We address a scheduling problem in the context of military aircraft maintenance where the goal is to meet the aircraft requirements for a number of missions in the presence of breakdowns. The assignment of aircraft to a mission must consider the requirements for the mission, the probability of aircraft failure, and capacity of the repair shop that maintains the aircraft. Therefore, a solution b...

Benders decomposition is a well-known procedure for solving a combinatorial optimization problem by defining it in terms of a master problem and a subproblem. Its effectiveness relies on the possibility of synthethising Benders cuts (or nogoods) that rule out not only one, but a large class of trial values for the master problem. In turns, this depends on the possibility of separating the subpr...

Nowadays, researches pay more attention to environmental concerns consisted of various communities. This study proposes a multi-echelon, multi-period closed-loop supply chain (CLSC). A comprehensive model considers the selection of selection of technology and environmental effects. The supply chain is under a build-to-order (BTO) environment. So, there is not a final product inventory. Also, th...

This document shows how to model two-stage stochastic linear programming problems in a GAMS environment. We will demonstrate using a small example, how GAMS can be used to formulate and solve this model as a large LP or using specialized stochastic solvers such as OSL-SE and DECIS. Finally a tailored implementation of the Benders Decomposition algorithm written in GAMS is used to solve the model.

We consider two-stage stochastic programming problems with integer recourse. The L-shaped method of stochastic linear programming is generalized to these problems by using generalized Benders decomposition. Nonlinear feasibility and optimality cuts are determined via general duality theory and can be generated when the second stage problem is solved by standard techniques. Finite convergence of...

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...

In the context of convex mixed integer nonlinear programming (MINLP), we investigate how the outer approximation method and the generalized Benders decomposition method are affected when the respective nonlinear programming (NLP) subproblems are solved inexactly. We show that the cuts in the corresponding master problems can be changed to incorporate the inexact residuals, still rendering equiv...

Semidefinite programs originating from the Kalman-Yakubovich-Popov lemma are convex optimization problems and there exist polynomial time algorithms that solve them. However, the number of variables is often very large making the computational time extremely long. Algorithms more efficient than general purpose solvers are thus needed. In this paper a generalized Benders decomposition algorithm ...

We describe a hybrid bi-level decomposition scheme that addresses the challenge of solving a large-scale two-stage stochastic programming problem with mixed-integer recourse, which results from a multi-scale capacity planning problem as described in part I of this paper series. The decomposition scheme combines bi-level decomposition with Benders decomposition, and relies on additional strength...