Cycle policy condition on t

[Thuener]

I am working on an inventory problem, and I have some constraints that are just for the initial stages, but I'm using a cycle policy.
For example, imagine a problem with 12 nodes (or months) that I have a constraint that is different for the first 4 stages.

if t <= 4
    @constraint(sp, A)
else 
    @constraint(sp, B)
end

If I use the cycle policy this constraint will also appear after the initial 4 months, on months 13,14,15 and 16. If there is an way to detect the cycle then I could do something like this:

if t <= 4 && !node.cycle
    @constraint(sp, A)
else 
    @constraint(sp, B)
end

There is any flag for the subproblem to know that you are in cycle?

[odow]

There is any for the subproblem to know that you are in cycle?

No. The correct approach is to use a graph with 16 nodes:

julia> using SDDP

julia> graph = SDDP.LinearGraph(12);

julia> for t in 1:4
           SDDP.add_node(graph, 12 + t)
           p = t == 1 ? 0.95 : 1.0
           SDDP.add_edge(graph, 11 + t => 12 + t, p)
       end

julia> SDDP.add_edge(graph, 16 => 5, 1.0)

julia> graph
Root
 0
Nodes
 1
 2
 3
 4
 5
 6
 7
 8
 9
 10
 11
 12
 13
 14
 15
 16
Arcs
 0 => 1 w.p. 1.0
 1 => 2 w.p. 1.0
 2 => 3 w.p. 1.0
 3 => 4 w.p. 1.0
 4 => 5 w.p. 1.0
 5 => 6 w.p. 1.0
 6 => 7 w.p. 1.0
 7 => 8 w.p. 1.0
 8 => 9 w.p. 1.0
 9 => 10 w.p. 1.0
 10 => 11 w.p. 1.0
 11 => 12 w.p. 1.0
 12 => 13 w.p. 0.95
 13 => 14 w.p. 1.0
 14 => 15 w.p. 1.0
 15 => 16 w.p. 1.0
 16 => 5 w.p. 1.0

[Thuener]

Thanks.
I taught about this approach, the downside is that it will create more nodes leading to more convergence time. For 4 nodes is would be ok, but for 12 maybe it would be too much.

[odow]

It probably won't make that much of a difference. In an acyclic graph, the solution scales approximately linearly in the number of nodes. In a cyclic graph, I don't think anyone has a result, but I assume that it's the expected number of nodes in the forward pass. So 12 * (1 - p) is 240 nodes. Adding an extra 4 won't change much.