Maximizing a class of submodular utility functions with constraints

Motivated by stochastic 0-1 integer programming problems with an expected utility objective, we study the mixed-integer nonlinear set: where N is a positive integer, is a concave function, are nonnegative vectors, d is a real number and B is a positive real number. We propose a family of inequalities for the convex hull of P by exploiting submodularity of the function over and the knapsack constraint . Computational effectiveness of the proposed inequalities within a branch-and-cut framework is illustrated using instances of an expected utility capital budgeting problem.