Question

Find a vector x which minimizes c . x subject to the constraint m . x >= b, x integer.

Here’s a sample input set:

c : {1,2,3}
m : {{1,0,0},
     {0,1,0},
     {1,0,1}}
b : {1,1,1}

With output:

x = {1,1,0}

What are good tools for solving this sort of problem, and examples of how to use them?

Answer 1

Mathematica

Mathematica has this built in. (NB: Mathematica is not free software.)

LinearProgramming[c, m, b, Automatic, Integers]

outputs:

{1, 1, 0}