Here and now solution

[hghayoom]

Hi Oscar,
I hope you are doing well.
I am working on a Here and now problem. I had a course that taught me "Hare and now Problem has only one solution". ( I am not sure if it is exactly correct??).
To validate that I used your example Here. Then I drew the diagrams for the code and I expected to see a line in the graphs because the answers should be the same for all simulations. I get bounds in all my variables. Could you please clarify it for me? This is the Picture I get.

Here is the Code:

using SDDP,Plots , Plots.PlotMeasures,Gurobi
import HiGHS
import Distributions
decision_hazard_2 = SDDP.LinearPolicyGraph(
    stages = 5,  # <-- changed
    sense = :Min,
    lower_bound = 0.0,
    optimizer = HiGHS.Optimizer,
) do sp, node
    @variables(sp, begin
        0 <= x_storage <= 8, (SDDP.State, initial_value = 6)
        u_thermal >= 0, (SDDP.State, initial_value = 0)
        u_hydro >= 0
        u_unmet_demand >= 0
    end)
    if node == 1                                        # <-- new
        @constraint(sp, x_storage.out == x_storage.in)  # <-- new
        @stageobjective(sp, 0)                          # <-- new
    else
        @constraint(sp, u_thermal.in + u_hydro == 9 - u_unmet_demand)
        @constraint(sp, c_balance, x_storage.out == x_storage.in - u_hydro + 0)
        SDDP.parameterize(sp, [2, 3]) do ω
            return set_normalized_rhs(c_balance, ω)
        end
        @stageobjective(sp, 500 * u_unmet_demand + 20 * u_thermal.in)
    end
end

SDDP.train(decision_hazard_2; iteration_limit = 100)
simulations = SDDP.simulate(
    # The trained model to simulate.
    decision_hazard_2,
    # The number of replications.
    100,
    # A list of names to record the values of.
    sampling_scheme = SDDP.InSampleMonteCarlo(
            terminate_on_cycle = false,
            terminate_on_dummy_leaf = true,
    ),
    [:x_storage,:u_thermal,:u_hydro,:u_unmet_demand,],
)

Plots.plot(
    SDDP.publication_plot(simulations, title = "x_storage") do data
        return data[:x_storage].in
    end,
    SDDP.publication_plot(simulations, title = "u_thermal") do data
        return data[:u_thermal].out
    end,
    SDDP.publication_plot(simulations, title = "u_hydro") do data
        return data[:u_hydro]
    end,
    SDDP.publication_plot(simulations, title = "u_unmet_demand") do data
        return data[:u_unmet_demand]
    end,
   
    ;
    margin=20mm,
    left_margin=100mm,
    guidefontsize=100,
    xtickfontsize=60,
    ytickfontsize=60,
    xticks = 0:5:52,
    titlefontsize=100,
    xlabel = "Stage",
    ylims = (0,10),
    layout = (1, 4),
    size = (5000, 1000),
)
Plots.savefig("HereNow.pdf")

Your insights are appreciated.
Thanks,
Hadi

[Oscar Dowson]

Your model looks correct.

I had a course that taught me "Here and now Problem has only one solution". ( I am not sure if it is exactly correct??)

This isn't true in multistage. Here-and-now just means that you choose the value of a control in period t-1 but use it in period t. It's not the case that the control needs to be the same in every time period (that's a different model again).

I don't find the literature on stochastic programming helpful. Just try to model your problem as the agent would make decisions, and ignore the theory around hazard-decision/wait-and-see/non-anticipativity.

What decisions does an agent make? When do they make those decisions? What information do they have available to them?

I expected to see a line in the graphs because the answers should be the same for all simulations

This is not what you should expect. See previous answer.

Instead of

SDDP.publication_plot(simulations, title = "u_thermal") do data
    return data[:u_thermal].out
end

you probably want

SDDP.publication_plot(simulations, title = "u_thermal") do data
    return data[:u_thermal].in
end

So that the plot is showing the quantity of thermal used in period t, not the quantity that was decided in period t for use in period t+1.

[hghayoom]

Hi Oscar,
Thanks for the illustration.
Now it is clear to me what happens in multistage or how to model it.
I think in a classic two-stage stochastic problem because we only have two stages, here and now problems have only one solution. but in multistage it is not essentially correct.

Thanks,
Hadi

[Oscar Dowson]

here and now problems have only one solution

I still dislike this idea.

You could have a problem where some of the controls are chosen in the previous step and some aren't. For example, maybe you need to choose your coal generation in t-1, but you can choose OCGT generation in stage t. Is that a here-and-now or wait-and-see problem?

I find it better to just ignore the labels. Everything is a graph and you can make some variables "here-and-now" with an explicit modeling choice.

[hghayoom]

Dear Oscar
You are correct. and I learned a lot.
Thanks for illustrating everything.

[Oscar Dowson]

No problem. Closing because this seems resolved.