4
$\begingroup$

I have a constraint of the following form that describes the growth of trees, where the population of trees in period $t$ is the previous period's population minus some trees infected with a virus:

$$ S_{t}^{ij} = S_{t-1}^{ij} - I_{t-1}^{ij} $$ $$ S_{t}\ge0,I_{t} \ge 0$$

From this constraint, you can see that it is possible for $ I_{t-1}^{ij} $ to be larger than $S_{t-1}^{ij}$ , but I need to be able to incorporate the fact that in any period $S_{t}^{ij} $ can never be less than 0 because you cannot have negative trees.

I am wondering if there is any way to incorporate this besides including a max constraint of the form :$$ S_{t}^{ij} = \max\{S_{t-1}^{ij} - I_{t-1}^{ij}, 0 \}$$

When I include the max constraint and then linearize it, my problem becomes very challenging to solve, so I am wondering if there's maybe some other way I can try to reformulate the constraint so to avoid the binary variables.

$\endgroup$
5
$\begingroup$

Why not just impose $S_t^{ij} \ge 0$?

| improve this answer | |
$\endgroup$
3
$\begingroup$

As @RobPratt states why not impose $S^{ij}_t\geq0$? Especially it seems rather reasonable to inforce this through $S^{ij}_t\geq I^{ij}_t $ given that there probably cannot be more infected trees than there are trees.

| improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.