  In this paper, we analyze how sequentially introducing decision variables
into an integer program (IP) affects the value function and its level sets. We
use a Gilmore-Gomory approach to find parametrized IP value functions over a
restricted set of variables. We introduce the notion of maximal connected
subsets of level sets - volumes in which changes to the constraint right-hand
side have no effect on the value function - and relate these structures to IP
value functions and optimal solutions.
