Update air conditioning example

[Thuener]

Closes #798

• Add reference to Birge and Louveaux
• Show the optimal values and test them

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 93.54%. Comparing base (b4c0a25) to head (27be7d3).

Additional details and impacted files

@@           Coverage Diff           @@
##           master     #801   +/-   ##
=======================================
  Coverage   93.54%   93.54%           
=======================================
  Files          26       26           
  Lines        3519     3519           
=======================================
  Hits         3292     3292           
  Misses        227      227           

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[Thuener]

@odow how do you do format checks locally?

[odow]

SDDP.jl/.github/workflows/format_check.yml

Lines 23 to 27 in b4c0a25

	using JuliaFormatter
	format("docs"; verbose = true)
	format("benchmarks"; verbose = true)
	format("src"; verbose = true)
	format("test"; verbose = true)

[odow]

But I assumed @bernardokp wanted the examples fleshed out into proper literate tutorials (like the JuMP ones), not just some extra prints added.

[bernardokp]

Yeah, that would be ideal.

[Thuener]

Like this https://jump.dev/JuMP.jl/stable/tutorials/linear/diet/?

[bernardokp]

I mean, that would be a luxury!!!

[Thuener]

That will take some time. I taught it was just an small change, I don't have this time to spare right now.

[odow]

That will take some time

That's why I haven't done it 😄

[Thuener]

I'm not crazy, I asked before creating the PR 😅

[Thuener]

If the goal is to create a tutorial, I can't promise anything now. @bernardokp you can help create the text? At least give me an initial version, I will extend it and create the code for it.

[bernardokp]

I certainly can help. As a matter of fact, it would be nice if we could create sort of a procedure to do it because I will probably create more examples in the very near future.

[bernardokp]

Is that what you want, @Thuener ?

The air conditioning example first appeared in the book Introduction to Stochastic Programming, by Birge and Louveaux, 1997, Springer-Verlag, New York. It is on page 237, example 1. For a rescaled problem, they report an optimal first-stage solution of $x^1 = 2$, which corresponds to production in the model, and $y^1 = 1$, which corresponds to stored_production.out in the model. Finally, they report an optimal value of 6.25.