[Help-glpk] minimising after maximising

[Nick Farrell]

I'm pretty new to linear programming and would like a quick tip.

In the script below, what I *want* to happen is that I first choose the worst (ie: max) of x[p] and 3, and then solve for the minimum sum of these values.

ie: I would like z to look like: {1, 2, 3, 3, 3} and then to minimise on the sum of these.

In this artificial example given below, I know I could use the max() preprocessor operator on x[], prior to solving. However, in 'real life' x[] will depend on a collection of variables, and so that won't be available to me. The solver will be moving through the solution space, and at a given point, I want to ensure that z[p] is either x[p] or (say) 3, whatever is greater, but then the overall solution is based on minimising sum z[p]

Thanks for any help.

Nick.

set x := {1, 2, 3, 4, 5};

var z{p in x} >= 0;

s.t. m1z{p in x}: z[p] <= p;

s.t. m2z{p in x}: z[p] <= 3;

maximize zeach{p in x}:

    z[p] ;

minimize zmin:

    sum{p in x} z[p];  # substituting zeach[p] for z[p] gives a compiler error

solve;