Stochastic Programming

Joint dynamic probabilistic constraints with projected linear decision rules

  • Vincent Guigues
  • René Henrion
    • Categories Stochastic Programming

    We consider multistage stochastic linear optimization problems combining joint dynamic probabilistic constraints with hard constraints. We develop a method for projecting decision rules onto hard constraints of wait-and-see type. We establish the relation between the original (infinite dimensional) problem and approximating problems working with projections from different subclasses of decision policies. Considering the subclass of … Read more

    Multistep stochastic mirror descent for risk-averse convex stochastic programs based on extended polyhedral risk measures

  • Vincent Guigues
    • Categories Nonlinear Optimization, Stochastic Programming Tags , , ,

    We consider risk-averse convex stochastic programs expressed in terms of extended polyhedral risk measures. We derive computable confidence intervals on the optimal value of such stochastic programs using the Robust Stochastic Approximation and the Stochastic Mirror Descent (SMD) algorithms. When the objective functions are uniformly convex, we also propose a multistep extension of the Stochastic … Read more

    On the Number of Stages in Multistage Stochastic Programs

  • Giovanni Pantuso
    • Categories Stochastic Programming Tags , ,

    Multistage stochastic programs are a viable modeling tool for sequential decisions conditional on information revealed at different points in time (stages). However, as the number of stages increases their applicability is soon halted by the curse of dimensionality. A typical, sometimes forced, alternative is to approximate stages by their expected values thus considering fewer stages … Read more

    A characterization of Nash equilibrium for the games with random payoffs

  • Abdel Lisser
  • Vikas Vikram Singh
    • Categories Game Theory, Stochastic Programming Tags , , , , ,

    We consider a two player bimatrix game where the entries of the payoff matrices are random variables. We formulate this problem as a chance-constrained game by considering that the payoff of each player is defined using a chance constraint. We consider the case where the entries of the payoff matrices are independent normal/Cauchy random variables. … Read more

    PIPS-SBB: A parallel distributed-memory branch-and-bound algorithm for stochastic mixed-integer programs

  • Lluís-Miquel Munguía
  • Deepak Rajan
  • Geoffrey Oxberry
    • Categories (Mixed) Integer Linear Programming, Parallel Algorithms, Stochastic Programming Tags , ,

    Stochastic mixed-integer programs (SMIPs) deal with optimization under uncertainty at many levels of the decision-making process. When solved as extensive formulation mixed- integer programs, problem instances can exceed available memory on a single workstation. To overcome this limitation, we present PIPS-SBB: a distributed-memory parallel stochastic MIP solver that takes advantage of parallelism at multiple levels … Read more

    Bulk Ship Fleet Renewal and Deployment under Uncertainty: A Multi-Stage Stochastic Programming Approach

  • Ayse Nur Arslan
  • Dimitri J. Papageorgiou
    • Categories Stochastic Programming, Supply Chain Management, Transportation Tags , , , , ,

    We study a maritime fleet renewal and deployment problem under demand and charter cost uncertainty. A decision-maker for an industrial bulk shipping company must determine a suitable fleet size, mix, and deployment strategy to satisfy stochastic demand over a given planning horizon. She may acquire vessels in two ways: time chartering and voyage chartering. Time … Read more

    Data-Driven Inverse Optimization with Imperfect Information

  • Grani A. Hanasusanto
  • Daniel Kuhn
  • Peyman Mohajerin Esfahani
  • Soroosh Shafieezadeh-Abadeh
    • Categories Linear, Cone and Semidefinite Programming, Robust Optimization, Stochastic Programming Tags , ,

    In data-driven inverse optimization an observer aims to learn the preferences of an agent who solves a parametric optimization problem depending on an exogenous signal. Thus, the observer seeks the agent’s objective function that best explains a historical sequence of signals and corresponding optimal actions. We focus here on situations where the observer has imperfect … Read more

    Distributionally Robust Stochastic Programming

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

    In this paper we study distributionally robust stochastic programming in a setting where there is a specified reference probability measure and the uncertainty set of probability measures consists of measures in some sense close to the reference measure. We discuss law invariance of the associated worst case functional and consider two basic constructions of such … Read more

    Distributionally robust inventory control when demand is a martingale

  • David A. Goldberg
  • Linwei Xin
    • Categories Applications - OR and Management Sciences, Robust Optimization, Stochastic Programming Tags , , , , ,

    Demand forecasting plays an important role in many inventory control problems. To mitigate the potential harms of model misspecification in this context, various forms of distributionally robust optimization have been applied. Although many of these methodologies suffer from the problem of time-inconsistency, the work of Klabjan, Simchi-Levi and Song [85] established a general time-consistent framework … Read more

    Branch and Price for Chance Constrained Bin Packing

  • Brian T. Denton
  • Xiaolan Xie
  • Z. Zhang
    • Categories Applications - OR and Management Sciences, Stochastic Programming

    This article considers two versions of the stochastic bin packing problem with chance constraints. In the first version, we formulate the problem as a two-stage stochastic integer program that considers item-to-bin allocation decisions in the context of chance constraints on total item size within the bins. Next, we describe a distributionally robust formulation of the … Read more