We consider the Sample Average Approximation (SAA) method for 2-stage stochastic optimization problems with recourse and prove a polynomial time convergence theorem for the SAA method. In the 2-stage recourse model, where one makes decisions in two steps. First, given only distributional information about (some of) the data, one commits on initial (first-stage) actions, and then once the actual...

In this paper we review the Disjunctive Decomposition (D) algorithm for two-stage Stochastic Mixed Integer Programs (SMIP). This novel method uses the principles of disjunctive programming to develop cuttingplane-based approximations of the feasible set of the second stage problem. At the core of this approach is the Common Cut Coefficient Theorem, which provides a mechanism for transforming cu...

We study an adaptive partition-based approach for solving two-stage stochastic programs with fixed recourse. A partition-based formulation is a relaxation of the original stochastic program, and we study a finitely converging algorithm in which the partition is adaptively adjusted until it yields an optimal solution. A solution guided refinement strategy is developed to refine the partition by ...

In this paper, a general scheme for generating extra cuts during the execution of a Benders decomposition algorithm is presented. These cuts are based on feasible and infeasible master problem solutions generated by means of a heuristic. This article includes general guidelines and a case study with a fixed charge network design problem. Computational tests with instances of this problem show t...

A newmulti-generation of cuts algorithm is presented in this paper to improve the efficiency of Benders decomposition approach for the cases that optimality cuts are difficult to be achieved within the iterations of the algorithm. This strategy is referred to as maximum feasible subsystem (MFS) cut generation strategy. In this approach in each iteration of the Benders algorithm an additional cu...

In this paper, a general scheme for generating extra cuts during the execution of a Benders decomposition algorithm is presented. These cuts are based on feasible and infeasible master problem solutions generated by means of a heuristic. This article includes general guidelines and a case study with a fixed charge network design problem. Computational tests with instances of this problem show t...

Given a connected and undirected graph G, the degree preserving spanning tree problem (DPSTP) asks for a spanning tree of G with the maximum number of vertices with the same degree in the tree and in G. These are called full degree vertices. We introduce integer programming formulations, valid inequalities and four exact solution approaches based on different formulations. Two branch-and-bound ...

This paper addresses a class of two-stage robust optimization models with an exponential number scenarios given implicitly. We apply Dantzig–Wolfe decomposition to exploit the structure these and show that original problem reduces single-stage problem. propose Benders algorithm for reformulated also develop heuristic dualizes linear programming relaxation inner maximization in model iteratively...

This paper presents a multistage stochastic linear programming problem solved by a stochastic nested Benders decomposition algorithm. The algorithm allows the node aggregation and division of the scenario tree into connected subtrees forming arbitrary subproblems that will be solved as the algorithm proceeds. Different aggregation strategies have been tested and numerical results of the applica...