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Parallel Computing for Two-Stage Stochastic Infrastructure Planning

Published Online:1 Nov 2026https://doi.org/10.1287/educ.2026.0309
Acknowledgments

The authors thank Gurobi for providing licenses to the Gurobi Optimizer, used for this work. The authors also thank the volume editors and four reviewers of this tutorial for their feedback, which helped make this tutorial stronger. Artificial intelligence (AI) has not been used anywhere in the body text presented in this manuscript. AI was used, prompted by the authors, to create the diagrams and the code examples. The products were verified by the authors, who are solely responsible for their correctness.

Endnotes

1 Infrastructure planning problems for electrical power systems are commonly called CEP problems. To avoid confusion, we use “stochastic infrastructure planning problem” (SIPP) to refer to the generic problem and “CEP” only for the case of the electric grid.

2 Throughout this tutorial, we use bold letters to refer to vectors, capital letters to refer to matrices, and script capital letters (as well as Ω for scenarios) to refer to sets.

3 It is also possible to bundle scenarios together so that subproblems correspond to subsets of the uncertainty set, but this is out of scope for this tutorial; see, for example, Ryan et al. [63].

4 The package mpi-sppy requires Python but supports several modeling languages for providing the description of the optimization problem. The example presented in this tutorial was developed using Pyomo, which is required to reproduce the tests (or the reader will need to translate them to the supported language of their choice). We refer the reader to Bynum et al. [9] for guidance using Pyomo.

5 For reproducibility by the reader, note that the examples in this tutorial were developed and tested with Pyomo 6.10.2 and Gurobi 11.0.3. For an open-source solver alternative, HiGHS 1.14 (Huangfu and Hall [37]) was used (results not shown here). A released version of mpi-sppy > 0.13.1 (strictly above) should be used to ensure access to the examples of this tutorial. The relief examples directory in GitHub also includes shell scripts with the command-line instructions of each example presented here.

6 The examples here use the Gurobi solver, which is accessible to many researchers via academic licenses. For an open-source alternative, the reader may want to try HiGHS, CBC (COIN-OR Branch and Cut solver) or GLPK (GNU linear programming kit solver).

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