On Generating Lagrangian Cuts for Two-Stage Stochastic Integer Programs

Decomposition algorithms with parametric Gomory cuts for two-stage stochastic integer programs

We consider a class of two-stage stochastic integer programs with binary variables in the first stage and general integer variables in the second stage. We develop decomposition algorithms akin to the L-shaped or Benders’ methods by utilizing Gomory cuts to obtain iteratively tighter approximations of the second-stage integer programs. We show that the proposed methodology is flexible in that i...

Computations with disjunctive cuts for two-stage stochastic mixed 0-1 integer programs

Two-stage stochastic mixed-integer programming (SMIP) problems with recourse are generally difficult to solve. This paper presents a first computational study of a disjunctive cutting plane method for stochastic mixed 0-1 programs that uses lift-and-project cuts based on the extensive form of the two-stage SMIP problem. An extension of the method based on where the data uncertainty appears in t...

Partial Decomposition Strategies for Two-Stage Stochastic Integer Programs

We propose the concept of partial Benders decomposition, based on the idea of retaining a subset of scenario subproblems in the master formulation and develop a theory to support it that illustrates how it may be applied to any stochastic integer program with continuous recourse. Such programs are used to model many practical applications such as the one considered in this paper, network design...

Decomposition Methods for Two-Stage Stochastic Integer Programs

Generating Disjunctive Cuts for Mixed Integer Programs — Doctoral Dissertation

This report constitutes the Doctoral Dissertation for Michael Perregaard and is a collection of results on the efficient generation of disjunctive cuts for mixed integer programs. Disjunctive cuts is a very broad class of cuts for mixed integer programming. In general, any cut that can be derived from a disjunctive argument can be considered a disjunctive cut. Here we consider specifically cuts...