Stochastic Programming

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

    Solving Stochastic and Bilevel Mixed-Integer Programs via a Generalized Value Function

  • Oleg A. Prokopyev
  • Andrew J. Schaefer
  • Onur Tavaslioglu
    • Categories (Mixed) Integer Linear Programming, Integer Programming, Stochastic Programming

    We introduce a generalized value function of a mixed-integer program, which is simultaneously parameterized by its objective and right-hand side. We describe its fundamental properties, which we exploit through three algorithms to calculate it. We then show how this generalized value function can be used to reformulate two classes of mixed-integer optimization problems: two-stage stochastic … Read more

    Data-Driven Chance Constrained Programs over Wasserstein Balls

  • Zhi Chen
  • Daniel Kuhn
  • Wolfram Wiesemann
    • Categories (Mixed) Integer Nonlinear Programming, Robust Optimization, Stochastic Programming Tags , ,

    We provide an exact deterministic reformulation for data-driven chance constrained programs over Wasserstein balls. For individual chance constraints as well as joint chance constraints with right-hand side uncertainty, our reformulation amounts to a mixed-integer conic program. In the special case of a Wasserstein ball with the $1$-norm or the $\infty$-norm, the cone is the nonnegative … Read more

    Multi-stage Stochastic Programming for Demand Response Optimization

  • Özlem Cavus
  • Hande Yaman
  • Munise Kübra Şahin
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences, Stochastic Programming Tags , , ,

    The increase in the energy consumption puts pressure on natural resources and environment and results in a rise in the price of energy. This motivates residents to schedule their energy consumption through demand response mechanism. We propose a multi-stage stochastic programming model to schedule different kinds of electrical appliances under uncertain weather conditions and availability … Read more

    Envelope Theorems for Multi-Stage Linear Stochastic Optimization

  • Goncalo Terca
  • David Wozabal
    • Categories Stochastic Programming Tags , , ,

    We propose a method to compute derivatives of multi-stage linear stochastic optimization problems with respect to parameters that influence the problem’s data. Our results are based on classical envelope theorems, and can be used in problems directly solved via their deterministic equivalents as well as in stochastic dual dynamic programming for which the derivatives of … Read more

    On Distributionally Robust Chance Constrained Programs with Wasserstein Distance

  • Weijun Xie
    • Categories Robust Optimization, Stochastic Programming

    This paper studies a distributionally robust chance constrained program (DRCCP) with Wasserstein ambiguity set, where the uncertain constraints should be satisfied with a probability at least a given threshold for all the probability distributions of the uncertain parameters within a chosen Wasserstein distance from an empirical distribution. In this work, we investigate equivalent reformulations and … Read more