Stochastic Programming

Time consistency and risk averse dynamic decision models: Definition, interpretation and practical consequences

  • Birgit Rudloff
  • Alexandre Street
  • Davi Valladão
    • Categories Finance and Economics, Stochastic Programming Tags , , , ,

    This paper aims at resolving a major obstacle to practical usage of time-consistent risk-averse decision models. The recursive objective function, generally used to ensure time consistency, is complex and has no clear/direct interpretation. Practitioners rather choose a simpler and more intuitive formulation, even though it may lead to a time inconsistent policy. Based on rigorous … Read more

    On the parallel solution of dense saddle-point linear systems arising in stochastic programming

  • Mihai Anitescu
  • Cosmin G. Petra
  • Miles Lubin
    • Categories Linear Programming, Parallel Algorithms, Stochastic Programming Tags , , ,

    We present a novel approach for solving dense saddle-point linear systems in a distributed-memory environment. This work is motivated by an application in stochastic optimization problems with recourse, but the proposed approach can be used for a large family of dense saddle-point systems, in particular those arising in convex programming. Although stochastic optimization problems have … Read more

    Construction of Risk-Averse Enhanced Index Funds

  • Miguel A. Lejeune
  • Gulay Samatli-Pac
    • Categories (Mixed) Integer Nonlinear Programming, Finance and Economics, Stochastic Programming Tags , , , ,

    We propose a partial replication strategy to construct risk-averse enhanced index funds. Our model takes into account the parameter estimation risk by defining the asset returns and the return covariance terms as random variables. The variance of the index fund return is forced to be below a low-risk threshold with a large probability, thereby limiting … Read more

    Stochastic Sequencing of Surgeries for a Single Surgeon Operating in Parallel Operating Rooms

  • Camilo Mancilla
  • Robert H. Storer
    • Categories Applications - OR and Management Sciences, Scheduling, Stochastic Programming Tags , ,

    We develop algorithms for a stochastic two-machine single-server sequencing problem with waiting time, idle time and overtime costs. Scheduling surgeries for a single surgeon operating in two parallel operating rooms (ORs) motivates the work. The basic idea is that staff perform cleanup and setup in one OR while the surgeon is operating in the other. … Read more

    Sampling-based decomposition methods for multistage stochastic programs based on extended polyhedral risk measures

  • Vincent Guigues
  • Werner Romisch
    • Categories Stochastic Programming

    We define a risk averse nonanticipative feasible policy for multistage stochastic programs and propose a methodology to implement it. The approach is based on dynamic programming equations written for a risk averse formulation of the problem. This formulation relies on a new class of multiperiod risk functionals called extended polyhedral risk measures. Dual representations of … Read more

    Robust and Stochastically Weighted Multi-Objective Optimization Models and Reformulations

  • Jian Hu
  • Sanjay Mehrotra
    • Categories Multi-Criteria Optimization, Robust Optimization, Stochastic Programming Tags , , ,

    In this paper we introduce robust and stochastically weighted sum approaches to deterministic and stochastic multi-objective optimization. The robust weighted sum approach minimizes the worst case weighted sum of objectives over a given weight region. We study the reformulations of the robust weighted sum problem under different definitions of deterministic weight regions. We next introduce … Read more

    The value of rolling horizon policies for risk-averse hydro-thermal planning

  • Vincent Guigues
  • Claudia Sagastizábal
    • Categories Applications - OR and Management Sciences, Robust Optimization, Stochastic Programming

    We consider the optimal management of a hydro-thermal power system in the mid and long terms. From the optimization point of view, this amounts to a large-scale multistage stochastic linear program, often solved by combining sampling with decomposition algorithms, like stochastic dual dynamic programming. Such methodologies, however, may entail prohibitive computational time, especially when applied … Read more

    On the Complexity of Non-Overlapping Multivariate Marginal Bounds for Probabilistic Combinatorial Optimization Problems

  • Xuan Vinh Doan
  • Karthik Natarajan
    • Categories Combinatorial Optimization, Stochastic Programming Tags , ,

    Given a combinatorial optimization problem with an arbitrary partition of the set of random objective coefficients, we evaluate the tightest possible bound on the expected optimal value for joint distributions consistent with the given multivariate marginals of the subsets in the partition. For univariate marginals, this bound was first proposed by Meilijson and Nadas (Journal … Read more

    Convex duality in stochastic programming and mathematical finance

  • Teemu Pennanen
    • Categories Convex and Nonsmooth Optimization, Finance and Economics, Stochastic Programming Tags , ,

    This paper proposes a general duality framework for the problem of minimizing a convex integral functional over a space of stochastic processes adapted to a given filtration. The framework unifies many well-known duality frameworks from operations research and mathematical finance. The unification allows the extension of some useful techniques from these two fields to a … Read more

    Inexact Bundle Methods for Two-Stage Stochastic Programming

  • Welington de Oliveira
  • Claudia Sagastizábal
  • Susana Scheimberg
    • Categories Nonlinear Optimization, Stochastic Programming Tags , ,

    Stochastic programming problems arise in many practical situations. In general, the deterministic equivalents of these problems can be very large and may not be solvable directly by general-purpose optimization approaches. For the particular case of two-stage stochastic programs, we consider decomposition approaches akin to a regularized L-shaped method that can handle inexactness in the subproblem … Read more