Duality gaps in stochastic integer programming

In this note, we explore the implications of a result that suggests that th e duality gap caused by a Lagrangian relaxation of the nonanticipativity co nstraints in a stochastic mixed integer (binary) program diminishes as the number of scenarios increases. By way of an example, we illustrate that thi s is not the case. In general, the duality gap remains bounded away from ze ro.