Asset management with modifications
This tutorial was generated using Literate.jl. Download the source as a .jl file. Download the source as a .ipynb file.
A modified version of the Asset Management Problem Taken from the book J.R. Birge, F. Louveaux, Introduction to Stochastic Programming, Springer Series in Operations Research and Financial Engineering, Springer New York, New York, NY, 2011
using SDDP, HiGHS, Test
function asset_management_stagewise(; cut_type)
w_s = [1.25, 1.06]
w_b = [1.14, 1.12]
Phi = [-1, 5]
Psi = [0.02, 0.0]
model = SDDP.MarkovianPolicyGraph(
sense = :Max,
transition_matrices = Array{Float64,2}[
[1.0]',
[0.5 0.5],
[0.5 0.5; 0.5 0.5],
[0.5 0.5; 0.5 0.5],
],
upper_bound = 1000.0,
optimizer = HiGHS.Optimizer,
) do subproblem, node
t, i = node
@variable(subproblem, xs >= 0, SDDP.State, initial_value = 0)
@variable(subproblem, xb >= 0, SDDP.State, initial_value = 0)
if t == 1
@constraint(subproblem, xs.out + xb.out == 55 + xs.in + xb.in)
@stageobjective(subproblem, 0)
elseif t == 2 || t == 3
@variable(subproblem, phi)
@constraint(
subproblem,
w_s[i] * xs.in + w_b[i] * xb.in + phi == xs.out + xb.out
)
SDDP.parameterize(subproblem, [1, 2], [0.6, 0.4]) do ω
JuMP.fix(phi, Phi[ω])
@stageobjective(subproblem, Psi[ω] * xs.out)
end
else
@variable(subproblem, u >= 0)
@variable(subproblem, v >= 0)
@constraint(
subproblem,
w_s[i] * xs.in + w_b[i] * xb.in + u - v == 80,
)
@stageobjective(subproblem, -4u + v)
end
end
SDDP.train(
model;
cut_type = cut_type,
log_frequency = 10,
risk_measure = (node) -> begin
if node[1] != 3
SDDP.Expectation()
else
SDDP.EAVaR(lambda = 0.5, beta = 0.5)
end
end,
)
@test SDDP.calculate_bound(model) ≈ 1.278 atol = 1e-3
return
end
asset_management_stagewise(cut_type = SDDP.SINGLE_CUT)
asset_management_stagewise(cut_type = SDDP.MULTI_CUT)-------------------------------------------------------------------
SDDP.jl (c) Oscar Dowson and contributors, 2017-23
-------------------------------------------------------------------
problem
nodes : 7
state variables : 2
scenarios : 3.20000e+01
existing cuts : false
options
solver : serial mode
risk measure : #4
sampling scheme : SDDP.InSampleMonteCarlo
subproblem structure
VariableRef : [5, 7]
AffExpr in MOI.EqualTo{Float64} : [1, 1]
VariableRef in MOI.GreaterThan{Float64} : [2, 5]
VariableRef in MOI.LessThan{Float64} : [1, 1]
numerical stability report
matrix range [1e+00, 1e+00]
objective range [2e-02, 4e+00]
bounds range [1e+03, 1e+03]
rhs range [6e+01, 8e+01]
-------------------------------------------------------------------
iteration simulation bound time (s) solves pid
-------------------------------------------------------------------
10 4.375000e+00 6.798204e+00 1.585679e-01 278 1
20 1.230957e+01 1.358825e+00 1.765730e-01 428 1
30 8.859026e+00 1.278410e+00 2.106240e-01 706 1
40 -2.315795e+01 1.278410e+00 2.374361e-01 856 1
49 3.014193e+01 1.278410e+00 2.627370e-01 991 1
-------------------------------------------------------------------
status : simulation_stopping
total time (s) : 2.627370e-01
total solves : 991
best bound : 1.278410e+00
simulation ci : -1.755629e+00 ± 5.526921e+00
numeric issues : 0
-------------------------------------------------------------------
-------------------------------------------------------------------
SDDP.jl (c) Oscar Dowson and contributors, 2017-23
-------------------------------------------------------------------
problem
nodes : 7
state variables : 2
scenarios : 3.20000e+01
existing cuts : false
options
solver : serial mode
risk measure : #4
sampling scheme : SDDP.InSampleMonteCarlo
subproblem structure
VariableRef : [5, 7]
AffExpr in MOI.EqualTo{Float64} : [1, 1]
VariableRef in MOI.GreaterThan{Float64} : [2, 5]
VariableRef in MOI.LessThan{Float64} : [1, 1]
numerical stability report
matrix range [1e+00, 1e+00]
objective range [2e-02, 4e+00]
bounds range [1e+03, 1e+03]
rhs range [6e+01, 8e+01]
-------------------------------------------------------------------
iteration simulation bound time (s) solves pid
-------------------------------------------------------------------
10 -2.454000e+00 1.647363e+00 3.884983e-02 278 1
20 -3.575118e+00 1.278410e+00 6.837082e-02 428 1
30 -5.003795e+01 1.278410e+00 1.220548e-01 706 1
40 6.835609e+00 1.278410e+00 1.679418e-01 856 1
-------------------------------------------------------------------
status : simulation_stopping
total time (s) : 1.679418e-01
total solves : 856
best bound : 1.278410e+00
simulation ci : 4.369345e+00 ± 4.780393e+00
numeric issues : 0
-------------------------------------------------------------------