Stochastic Programming

An Alternating Direction Method for Chance-Constrained Optimization Problems with Discrete Distributions

  • Xiaodi Bai
  • Jie Sun
  • Xiaoling Sun
  • Xiaojin Zheng
    • Categories (Mixed) Integer Nonlinear Programming, Nonlinear Optimization, Stochastic Programming

    We consider a chance-constrained optimization problem (CCOP), where the random variables follow finite discrete distributions. The problem is in general nonconvex and can be reformulated as a mixed-integer program. By exploiting the special structure of the probabilistic constraint, we propose an alternating direction method for finding suboptimal solutions of CCOP. At each iteration, this method … Read more

    On the convergence of decomposition methods for multi-stage stochastic convex programs

  • Pierre Girardeau
  • Vincent Leclère
  • Andrew B. Philpott
    • Categories Convex Optimization, Dynamic Programming, Stochastic Programming Tags , , , ,

    We prove the almost-sure convergence of a class of sampling-based nested decomposition algorithms for multistage stochastic convex programs in which the stage costs are general convex functions of the decisions, and uncertainty is modelled by a scenario tree. As special cases, our results imply the almost-sure convergence of SDDP, CUPPS and DOASA when applied to … Read more

    Optimization with multivariate conditional value-at-risk constraints

  • Nilay Noyan
  • Gabor Rudolf
    • Categories Applications - OR and Management Sciences, Multi-Criteria Optimization, Stochastic Programming

    For many decision making problems under uncertainty, it is crucial to develop risk-averse models and specify the decision makers’ risk preferences based on multiple stochastic performance measures (or criteria). Incorporating such multivariate preference rules into optimization models is a fairly recent research area. Existing studies focus on extending univariate stochastic dominance rules to the multivariate … Read more

    Stochastic integer programming based algorithms for adaptable open block surgery scheduling

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

    We develop algorithms for adaptable schedule problems with patient waiting time, surgeon waiting time, OR idle time and overtime costs. Open block surgery scheduling of multiple surgeons operating in multiple operating rooms (ORs) motivates the work. We investigate creating an “adaptable” schedule of surgeries under knowledge that this schedule will change (be rescheduled) during execution … Read more

    Consistency of sample estimates of risk averse stochastic programs

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

    In this paper we study asymptotic consistency of law invariant convex risk measures and the corresponding risk averse stochastic programming problems for independent identically distributed data. Under mild regularity conditions we prove a Law of Large Numbers and epiconvergence of the corresponding statistical estimators. This can be applied in a straight forward way to establishing … Read more

    Parallel distributed-memory simplex for large-scale stochastic LP problems

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

    We present a parallelization of the revised simplex method for large extensive forms of two-stage stochastic linear programming (LP) problems. These problems have been considered too large to solve with the simplex method; instead, decomposition approaches based on Benders decomposition or, more recently, interior-point methods are generally used. However, these approaches do not provide optimal … Read more

    Complexity of Bilevel Coherent Risk Programming

  • Jonathan Eckstein
    • Categories Stochastic Programming Tags , ,

    This paper considers a bilevel programming approach to applying coherent risk measures to extended two-stage stochastic programming problems. This formulation technique avoids the time-inconsistency issues plaguing naive models and the incomposability issues which cause time-consistent formulations to have complicated, hard-to-explain objective functions. Unfortunately, the analysis here shows that such bilevel formulations, when using the standard … Read more

    The optimal harvesting problem under risk aversion

  • Bernardo K. Pagnoncelli
  • Adriana Piazza
    • Categories Applications - OR and Management Sciences, Stochastic Programming Tags , , ,

    We study the exploitation of a one species forest plantation when timber price is uncertain. The work focuses on providing optimality conditions for the optimal harvesting policy in terms of the parameters of the price process and the discount factor. We use risk averse stochastic dynamic programming and use the Conditional Value-at-Risk (CVaR) as our … Read more

    Risk-Averse Control of Undiscounted Transient Markov Models

  • Özlem Cavus
  • Andrzej Ruszczyński
    • Categories Dynamic Programming, Stochastic Programming

    We use Markov risk measures to formulate a risk-averse version of the undiscounted total cost problem for a transient controlled Markov process. We derive risk-averse dynamic programming equations and we show that a randomized policy may be strictly better than deterministic policies, when risk measures are employed. We illustrate the results on an optimal stopping … Read more

    Stochastic Optimization Approach to Water Management in Cooling-Constrained Power Plants

  • Emil M. Constantinescu
  • Victor M. Zavala
  • Urmila Diwekar
  • Juan M. Salazar
    • Categories Applications - OR and Management Sciences, Constrained Nonlinear Optimization, Stochastic Programming

    We propose a stochastic optimization framework to perform water management in coolingconstrained power plants. The approach determines optimal set-points to maximize power output in the presence of uncertain weather conditions and water intake constraints. Weather uncertainty is quantified in the form of ensembles using the state-of-the-art numerical weather prediction model WRF. The framework enables us … Read more