Mixed integer programming for the 0–1 maximum probability model

In this paper we study the 0–1 maximum probability model that consists in maximizing the probability that a certain quantity c^Tx is greater than a prescribed constant t, where c and x are n vectors. c1,…,cn are mutually independent and normally distributed random variables and x is a vector of n binary variables such that Ax⩽b, where b is an m vector and A is an m×n matrix. 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 with up to 100 random variables in a few seconds of CPU time.