JuDGE.jl: a Julia package for optimizing capacity expansion

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

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

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

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

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

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

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

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

Improving the Performance of Stochastic Dual Dynamic Programming

This paper is concerned with tuning the Stochastic Dual Dynamic Programming algorithm to make it more computationally efficient. We report the results of some computational experiments on a large-scale hydrothermal scheduling model developed for Brazil. We find that the best improvements in computation time are obtained from an implementation that increases the number of scenarios … Read more

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

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