stochastic programming

A General Heuristic Method for Joint Chance-Constrained Stochastic Programs with Discretely Distributed Parameters

  • Eric B. Beier
  • Matthew W. Tanner
    • Categories Basic Sciences Applications, Meta Heuristics, Stochastic Programming Tags , , ,

    We present a general metaheuristic for joint chance-constrained stochastic programs with discretely distributed parameters. We give a reformulation of the problem that allows us to define a finite solution space. We then formulate a novel neighborhood for the problem and give methods for efficiently searching this neighborhood for solutions that are likely to be improving. … Read more

    Tractable algorithms for chance-constrained combinatorial problems

  • Olivier Klopfenstein
    • Categories Combinatorial Optimization, Robust Optimization, Stochastic Programming Tags , , , , ,

    This paper aims at proposing tractable algorithms to find effectively good solutions to large size chance-constrained combinatorial problems. A new robust model is introduced to deal with uncertainty in mixed-integer linear problems. It is shown to be strongly related to chance-constrained programming when considering pure 0-1 problems. Furthermore, its tractability is highlighted. Then, an optimization … Read more

    An integer programming approach for linear programs with probabilistic constraints

  • Shabbir Ahmed
  • James R. Luedtke
  • George L. Nemhauser
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming Tags , , , ,

    Linear programs with joint probabilistic constraints (PCLP) are difficult to solve because the feasible region is not convex. We consider a special case of PCLP in which only the right-hand side is random and this random vector has a finite distribution. We give a mixed-integer programming formulation for this special case and study the relaxation … Read more

    E-model for Transportation Problem of Linear Stochastic Fractional Programming

  • Vincent Charles
    • Categories Applications - OR and Management Sciences, Stochastic Programming, Transportation Tags , , ,

    This paper deals with the so-called transportation problem of linear stochastic fractional programming, and emphasizes the wide applicability of LSFP. The transportation problem, received this name because many of its applications involve in determining how to optimally transport goods. However, some of its applications (e.g., production scheduling) actually have nothing to do with transportation. The … Read more

    An Exact Solution Approach for Portfolio Optimization Problems under Stochastic and Integer Constraints

  • Pierre Bonami
  • Miguel A. Lejeune
    • Categories (Mixed) Integer Nonlinear Programming, Finance and Economics, Stochastic Programming Tags , , ,

    In this paper, we study extensions of the classical Markowitz mean-variance portfolio optimization model. First, we consider that the expected asset returns are stochastic by introducing a probabilistic constraint which imposes that the expected return of the constructed portfolio must exceed a prescribed return threshold with a high confidence level. We study the deterministic equivalents … Read more

    From CVaR to Uncertainty Set: Implications in Joint Chance Constrained Optimization

  • Wenqing Chen
  • Jie Sun
  • Chung-Piaw Teo
  • Melvyn Sim
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    In this paper we review the different tractable approximations of individual chance constraint problems using robust optimization on a varieties of uncertainty set, and show their interesting connections with bounds on the condition-value-at-risk CVaR measure popularized by Rockafellar and Uryasev. We also propose a new formulation for approximating joint chance constrained problems that improves upon … Read more

    Inverse Stochastic Linear Programming

  • Lewis Ntaimo
  • Andrew J. Schaefer
  • Gorkem Saka
    • Categories Stochastic Programming Tags , ,

    Inverse optimization perturbs objective function to make an initial feasible solution optimal with respect to perturbed objective function while minimizing cost of perturbation. We extend inverse optimization to two-stage stochastic linear programs. Since the resulting model grows with number of scenarios, we present two decomposition approaches for solving these problems. CitationUnpublished: 07-1, University of Pittsburgh, … Read more

    Extending Algebraic Modelling Languages for Stochastic Programming

  • Robert Fourer
  • Gautam Mitra
  • Mustapha Sadki
  • Christian Valente
    • Categories Modeling Languages and Systems, Optimization Software Design Principles, Stochastic Programming Tags

    Algebraic modelling languages have gained wide acceptance and use in Mathematical Programming by researchers and practitioners. At a basic level, stochastic programming models can be defined using these languages by constructing their deterministic equivalent. Unfortunately, this leads to very large model data instances. We propose a direct approach in which the random values of the … Read more

    StAMPL: A Filtration-Oriented Modeling Tool for Stochastic Programming

  • Robert Fourer
  • Leonardo B. Lopes
    • Categories Modeling Languages and Systems, Optimization Software Design Principles, Stochastic Programming Tags , ,

    Every multistage stochastic programming problem with recourse (MSPR) contains a filtration process. In this research, we created a notation that makes the filtration process the central syntactic construction of the MSPR. As a result, we achieve lower redundancy and higher modularity than is possible with the mathematical notation commonly associated with stochastic programming. To experiment … Read more

    Valid Inequalities and Restrictions for Stochastic Programming Problems with First Order Stochastic Dominance Constraints

  • Nilay Noyan
  • Andrzej Ruszczyński
    • Categories Stochastic Programming Tags , , ,

    Stochastic dominance relations are well-studied in statistics, decision theory and economics. Recently, there has been significant interest in introducing dominance relations into stochastic optimization problems as constraints. In the discrete case, stochastic optimization models involving second order stochastic dominance (SSD) constraints can be solved by linear programming (LP). However, problems involving first order stochastic dominance … Read more