Stochastic Programming

Risk averse stochastic programming: time consistency and optimal stopping

  • Alois Pichler
  • Alexander Shapiro
    • Categories Dynamic Programming, Stochastic Programming Tags , , , , ,

    Bellman formulated a vague principle for optimization over time, which characterizes optimal policies by stating that a decision maker should not regret previous decisions retrospectively. This paper addresses time consistency in stochastic optimization. The problem is stated in generality first. The paper discusses time consistent decision-making by addressing risk measures which are recursive, nested, dynamically … Read more

    Asymptotic results of Stochastic Decomposition for Two-stage Stochastic Quadratic Programming

  • Junyi Liu
  • Suvrajeet Sen
    • Categories Convex and Nonsmooth Optimization, Stochastic Programming Tags , ,

    This paper presents stochastic decomposition (SD) algorithms for two classes of stochastic programming problems: 1) two-stage stochastic quadratic-linear programming (SQLP) in which a quadratic program defines the objective function in the first stage and a linear program defines the value function in the second stage; 2) two-stage stochastic quadratic-quadratic programming (SQQP) which has quadratic programming … Read more

    On Solving Two-Stage Distributionally Robust Disjunctive Programs with a General Ambiguity Set

  • Manish Bansal
  • Sanjay Mehrotra
    • Categories 0-1 Programming, Stochastic Programming

    We introduce two-stage distributionally robust disjunctive programs (TSDR-DPs) with disjunctive constraints in both stages and a general ambiguity set for the probability distributions. The TSDR-DPs subsume various classes of two-stage distributionally robust programs where the second stage problems are non-convex programs (such as mixed binary programs, semi-continuous program, nonconvex quadratic programs, separable non-linear programs, etc.). … Read more

    The Distributionally Robust Chance Constrained Vehicle Routing Problem

  • Shubhechyya Ghosal
  • Wolfram Wiesemann
    • Categories Robust Optimization, Stochastic Programming, Transportation Tags , ,

    We study a variant of the capacitated vehicle routing problem (CVRP), which asks for the cost-optimal delivery of a single product to geographically dispersed customers through a fleet of capacity-constrained vehicles. Contrary to the classical CVRP, which assumes that the customer demands are deterministic, we model the demands as a random vector whose distribution is … Read more

    The Value of Multi-stage Stochastic Programming in Risk-averse Unit Commitment under Uncertainty

  • Shabbir Ahmed
  • M. Selim Akturk
  • Özlem Cavus
  • Ali Irfan Mahmutogullari
    • Categories Stochastic Programming Tags , ,

    Day-ahead scheduling of electricity generation or unit commitment is an important and challenging optimization problem in power systems. Variability in net load arising from the increasing penetration of renewable technologies have motivated study of various classes of stochastic unit commitment models. In two-stage models, the generation schedule for the entire day is fixed while the … Read more

    Generalized Stochastic Frank-Wolfe Algorithm with Stochastic “Substitute” Gradient for Structured Convex Optimization

  • Robert M. Freund
  • Haihao Lu
    • Categories Convex Optimization, Nonlinear Optimization, Stochastic Programming Tags , , ,

    The stochastic Frank-Wolfe method has recently attracted much general interest in the context of optimization for statistical and machine learning due to its ability to work with a more general feasible region. However, there has been a complexity gap in the guaranteed convergence rate for stochastic Frank-Wolfe compared to its deterministic counterpart. In this work, … Read more

    Probabilistic Envelope Constrained Multiperiod Stochastic Emergency Medical Services Location Model and Decomposition Scheme

  • Erick Delage
  • Jinlin Li
  • Chun Peng
    • Categories Production and Logistics, Stochastic Programming, Transportation Tags , , , , ,

    This paper considers a multiperiod Emergency Medical Services (EMS) location problem and introduces two two-stage stochastic programming formulations that account for uncertainty about emergency demand. While the first model considers both a constraint on the probability of covering the realized emergency demand and minimizing the expected cost of doing so, the second one employs probabilistic … Read more

    A two-stage stochastic optimization model for the bike-sharing allocation and rebalancing problem

  • Rossana Cavagnini
  • Francesca Maggioni
  • Luca Bertazzi
  • Mike Hewitt
    • Categories Production and Logistics, Stochastic Programming Tags , , ,

    The Bike-sharing allocation and rebalancing problem is the problem of determining the initial daily allocation of bikes to stations in a bike-sharing system composed of one depot and multiple capacitated stations, in which bikes can be rebalanced at a point in time during the day. Due to the uncertain demand in each station, we propose … Read more

    Dynamic Scheduling of Home Health Care Patients to Medical Providers

  • Andre Augusto Cire
  • Adam Diamant
    • Categories Applications - OR and Management Sciences, Stochastic Programming Tags , , , ,

    Home care provides personalized medical care and social support to patients within their own home. Our work proposes a dynamic scheduling framework to assist in the assignment of patients to health practitioners (HPs) at a single home care agency. We model the decision of which patients to assign to HPs as a discrete-time Markov decision … Read more

    Data-Driven Distributionally Robust Chance-Constrained Optimization with Wasserstein Metric

  • Ran Ji
  • Miguel A. Lejeune
    • Categories Robust Optimization, Second-Order Cone Programming, Stochastic Programming Tags , ,

    We study distributionally robust chance-constrained programming (DRCCP) optimization problems with data-driven Wasserstein ambiguity sets. The proposed algorithmic and reformulation framework applies to distributionally robust optimization problems subjected to individual as well as joint chance constraints, with random right-hand side and technology vector, and under two types of uncertainties, called uncertain probabilities and continuum of realizations. … Read more