stochastic programming

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 Decision Rule Approach to Optimization under Uncertainty: Methodology and Applications

  • Angelos Georghiou
  • Daniel Kuhn
  • Wolfram Wiesemann
    • Categories Applications - OR and Management Sciences, Robust Optimization Tags , , ,

    Dynamic decision-making under uncertainty has a long and distinguished history in operations research. Due to the curse of dimensionality, solution schemes that naively partition or discretize the support of the random problem parameters are limited to small and medium-sized problems, or they require restrictive modeling assumptions (e.g., absence of recourse actions). In the last few … Read more

    Optimizing Trading Decisions for Hydro Storage Systems using Approximate Dual Dynamic Programming

  • Nils Löhndorf
  • David Wozabal
  • Stefan Minner
    • Categories Applications - OR and Management Sciences, Dynamic Programming, Stochastic Programming Tags , , ,

    We propose a new approach to optimize operations of hydro storage systems with multiple connected reservoirs which participate in wholesale electricity markets. Our formulation integrates short-term intraday with long-term interday decisions. The intraday problem considers bidding decisions as well as storage operation during the day and is formulated as a stochastic program. The interday problem … Read more

    Higher-Order Confidence Intervals for Stochastic Programming using Bootstrapping

  • Mihai Anitescu
  • Cosmin G. Petra
    • Categories Constrained Nonlinear Optimization, Stochastic Programming Tags , ,

    We study the problem of constructing confidence intervals for the optimal value of a stochastic programming problem by using bootstrapping. Bootstrapping is a resampling method used in the statistical inference of unknown parameters for which only a small number of samples can be obtained. One such parameter is the optimal value of a stochastic optimization … Read more

    Stochastic approaches for solving Rapid Transit Network Design models with random demand

  • Gemayqzel Bouza
  • Ángel Marín
    • Categories Civil and Environmental Engineering, Stochastic Programming, Transportation Tags , , ,

    We address rapid transit network design problems characterized by uncertainty in the input data. Network design has a determinant impact on the future e ective- ness of the system. Design decisions are made with a great degree of uncertainty about the conditions under which the system will be required to operate. The de- mand is one … Read more

    A copula-based heuristic for scenario generation

  • Michal Kaut
    • Categories Stochastic Programming Tags , ,

    This paper presents a new heuristic for generating scenarios for two-stage stochastic programs. The method uses copulas to describe the dependence between the marginal distributions, instead of the more common correlations. The heuristic is then tested on a simple portfolio-selection model, and compared to two other scenario-generation methods. Citation Published in Computational Management Science, 11 … Read more

    Probabilistic Set Covering with Correlations

  • Shabbir Ahmed
  • Dimitri J. Papageorgiou
    • Categories Integer Programming, Stochastic Programming Tags , , , ,

    We consider a probabilistic set covering problem where there is uncertainty regarding whether a selected set can cover an item, and the objective is to determine a minimum-cost combination of sets so that each item is covered with a pre-specified probability. To date, literature on this problem has focused on the special case in which … Read more

    Implementing the simplex method as a cutting-plane method

  • Krisztian Eretnek
  • Csaba I. Fábián
  • Olga Papp
    • Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming Tags , , , ,

    We show that the simplex method can be interpreted as a cutting-plane method, assumed that a special pricing rule is used. This approach is motivated by the recent success of the cutting-plane method in the solution of special stochastic programming problems. We compare the classic Dantzig pricing rule and the rule that derives from the … Read more

    A Branch-and-Cut Decomposition Algorithm for Solving Chance-Constrained Mathematical Programs with Finite Support

  • James R. Luedtke
    • Categories Stochastic Programming Tags , , , ,

    We present a new approach for exactly solving chance-constrained mathematical programs having discrete distributions with nite support and random polyhedral constraints. Such problems have been notoriously difficult to solve due to nonconvexity of the feasible region, and most available methods are only able to nd provably good solutions in certain very special cases. Our approach … Read more

    Stochastic programs without duality gaps

  • Teemu Pennanen
  • Ari-Pekka Perkkiö
    • Categories Stochastic Programming Tags , ,

    This paper studies dynamic stochastic optimization problems parametrized by a random variable. Such problems arise in many applications in operations research and mathematical finance. We give sufficient conditions for the existence of solutions and the absence of a duality gap. Our proof uses extended dynamic programming equations, whose validity is established under new relaxed conditions … Read more