Finiteness Theorems in Stochastic Integer Programming

Finiteness Theorems in Stochastic Integer Programming

We study Graver test sets for families of linear multi-stage stochastic integer programs with varying number of scenarios. We show that these test sets can be decomposed into finitely many “building blocks”, independent of the number of scenarios, and we give an effective procedure to compute them. The paper includes an introduction to Nash-Williams’ theory of better-quasi-orderings, which is u...

Stochastic Integer Programming: Limit Theorems and Confidence Intervals

We consider empirical approximations (sample average approximations) of two-stage stochastic mixed-integer linear programs and derive central limit theorems for the objectives and optimal values. The limit theorems are based on empirical process theory and the functional delta method. We also show how these limit theorems can be used to derive confidence intervals for optimal values via resampl...

Stochastic Integer Programming Bibliography

Stochastic Integer Programming

1. Books and Surveys 2. Theory 2.1 Structural properties of the EVF 2.2 Complexity related results 3. General Purpose Algorithms 3.1 Benders’ decomposition methods 3.2 Gröbner basis methods 3.3 Convex approximations of SIR models 3.4 Other methods 4. Solution of Specific Problems 4.1 Production planning and scheduling problems 4.2 Network and routing problems 4.3 Location problems 4.4 Other pro...

Sensitivity theorems in integer linear programming

We consider integer linear programming problems with a fixed coefficient matrix and varying objective function and right-hand-side vector. Among our results, we show that, for any optimal solution to a linear program max{wx: Ax <~ b}, the distance to the nearest optimal solution to the corresponding integer program is at most the dimension of the problem multiplied by the largest subdeterminant...