Wednesday, April 29, 2009

Ceiling in OML

Hello, I have to deal with an objective function of the following form: min [C1 * ceiling (X/m) plus C2 * (X-ceiling(X/m))];
where C1, C2, m are parameters and X is the decision variable. Ceiling is a mathematical operator that rounds a number up, to the nearest integer (see Excel's definition).
My first question is: is the Ceiling operator defined in OML?
My second question: is there a solver within the Microsoft Solver Foundation that can handle this type of objective function?
Thank you.

I believe you can do the following in OML:

Let Y be an integer variable with the constraint

X/m ≤ Y ≤ 1+X/m

then minimize

C1 * Y + C2 * (X-Y)

Hopefully the rest of the model is linear. In that case this is a much better formulation as it gets rid of a non-smooth function: solvers often have troubles with that.

See also http://yetanothermathprogrammingconsultant.blogspot.com/2009/02/floor-in-minlp-model.html and http://yetanothermathprogrammingconsultant.blogspot.com/2008/08/gams-documentation-endogenous-floor.html.