In CPLEX, piecewise-based stepwise example result

Question

I'm a student studying optimization using CPLEX. I created a simple stepwise example, but I have some doubts about the results.

dvar float x;
dvar float y;

dexpr float z= piecewise {0->0; 10->0; 0->10; 5->10; 0->20; 5->20; 0} (1,10) x;
dexpr float goal = y+z;

minimize goal;

subject to {

9<=x;
x<=18;
4<=y;
y<=10;
}

In the above formula, I expected x and y to be 9 and 4 respectively, and the solution to yield the expected result of 14. (when x is 9, z becomes 10, so y+z=4+10=14.) However, why does the decision variable show x as 10 and the goal as 19 instead?

I would appreciate your response. Thank you.

Answer 1

Your piecewise is discontinuous, which means for 10 the result is either 10 or 15

dvar float x;
dvar float y;

dvar float z;
dvar float goal;

pwlFunction f=piecewise {0->0; 10->0; 0->10; 5->10; 0->20; 5->20; 0} (1,10);

minimize goal;

subject to {
  
   z== f(x);
 goal== y+z;

9<=x;
x<=18;
4<=y;
y<=10;

}

execute
{
  writeln(z);
  writeln(f(x));
}

what you could do in order to remove this choice is write

(x==10) => (z==15);

and then

dvar float x;
dvar float y;

dvar float z;
dvar float goal;

pwlFunction f=piecewise {0->0; 10->0; 0->10; 5->10; 0->20; 5->20; 0} (1,10);

minimize goal;

subject to {
  
   z== f(x);
 goal== y+z;

9<=x;
x<=18;
4<=y;
y<=10;

(x==10) => (z==15);

}

execute
{
  writeln(z);
  writeln(f(x));
}

gives

10
10

and you get x=9