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_2021_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.

Policy graphs

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

@article{dowson_2020_policy_graph,
	title   = {The policy graph decomposition of multistage stochastic optimization problems},
	journal = {Networks},
	author  = {Dowson, O.},
	doi     = {https://doi.org/10.1002/net.21932},
	year    = {2020},
	volume  = {76},
	issue   = {1},
	pages   = {3-23}
}

Here is an earlier preprint.

Partially observable

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

@article{dowson_2020_pomsp,
	title   = {Partially observable multistage stochastic programming},
	journal = {Operations Research Letters},
	author  = {Dowson, O. and Morton, D.P. and Pagnoncelli, B.K.},
	doi     = {https://doi.org/10.1016/j.orl.2020.06.005},
	year    = {2020},
	volume  = {48},
	issue   = {4},
	pages   = {505-512}
}

Here is an earlier preprint.

Objective states

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

@article{downward_2020_objective,
	title   = {Stochastic dual dynamic programming with stagewise-dependent objective uncertainty},
	journal = {Operations Research Letters},
	author  = {Downward, A. and Dowson, O. and Baucke, R.},
	doi     = {https://doi.org/10.1016/j.orl.2019.11.002},
	year    = {2020},
	volume  = {48},
	issue   = {1},
	pages   = {33-39}
}

Here is an earlier preprint.

Entropic

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

@article{dowson_2022_entropic,
	title   = {Incorporating convex risk measures into multistage stochastic programming algorithms},
	journal = {Annals of Operations Research},
	author  = {Dowson, O. and Morton, D.P. and Pagnoncelli, B.K.},
	doi     = {https://doi.org/10.1007/s10479-022-04977-w},
	year    = {2022},
}

Here is an earlier preprint.

Bi-objective

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

@article{dowson_2022_biobjective,
	title   = {Bi-objective multistage stochastic linear programming},
	journal = {Mathematical Programming},
	author  = {Dowson, O. and Morton, D.P. and Downward, A.},
	doi     = {https://doi.org/10.1007/s10107-022-01872-x},
	year    = {2022},
	volume  = {196},
	pages   = {907–933}
}

Here is an earlier preprint.