Mixed integer programming for the 0-1 maximum probability model
Résumé
In this paper we study the 0-1 maximum probability model where c and x are n vectors, b is an m vector and A is an matrix. are mutually independent and normally distributed random variables and t is a given constant. It is known that this problem can be formulated as a nonlinear fractional program. We show how to solve it exactly using mixed integer programming. The advantage of the approach is that it requires only standard, commercially available software. The computational results which we present show that this technique makes it possible to treat instances comprising up to 100 random variables in a few seconds of CPU time.
Keywords: Stochastic integer programming; Maximum probability model; Mixed integer programming; Computational experiments