Asset management with modifications
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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, Testfunction 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 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 returnendasset_management_stagewise(; cut_type = SDDP.SINGLE_CUT)asset_management_stagewise(; cut_type = SDDP.MULTI_CUT)-------------------------------------------------------------------
SDDP.jl (c) Oscar Dowson and contributors, 2017-26
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problem
nodes : 7
state variables : 2
scenarios : 3.20000e+01
existing cuts : false
options
solver : serial mode
risk measure : #9
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]
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iteration simulation bound time (s) solves pid
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10 -7.690656e+00 2.366592e+00 9.819484e-02 278 1
20 1.266135e+00 1.306623e+00 1.051810e-01 428 1
30 2.252026e-01 1.280382e+00 1.124198e-01 578 1
40 -1.051817e+00 1.278410e+00 1.243939e-01 856 1
50 7.320288e+00 1.278410e+00 1.315598e-01 1006 1
56 1.111084e+01 1.278410e+00 1.361990e-01 1096 1
-------------------------------------------------------------------
status : simulation_stopping
total time (s) : 1.361990e-01
total solves : 1096
best bound : 1.278410e+00
numeric issues : 0
-------------------------------------------------------------------
-------------------------------------------------------------------
SDDP.jl (c) Oscar Dowson and contributors, 2017-26
-------------------------------------------------------------------
problem
nodes : 7
state variables : 2
scenarios : 3.20000e+01
existing cuts : false
options
solver : serial mode
risk measure : #9
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
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10 2.007061e+00 1.281639e+00 1.611710e-02 278 1
20 1.426676e+01 1.278410e+00 2.623296e-02 428 1
30 1.522212e+00 1.278410e+00 4.234505e-02 706 1
40 -4.523775e+01 1.278410e+00 5.470514e-02 856 1
-------------------------------------------------------------------
status : simulation_stopping
total time (s) : 5.470514e-02
total solves : 856
best bound : 1.278410e+00
numeric issues : 0
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