficult to estimate accurately, and instead models random variables as uncertain parameters belonging to … Read more

    Computing robust basestock levels

  • Daniel Bienstock
  • Nuri Ozbay
    • Categories Applications - OR and Management Sciences Tags ,

    This paper considers how to optimally set the basestock level for a single buffer when demand is uncertain, in a robust framework. We present a family of algorithms based on decomposition that scale well to problems with hundreds of time periods, and theoretical results on more general models. Citation CORC report TR-2005-09, Columbia University, November … Read more

    Efficient Schemes for Robust IMRT Treatment Planning

  • Arinbjorn Olafsson
  • Stephen Wright
    • Categories Biomedical Applications, Robust Optimization Tags ,

    We use robust optimization techniques to formulate an IMRT treatment planning problem in which the dose matrices are uncertain, due to both dose calculation errors and inter-fraction positional uncertainty of tumor and organs. When the uncertainty is taken into account, the original linear programming formulation becomes a second-order cone program. We describe a novel and … Read more