A general question on MIP formulation

[Carlos Suazo M.]

Guys,

Consider we have a sequentially dependent decision model, so the decisions made at a particular time will affect decisions made later. 

Suppose in a multi-period (n periods) problem, for example, we introduce a binary decision variable called I_t into each period t to show how a decision should be made in each period.

Let n = 4, then dependency is expressed as follows:

I_1 <= I_2

I_2 <= I_3

I_3 <= I_4

How will affect convergence time if we add following constraints??? Is it recommendable? 

I_1 <= I_3

I_1 <= I_4

I_2 <= I_4

Will these additional constraints help convergence during branch and cut execution???

Is there any option in Gurobi to implement this constraint in a efficient way????

Many thanks in advance,

Carlos

[Tobias Achterberg]

This is a good question. Since the variables are binary, Gurobi should be able
to find all the implied inequalities by probing, so there should not be any need
to add them explicitly. My intuition is that they will just blow up the model.
But you can never know what their impact is on cutting plane separation. Maybe
they will help. Thus, you need to try.

There is no direct option in Gurobi to help you adding those redundant
constraints. But it should be very easy in any programming language to add those.


Regards,

Tobias