Below I need solve for the binary variables $x_1,x_2,y_1,y_2,z_1,z_2$ that minimize the functions $f(x), f(y), f(z)$, subject to the 5 constraints that follow. By binary I mean they can only be 1 or 0. [Edit: $u_1,u_2,h$ are non-negative real valued. The functions to be minimized must also be non-negative. This is a much reduced version of a big workshift scheduling problem.]
I appreciate any advice as to what sort of strategy I might use. Thanks.