Solve Ax <= b with some unknown values of [b]? but with a relationship between them

I am using the solver "intlinprog" to solve an integer linear programming problem with inequality Ax<=b. This is one case I have already solved it. I have another case when some values of [b] vector are unknown, however, there is a relation between them and all u's are either 0 or 1.

Ex: . .

x1+x2+x3+x4+x5+x9 <= u1

x4+x6+x8 <= u2

. .

9 eq's with 9 unknown x's.

u1 and u2.. are unknown constant values but there is a relationship between them, say, u1+u2+u3+u4>3 (if we have 4 u's, one of them is zero and the rest are one).

I want the solver finds the values of u's (=0 or 1) in a way that it minimizes the total objective fn = min {x1+...+x2}. The result should be the values of x and u.

Can we solve such a problem?

Thanks in advance

Answer 1

[Torsten]

If the u's are also unknown, you will have to put them to the other unknowns x1,...,x9 as x10,x11,x12 and x13.

Best wishes

Torsten.

[Ismaeel]

Thanks Torsten. I've already done your suggestion but that doesn't lead to a minimized solution. I've tested on 60x60 equations with 10 u's. The result of this data is known and equals to 14 x's instead of what I got which was 17 x's. This is after selecting only first x's that are not greater than the system size which is 60 from the whole result of x which includes u's but substracted.

[Matt J]

Torsten's suggestion should have worked. We would need to see code to analyze what went wrong.