We introduce a family of subadditive functions called Generator Functions for mixed integer linear programs. These functions were previously defined for pure integer programs with non-negative entries by Klabjan [13]. They are feasible in the subadditive dual and we show that they are enough to achieve strong duality. Several properties of the functions are shown. We then use this class of func...

We describe a general technique for determining upper bounds on maximal values (or lower bounds on minimal costs) in stochastic dynamic programs. In this approach, we relax the nonanticipativity constraints that require decisions to depend only on the information available at the time a decision is made and impose a “penalty” that punishes violations of nonanticipativity. In applications, the h...

We consider the class of linear programs that can be formulated with infinitely many variables and constraints but where each constraint has only finitely many variables. This class includes virtually all infinite horizon planning problems modeled as infinite stage linear programs. Examples include infinite horizon production planning under time-varying demands and equipment replacement under t...

In integer programming, {0, 1/2}-cuts are Gomory–Chvátal cuts that can be derived from the original linear system by using coefficients of value 0 or 1/2 only. The separation problem for {0, 1/2}-cuts is strongly NP-hard. We show that separation remains strongly NP-hard, even when all integer variables are binary. © 2011 Elsevier B.V. All rights reserved.