Erwin Kalvelagen
2020-12-21 19:34:51
(1) Strictly speaking, the Simplex Method is only for continuous problems.
(2) INEQ1 OR INEQ2 can be done by adding binary variables. I have never seen a model with INEQ1 XOR INEQ2. I suspect in your case we just can use INEQ1 OR INEQ2.
(3) An OR is often modeled as:
a(i)+w(i) ≤ w(j) + M*δ(i,j)
a(j)+w(j) ≤ w(i) + M*(1-δ(i,j))
δ(i,j) ∈ {0,1}
Here M is a big-M: a large enough constant. Often we can limit these constraints to the case where i<j due to symmetry.
Yes, it is an OR , i already added binary variables but the problem is when i want to formulate the table which correspond to the standard form, w(i) and w(j) should be computed by the ILP so how can i define the budget in my table ?!
Not sure what your "standard form" is. This is mostly used in chapter 1 of text books, but software tools for MIP models are usually more flexible in what they can accept.