scenario generation

A Quasi-Newton Algorithm for Optimal Discretization of Markov Processes

  • Nils Löhndorf
  • David Wozabal
    • Categories Stochastic Programming Tags , , , , ,

    In stochastic programming and stochastic-dynamic programming discretization of random model parameters is often unavoidable. We propose a quasi-Newton learning algorithm to discretize multi-dimensional, continuous discrete-time Markov processes to scenario lattices by minimizing the Wasserstein distance between the unconditional distributions of process and lattice. Scenario lattices enable accurate discretization of the conditional distributions of Markov processes … Read more

    Scenario generation using historical data paths

  • Michal Kaut
    • Categories Stochastic Programming Tags ,

    In this paper, we present a method for generating scenarios by selection from historical data. We start with two models for a univariate single-period case and then extend the better-performing one to the case of selecting sequences of multivariate data. We then test the method on data series for wind- and solar-power generation in Scandinavia. … Read more

    Robust Optimal Discrete Arc Sizing for Tree-Shaped Potential Networks

  • Martin Robinius
  • Lars Schewe
  • Martin Schmidt
  • Johannes Thürauf
  • Detlef Stolten
  • Lara Welder
    • Categories (Mixed) Integer Linear Programming, Applications - Science and Engineering, Robust Optimization Tags , , , , ,

    We consider the problem of discrete arc sizing for tree-shaped potential networks with respect to infinitely many demand scenarios. This means that the arc sizes need to be feasible for an infinite set of scenarios. The problem can be seen as a strictly robust counterpart of a single-scenario network design problem, which is shown to … Read more

    Optimal scenario generation and reduction in stochastic programming

  • René Henrion
  • Werner Romisch
    • Categories Semi-infinite Programming, Stochastic Programming Tags , , ,

    Scenarios are indispensable ingredients for the numerical solution of stochastic optimization problems. Earlier approaches for optimal scenario generation and reduction are based on stability arguments involving distances of probability measures. In this paper we review those ideas and suggest to make use of stability estimates based on distances containing minimal information, i.e., on data appearing … Read more

    Forecast-based scenario-tree generation method

  • Michal Kaut
    • Categories Stochastic Programming Tags ,

    Sometimes, the best available information about an uncertain future is a single forecast. On the other hand, stochastic-programming models need future data in the form of scenario trees. While a single forecast does not provide enough information to construct a scenario tree, a forecast combined with historical data does—but none of the standard scenario-generation methods … Read more

    An empirical analysis of scenario generation methods for stochastic optimization

  • Nils Löhndorf
    • Categories Stochastic Programming Tags , , , , , , ,

    This work presents an empirical analysis of popular scenario generation methods for stochastic optimization, including quasi-Monte Carlo, moment matching, and methods based on probability metrics, as well as a new method referred to as Voronoi cell sampling. Solution quality is assessed by measuring the error that arises from using scenarios to solve a multi-dimensional newsvendor … Read more

    Generating moment matching scenarios using optimization techniques

  • Sanjay Mehrotra
  • Dávid Papp
    • Categories Stochastic Programming Tags , ,

    An optimization based method is proposed to generate moment matching scenarios for numerical integration and its use in stochastic programming. The main advantage of the method is its flexibility: it can generate scenarios matching any prescribed set of moments of the underlying distribution rather than matching all moments up to a certain order, and the … 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

    What Multistage Stochastic Programming Can Do for Network Revenue Management

  • Victor DeMiguel
  • Nishant Mishra
    • Categories Airline Optimization, Stochastic Programming Tags , ,

    Airlines must dynamically choose how to allocate their flight capacity to incoming travel demand. Because some passengers take connecting flights, the decisions for all network flights must be made simultaneously. To simplify the decision making process, most practitioners assume demand is deterministic and equal to average demand. We propose a multistage stochastic programming approach that … Read more