Re: [Help-glpk] Multiple LP problem solving

[Andrew Makhorin]

> I guess I have to define the objective z as z1, then add the
> constraints for z2..zN, right? Otherwise, I don't know how I could
> define an objective z without specifying the coefficients for each
> variable, i.e. the columns in GLPK.
> 
> Am I right?

Not exactly. In my example I assumed that z1, z2, ... are variables that
appear in the left-hand sides of equality constraints that define the
objective linear forms. In principle, you don't need to introduce such
variables, i.e. you might use the following formulation (in MathProg
syntax):

var z;

s.t. z1: z >= a1 * x1 + b1 * x2 + ...
     z2: z >= a2 * x1 + b2 * x2 + ...
     z3: z >= a3 * x1 + b3 * x2 + ...

minimize obj: z;

See similar example models cf12a.mod and cf12b.mod included in the glpk
distribution.