Stochastic All Blacks

This tutorial was generated using Literate.jl. Download the source as a .jl file. Download the source as a .ipynb file.

using SDDP, HiGHS, Testfunction stochastic_all_blacks()    # Number of time periods    T = 3    # Number of seats    N = 2    # R_ij = price of seat i at time j    R = [3 3 6; 3 3 6]    # Number of noises    s = 3    offers = [        [[1, 1], [0, 0], [1, 1]],        [[1, 0], [0, 0], [0, 0]],        [[0, 1], [1, 0], [1, 1]],    ]    model = SDDP.LinearPolicyGraph(;        stages = T,        sense = :Max,        upper_bound = 100.0,        optimizer = HiGHS.Optimizer,    ) do sp, stage        # Seat remaining?        @variable(sp, 0 <= x[1:N] <= 1, SDDP.State, Bin, initial_value = 1)        # Action: accept offer, or don't accept offer        # We are allowed to accept some of the seats offered but not others        @variable(sp, accept_offer[1:N], Bin)        @variable(sp, offers_made[1:N])        # Balance on seats        @constraint(            sp,            balance[i in 1:N],            x[i].in - x[i].out == accept_offer[i]        )        @stageobjective(sp, sum(R[i, stage] * accept_offer[i] for i in 1:N))        SDDP.parameterize(sp, offers[stage]) do o            fix.(offers_made, o)            return        end        @constraint(sp, accept_offer .<= offers_made)    end    SDDP.train(model; duality_handler = SDDP.LagrangianDuality())    @test SDDP.calculate_bound(model) ≈ 8.0    returnendstochastic_all_blacks()

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         SDDP.jl (c) Oscar Dowson and contributors, 2017-26
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problem
  nodes           : 3
  state variables : 2
  scenarios       : 2.70000e+01
  existing cuts   : false
options
  solver          : serial mode
  risk measure    : SDDP.Expectation()
  sampling scheme : SDDP.InSampleMonteCarlo
subproblem structure
  VariableRef                             : [9, 9]
  AffExpr in MOI.EqualTo{Float64}         : [2, 2]
  AffExpr in MOI.LessThan{Float64}        : [2, 2]
  VariableRef in MOI.GreaterThan{Float64} : [2, 3]
  VariableRef in MOI.LessThan{Float64}    : [3, 3]
  VariableRef in MOI.ZeroOne              : [4, 4]
numerical stability report
  matrix range     [1e+00, 1e+00]
  objective range  [1e+00, 6e+00]
  bounds range     [1e+00, 1e+02]
  rhs range        [0e+00, 0e+00]
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 iteration    simulation      bound        time (s)     solves  pid
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         1L  6.000000e+00  1.366667e+01  3.001904e-02        11   1
        28L  6.000000e+00  8.000000e+00  1.054877e+00       470   1
        40L  6.000000e+00  8.000000e+00  1.484363e+00       602   1
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status         : simulation_stopping
total time (s) : 1.484363e+00
total solves   : 602
best bound     :  8.000000e+00
numeric issues : 0
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