Stochastic 0–1 linear programming under limited distributional information

We consider the problem minX∈{0,1}n{c′x:aj′x⩽bj,j=1,…,m}, where the ajaj are random vectors with unknown distributions. The only information we are given regarding the random vectors ajaj are their moments, up to order k. We give a robust formulation, as a function of k, for the 0–1 integer linear program under this limited distributional information.