Introduction

Welcome to SDDP.jl, a package for solving large convex multistage stochastic programming problems using stochastic dual dynamic programming.

SDDP.jl is built on JuMP, so it supports a number of open-source and commercial solvers, making it a powerful and flexible tool for stochastic optimization.

The implementation of the stochastic dual dynamic programming algorithm in SDDP.jl is state of the art, and it includes support for a number of advanced features not commonly found in other implementations. This includes support for:

• infinite horizon problems
• convex risk measures
• mixed-integer state and control variables
• partially observable stochastic processes.

Installation

Install SDDP.jl as follows:

julia> import Pkg

julia> Pkg.add("SDDP")

License

SDDP.jl is licensed under the MPL 2.0 license.

Resources for getting started

There are a few ways to get started with SDDP.jl:

• Become familiar with JuMP by reading the JuMP documentation
• Read the introductory tutorial An introduction to SDDP.jl
• Browse some of the examples, such as Example: deterministic to stochastic

Getting help

If you need help, please open a GitHub issue.

How the documentation is structured

Having a high-level overview of how this documentation is structured will help you know where to look for certain things.

• Tutorials contains step-by-step explanations of how to use SDDP.jl. Once you've got SDDP.jl installed, start by reading An introduction to SDDP.jl.

• Guides contains "how-to" snippets that demonstrate specific topics within SDDP.jl. A good one to get started on is Debug a model.

• Explanation contains step-by-step explanations of the theory and algorithms that underpin SDDP.jl. If you want a basic understanding of the algorithm behind SDDP.jl, start with Introductory theory.

• Examples contain worked examples of various problems solved using SDDP.jl. A good one to get started on is the Hydro-thermal scheduling problem. In particular, it shows how to solve an infinite horizon problem.

• The API Reference contains a complete list of the functions you can use in SDDP.jl. Look here if you want to know how to use a particular function.

Citing SDDP.jl

If you use SDDP.jl, we ask that you please cite the following:

@article{dowson_sddp.jl,
	title = {{SDDP}.jl: a {Julia} package for stochastic dual dynamic programming},
	journal = {INFORMS Journal on Computing},
	author = {Dowson, O. and Kapelevich, L.},
	doi = {https://doi.org/10.1287/ijoc.2020.0987},
	year = {2021},
	volume = {33},
	issue = {1},
	pages = {27-33},
}

Here is an earlier preprint.

If you use the infinite horizon functionality, we ask that you please cite the following:

@article{dowson_policy_graph,
	title = {The policy graph decomposition of multistage stochastic optimization problems},
	doi = {https://doi.org/10.1002/net.21932},
	journal = {Networks},
	author = {Dowson, O.},
	volume = {76},
	issue = {1},
	pages = {3-23},
	year = {2020}
}

Here is an earlier preprint.

If you use the partially observable functionality, we ask that you please cite the following:

@article{dowson_pomsp,
	title = {Partially observable multistage stochastic programming},
	doi = {https://doi.org/10.1016/j.orl.2020.06.005},
	journal = {Operations Research Letters},
	author = {Dowson, O. and Morton, D.P. and Pagnoncelli, B.K.},
	volume = {48},
	issue = {4},
	pages = {505-512},
	year = {2020}
}

Here is an earlier preprint.

If you use the objective state functionality, we ask that you please cite the following:

@article{downward_objective,
	title = {Stochastic dual dynamic programming with stagewise-dependent objective uncertainty},
	doi = {https://doi.org/10.1016/j.orl.2019.11.002},
	journal = {Operations Research Letters},
	author = {Downward, A. and Dowson, O. and Baucke, R.},
	volume = {48},
	issue = {1},
	pages = {33-39},
	year = {2020}
}

Here is an earlier preprint.

If you use the entropic risk measure, we ask that you please cite the following:

@article{dowson_entropic,
	title = {Incorporating convex risk measures into multistage stochastic programming algorithms},
	doi = {https://doi.org/10.1007/s10479-022-04977-w},
	journal = {Annals of Operations Research},
	author = {Dowson, O. and Morton, D.P. and Pagnoncelli, B.K.},
	year = {2022},
}

Here is an earlier preprint.