conditional-value-at-risk

Leveraging Decision Diagrams to Solve Two-stage Stochastic Programs with Binary Recourse and Logical Linking Constraints

  • Moira MacNeil
  • Merve Bodur
    • Categories Stochastic Programming Tags , , ,

    Two-stage stochastic programs with binary recourse are challenging to solve and efficient solution methods for such problems have been limited. In this work, we generalize an existing binary decision diagram-based (BDD-based) approach of Lozano and Smith (Math. Program., 2018) to solve a special class of two-stage stochastic programs with binary recourse. In this setting, the … Read more

    On Approximations of Data-Driven Chance Constrained Programs over Wasserstein Balls

  • Zhi Chen
  • Daniel Kuhn
  • Wolfram Wiesemann
    • Categories Robust Optimization Tags , , , ,

    Distributionally robust chance constrained programs minimize a deterministic cost function subject to the satisfaction of one or more safety conditions with high probability, given that the probability distribution of the uncertain problem parameters affecting the safety condition(s) is only known to belong to some ambiguity set. We study two popular approximation schemes for distributionally robust … Read more

    A Robust Optimization Method with Successive Linear Programming for Intensity Modulated Radiation Therapy

  • Masaaki Tamai
  • Makoto Yamashita
    • Categories Applications - OR and Management Sciences, Linear Programming, Robust Optimization Tags , , , ,

    Intensity modulated radiation therapy (IMRT) is one of radiation therapies for cancers, and it is considered to be effective for complicated shapes of tumors, since dose distributions from each irradiation can be modulated arbitrary. Fluence map optimization (FMO), which optimizes beam intensities with given beam angles, is often formulated as an optimization problem with dose … Read more

    The Value of Randomized Strategies in Distributionally Robust Risk Averse Network Interdiction Games

  • Erick Delage
  • Utsav Sadana
    • Categories Applications - OR and Management Sciences, Game Theory, Robust Optimization Tags , , ,

    Conditional Value at Risk (CVaR) is widely used to account for the preferences of a risk-averse agent in the extreme loss scenarios. To study the effectiveness of randomization in interdiction games with an interdictor that is both risk and ambiguity averse, we introduce a distributionally robust network interdiction game where the interdictor randomizes over the … Read more

    Stochastic Last-mile Delivery with Crowd-shipping and Mobile Depots

  • Merve Bodur
  • Kianoush Mousavi
  • Matthew J. Roorda
    • Categories Stochastic Programming, Transportation Tags , , , , , ,

    This paper proposes a two-tier last-mile delivery model that optimally selects mobile depot locations in advance of full information about the availability of crowd-shippers, and then transfers packages to crowd-shippers for the final shipment to the customers. Uncertainty in crowd-shipper availability is incorporated by modeling the problem as a two-stage stochastic integer program. Enhanced decomposition … Read more

    Risk-Neutral and Risk-Averse Transmission Switching for Load Shed Recovery

  • Manish Bansal
  • Adolfo Escobedo
  • Yingqiu Zhang
    • Categories Applications - OR and Management Sciences, Energy, Stochastic Programming Tags , , ,

    Maintaining an uninterrupted supply of electricity is a fundamental goal of power systems operators. However, due to critical outage events, customer demand or load is at times disconnected or shed temporarily. While deterministic optimization models have been devised to help operators expedite load shed recovery by harnessing the flexibility of the grid’s topology (i.e., transmission … Read more

    Sharing the Value-at-Risk under Distributional Ambiguity

  • Weijun Xie
  • Zhi Chen
    • Categories Applications - OR and Management Sciences, Robust Optimization, Stochastic Programming Tags , , ,

    This paper considers the problem of risk sharing, where a coalition of homogeneous agents, each bearing a random cost, aggregates their costs and shares the value-at-risk of such a risky position. Due to limited distributional information in practice, the joint distribution of agents’ random costs is difficult to acquire. The coalition, being aware of the … Read more

    Risk-Averse Bi-Level Stochastic Network Interdiction Model for Cyber-Security Risk Management

  • Tanveer Hossain Bhuiyan
  • Mahantesh Halappanavar
  • Hugh R. Medal
  • Apurba Nandi
    • Categories (Mixed) Integer Linear Programming, Network Optimization, Stochastic Programming Tags , , , ,

    Security of cyber networks is crucial; recent severe cyber-attacks have had a devastating effect on many large organizations. The attack graph, which maps the potential attack paths of a cyber network, is a popular tool for analyzing cyber system vulnerability. In this study, we propose a bi-level stochastic network interdiction model on an attack graph … Read more

    Two-stage stochastic programming model for routing multiple drones with fuel constraints

  • Sivakumar Rathinam
  • Kaarthik Sundar
  • Saravanan Venkatachalam
    • Categories Combinatorial Optimization, Stochastic Programming Tags , , , , , ,

    Uses of drones and unmanned vehicles (UAVs) in ground or aerial are increasing in both civil and military applications. This paper develops a two-stage stochastic optimization model with a recourse for a multiple drone-routing problem with fuel constraints under uncertainty for the travel between any pair of targets/refueling-sites/depot. We are given a set of n … Read more

    Incorporating Black-Litterman Views in Portfolio Construction when Stock Returns are a Mixture of Normals

  • Gérard Cornuéjols
  • Burak Kocuk
    • Categories Applications - OR and Management Sciences, Nonlinear Optimization Tags , , ,

    In this paper, we consider the basic problem of portfolio construction in financial engineering, and analyze how market-based and analytical approaches can be combined to obtain efficient portfolios. As a first step in our analysis, we model the asset returns as a random variable distributed according to a mixture of normal random variables. We then … Read more