Dick den Hertog

Adjustable robust treatment-length optimization in radiation therapy

  • Ali Ajdari
  • Thomas Bortfeld
  • Dick den Hertog
  • Stefan ten Eikelder
    • Categories Biomedical Applications, Robust Optimization Tags , ,

    Traditionally, optimization of radiation therapy (RT) treatment plans has been done before the initiation of RT course, using population-wide estimates for patients’ response to therapy. However, recent technological advancements have enabled monitoring individual patient response during the RT course, in the form of biomarkers. Although biomarker data remains subject to substantial uncertainties, information extracted from … Read more

    The Nutritious Supply Chain: Optimizing Humanitarian Food Aid

  • Dick den Hertog
  • Ozlem Ergun
  • R Goncalves
  • K Peters
  • H Fleuren
  • M Freeman
  • M Kavelj
  • S Silva
    • Categories Supply Chain Management

    The World Food Programme (WFP) is the largest humanitarian agency fighting hunger worldwide, reaching around 90 million people with food assistance in 80 countries each year. To deal with the operational complexities inherent in its mandate, WFP has been developing tools to assist its decision makers with integrating supply chain decisions across departments and functional … Read more

    A Distributionally Robust Analysis of the Program Evaluation and Review Technique

  • Dick den Hertog
  • Ernst Roos
    • Categories Robust Optimization, Scheduling Tags , ,

    Traditionally, stochastic project planning problems are modeled using the Program Evaluation and Review Technique (PERT). PERT is an attractive technique that is commonly used in practice as it requires specification of only a few characteristics of the activities’ duration. Moreover, its computational burden is extremely low. Over the years, four main disadvantages of PERT have … Read more

    Disjoint Bilinear Optimization: A Two-Stage Robust Optimization Perspective

  • Danique de Moor
  • Dick den Hertog
  • Ahmadreza Marandi
  • Lieven Vandenberghe
  • Jianzhe Zhen
    • Categories Robust Optimization Tags , , ,

    In this paper, we focus on a subclass of quadratic optimization problems, that is, disjoint bilinear optimization problems. We first show that disjoint bilinear optimization problems can be cast as two-stage robust linear optimization problems with fixed-recourse and right-hand-side uncertainty, which enables us to apply robust optimization techniques to solve the resulting problems. To this … Read more

    Tractable approximation of hard uncertain optimization problems

  • Aharon Ben-Tal
  • Frans J.C.T. de Ruiter
  • Dick den Hertog
  • Ernst Roos
  • Jianzhe Zhen
    • Categories Robust Optimization Tags , ,

    In many optimization problems uncertain parameters appear in a convex way, which is problematic as common techniques can only handle concave uncertainty. In this paper, we provide a systematic way to construct conservative approximations to such problems. Specifically, we reformulate the original problem as an adjustable robust optimization problem in which the nonlinearity of the … Read more

    Dual approach for two-stage robust nonlinear optimization

  • Frans J.C.T. de Ruiter
  • Dick den Hertog
  • Jianzhe Zhen
    • Categories Robust Optimization Tags , , ,

    Adjustable robust minimization problems in which the adjustable variables appear in a convex way are difficult to solve. For example, if we substitute linear decision rules for the adjustable variables, then the model becomes convex in the uncertain parameters, whereas for computational tractability we need concavity in the uncertain parameters. In this paper we reformulate … Read more

    Reducing conservatism in Robust Optimization

  • Dick den Hertog
  • Ernst Roos
    • Categories Robust Optimization Tags , ,

    Although Robust Optimization is a powerful technique in dealing with uncertainty in optimization, its solutions can be too conservative when it leads to an objective value much worse than the nominal solution or even to infeasibility of the robust problem. In practice, this can lead to robust solutions being disregarded in favor of the nominal … Read more

    Robust optimization for models with uncertain SOC and SDP constraints

  • Frans J.C.T. de Ruiter
  • Dick den Hertog
  • Ernst Roos
  • Jianzhe Zhen
    • Categories Robust Optimization Tags , , , ,

    In this paper we consider uncertain second-order cone (SOC) and semidefinite programming (SDP) constraints with polyhedral uncertainty, which are in general computationally intractable. We propose to reformulate an uncertain SOC or SDP constraint as a set of adjustable robust linear optimization constraints with an ellipsoidal or semidefinite representable uncertainty set, respectively. The resulting adjustable problem … Read more

    Extending the Scope of Robust Quadratic Optimization

  • Aharon Ben-Tal
  • Dick den Hertog
  • Ahmadreza Marandi
  • Bertrand Melenberg
    • Categories Quadratic Programming, Robust Optimization Tags , , ,

    We derive computationally tractable formulations of the robust counterparts of convex quadratic and conic quadratic constraints that are concave in matrix-valued uncertain parameters. We do this for a broad range of uncertainty sets. In particular, we show how to reformulate the support functions of uncertainty sets represented in terms of matrix norms and cones. Our … Read more

    Bridging the gap between predictive and prescriptive analytics – new optimization methodology needed

  • Dick den Hertog
  • Krzysztof Postek
    • Categories Other Topics

    Business analytics is becoming more and more important nowadays. Up to now predictive analytics appears to be much more applied in practice than prescriptive analytics. We argue that although optimization is used to obtain predictive models, and predictive tools are used to forecast parameters in optimization models, still the deep relation between the predictive and … Read more