[Help-glpk] KPI simple function

[Simone Atzeni]

Hi all,

I'm looking for two functions that could represent simple KPIs.

In other world, I would like two MILP, in this way:

MILP 1:

MAX J = 0.5 * Z1 + 0.5 * Z2

Z1 = -AX + C
Z2 = BX + D

and

MILP 2:

MAX J = 0.32 * Z1 + 0.68 * Z2

Z1 = -AX + C
Z2 = BX + D

Z1 and Z2 are the values of the KPI and they depend on X. The constraints should be equal but the results (the values of Z1 and Z2) should be different changing the coefficients fo the objective function, in this case (0.5 - 0.5) for the MILP1 and (0.32 - 0.68) for the MILP 2.

I can't find a good function. I need just functions where Z1 and Z2 depend on X but changing the coefficients in the objective functions change the values of Z1, Z2 and X.

MILPs I'm using are the follow:

MAX J = 0.5 Z.1 + 0.5 Z.2

Z.1 = 5X (0.196116135138184 Z.1 - 0.98058067569092 U.1 <= 0) (the equations have been normalized)

Z.2 = -3X + 4 (0.196116135138184 Z.2 + 0.115384615384615 U.1 <= 0.153846153846154)

and

MAX J = 0.32 Z.1 + 0.68 Z.2

Z.1 = 5X

Z.2 = -3X + 4

This is the picture of the two functions:

Both MILPs have the same solution.

Z.1 = 1

Z.2 = 0.666795

X = 0.2

In this case the weights, (0.5 - 0.5) for the MILP1 and (0.32 - 0.68) for the MILP 2, don't influence the results of the MILP. I want something in a way that the weights influence the results, so that the two MILPs have different result but they should being equal.

Can someone help me?

Thanks

Simone