Andrew B. Philpott

Sample Average Approximation and Model Predictive Control for Multistage Stochastic Optimization

  • Dominic S. T. Keehan
  • Andrew B. Philpott
  • Edward Anderson
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    Sample average approximation-based stochastic dynamic programming and model predictive control are two different methods of approaching multistage stochastic optimization. Model predictive control—despite a lack of theoretical backing—is often used instead of stochastic dynamic programming due to computational necessity. For settings where the stage reward is a convex function of the random terms, the stage dynamics … Read more

    Sample average approximation and model predictive control for inventory optimization

  • Dominic S. T. Keehan
  • Andrew B. Philpott
  • Edward Anderson
    • Categories Dynamic Programming, Stochastic Programming Tags , , ,

    We study multistage stochastic optimization problems using sample average approximation (SAA) and model predictive control (MPC) as solution approaches. MPC is frequently employed when the size of the problem renders stochastic dynamic programming intractable, but it is unclear how this choice affects out-of-sample performance. To compare SAA and MPC out-of-sample, we formulate and solve an … Read more

    JuDGE.jl: a Julia package for optimizing capacity expansion

  • Regan Baucke
  • Anthony Downward
  • Andrew B. Philpott
    • Categories Applications - OR and Management Sciences, Optimization Software and Modeling Systems, Stochastic Programming Tags , , , ,

    We present JuDGE.jl, an open-source Julia package for solving multistage stochastic capacity expansion problems using Dantzig-Wolfe decomposition. Models for JuDGE.jl are built using JuMP, the algebraic modelling language in Julia, and solved by repeatedly applying mixed-integer programming. We illustrate JuDGE.jl by formulating and solving a toy knapsack problem, and demonstrate the performance of JuDGE.jl on … Read more

    Improving sample average approximation using distributional robustness

  • Edward Anderson
  • Andrew B. Philpott
    • Categories Stochastic Programming Tags , ,

    We consider stochastic optimization problems in which we aim to minimize the expected value of an objective function with respect to an unknown distribution of random parameters. We analyse the out-of-sample performance of solutions obtained by solving a distributionally robust version of the sample average approximation problem for unconstrained quadratic problems, and derive conditions under … Read more

    Robust sample average approximation with small sample sizes

  • Edward Anderson
  • Andrew B. Philpott
    • Categories Robust Optimization, Stochastic Programming

    We consider solving stochastic optimization problems in which we seek to minimize the expected value of an objective function with respect to an unknown distribution of random parameters. Our focus is on models that use sample average approximation (SAA) with small sample sizes. We analyse the out-of-sample performance of solutions obtained by solving a robust … Read more

    Dynamic Risked Equilibrium

  • Michael C. Ferris
  • Andrew B. Philpott
    • Categories Game Theory, Stochastic Programming Tags , , ,

    We revisit the correspondence of competitive partial equilibrium with a social optimum in markets where risk-averse agents solve multistage stochastic optimization problems formulated in scenario trees. The agents trade a commodity that is produced from an uncertain supply of resources which can be stored. The agents can also trade risk using Arrow-Debreu securities. In this … Read more

    Payment Mechanisms for Electricity Markets with Uncertain Supply

  • Ryan Cory-Wright
  • Andrew B. Philpott
  • Golbon Zakeri
    • Categories Finance and Economics, Game Theory, Stochastic Programming Tags , , ,

    This paper provides a framework for deriving payment mechanisms for intermittent, flexible and inflexible electricity generators who are dispatched according to the optimal solution of a stochastic program that minimizes the expected cost of generation plus deviation. The first stage corresponds to a pre-commitment decision, and the second stage corresponds to real-time generation that adapts … Read more

    MIDAS: A Mixed Integer Dynamic Approximation Scheme

  • Joseph Frédéric Bonnans
  • Andrew B. Philpott
  • Faisal Wahid
    • Categories Dynamic Programming, Stochastic Programming Tags ,

    Mixed Integer Dynamic Approximation Scheme (MIDAS) is a new sampling-based algorithm for solving finite-horizon stochastic dynamic programs with monotonic Bellman functions. MIDAS approximates these value functions using step functions, leading to stage problems that are mixed integer programs. We provide a general description of MIDAS, and prove its almost-sure convergence to an epsilon-optimal policy when … Read more

    Optimization of Demand Response Through Peak Shaving

  • D. Craigie
  • Michael J. Todd
  • Andrew B. Philpott
  • Golbon Zakeri
    • Categories Applications - OR and Management Sciences, Linear Programming Tags , ,

    We consider a model in which a consumer of a resource over several periods must pay a per unit charge for the resource as well as a peak charge. The consumer has the ability to reduce his consumption in any period at some given cost, subject to a constraint on the total amount of reduction … Read more

    On solving multistage stochastic programs with coherent risk measures

  • Vitor de Matos
  • Erlon Finardi
  • Andrew B. Philpott
    • Categories Stochastic Programming Tags

    We consider a class of multistage stochastic linear programs in which at each stage a coherent risk measure of future costs is to be minimized. A general computational approach based on dynamic programming is derived that can be shown to converge to an optimal policy. By computing an inner approximation to future cost functions, we … Read more