stochastic programming

A multi-step interior point warm-start approach for large-scale stochastic linear programming

  • Marco Colombo
  • Andreas Grothey
    • Categories Stochastic Programming Tags , ,

    Interior point methods (IPM) have been recognised as an efficient approach for the solution of large scale stochastic programming problems due to their ability of exploiting the block-angular structure of the augmented system particular to this problem class. Stochastic programming problems, however, have exploitable structure beyond the simple matrix shape: namely the scenarios are typically … Read more

    Risk-Averse Two-Stage Stochastic Linear Programming: Modeling and Decomposition

  • Naomi Miller
  • Andrzej Ruszczyński
    • Categories Stochastic Programming Tags , ,

    We formulate a risk-averse two-stage stochastic linear programming problem in which unresolved uncertainty remains after the second stage. The objective function is formulated as a composition of conditional risk measures. We analyze properties of the problem and derive necessary and sufficient optimality conditions. Next, we construct two decomposition methods for solving the problem. The first … Read more

    Sample Average Approximation for Stochastic Dominance Constrained Programs

  • Tito Homem-de-Mello
  • Jian Hu
  • Sanjay Mehrotra
    • Categories Nonlinear Optimization, Stochastic Programming Tags , , , , ,

    In this paper we study optimization problems with second-order stochastic dominance constraints. This class of problems has been receiving increasing attention in the literature as it allows for the modeling of optimization problems where a risk-averse decision maker wants to ensure that the solution produced by the model dominates certain benchmarks. Here we deal with … Read more

    Distributionally Robust Optimization and its Tractable Approximations

  • Joel Goh
  • Melvyn Sim
    • Categories Robust Optimization Tags ,

    In this paper, we focus on a linear optimization problem with uncertainties, having expectations in the objective and in the set of constraints. We present a modular framework to obtain an approximate solution to the problem that is distributionally robust, and more flexible than the standard technique of using linear rules. Our framework begins by … Read more

    A Structure-Conveying Modelling Language for Mathematical and Stochastic Programming

  • Marco Colombo
  • Jacek Gondzio
  • Andreas Grothey
  • Jonathan Hogg
  • Kristian Woodsend
    • Categories Modeling Languages and Systems Tags , , ,

    We present a structure-conveying algebraic modelling language for mathematical programming. The proposed language extends AMPL with object-oriented features that allows the user to onstruct models from sub-models, and is implemented as a combination of pre- and post-processing phases for AMPL. Unlike traditional modelling languages, the new approach does not scramble the block structure of the … Read more

    On a time consistency concept in risk averse multi-stage stochastic programming

  • Alexander Shapiro
    • Categories Stochastic Programming Tags , , , ,

    In this paper we discuss time consistency of multi-stage risk averse stochastic programming problems. We approach the concept of time consistency from an optimization point of view. That is, at each state of the system optimality of a decision policy should not involve states which cannot happen in the future. We also discuss a relation … Read more

    Optimal Scenario Tree Reduction for Stochastic Streamflows in Power Generation Planning Problems

  • J.M. Damazio
  • Welington de Oliveira
  • Maria Elvira P. Maceira
  • Claudia Sagastizábal
  • D.D. Penna
    • Categories Stochastic Programming Tags , ,

    The mid-term operation planning of hydro-thermal power systems needs a large number of synthetic sequences to represent accurately stochastic streamflows. These sequences are generated by a periodic autoregressive model. If the number of synthetic sequences is too big, the optimization planning problem may be too difficult to solve. To select a small set of sequences … Read more

    A Multistage Stochastic Programming Approach to Open Pit Mine Production Scheduling with Uncertain Geology

  • Natashia Boland
  • Gary Froyland
  • Irina Dumitrescu
    • Categories Applications - OR and Management Sciences, Integer Programming, Stochastic Programming Tags , , ,

    The Open Pit Mine Production Scheduling Problem (OPMPSP) studied in recent years is usually based on a single geological estimate of material to be excavated and processed over a number of decades. However techniques have now been developed to generate multiple stochastic geological estimates that more accurately describe the uncertain geology. While some attempts have … Read more

    Progressive Hedging Innovations for a Class of Stochastic Resource Allocation Problems

  • David Strip
  • Jean-Paul Watson
  • David L. Woodruff
    • Categories Production and Logistics, Stochastic Programming Tags , ,

    Progressive hedging (PH) is a scenario-based decomposition technique for solving stochastic programs. While PH has been successfully applied to a number of problems, a variety of issues arise when implementing PH in practice, especially when dealing with very difficult or large-scale mixed-integer problems. In particular, decisions must be made regarding the value of the penalty … Read more

    The Facility Location Problem with Bernoulli Demands

  • Maria Albareda-Sambola
  • Francisco Saldanha-da-Gama
  • Elena Fernandez
    • Categories Stochastic Programming Tags ,

    In this paper we address a discrete capacitated facility location problem in which customers have Bernoulli demands. The problem is formulated as a two-stage stochastic program. The goal is to define an a priori solution for the location of the facilities and for the allocation of customers to the operating facilities that minimize the expected … Read more