Abstract
One of the classical problems in the structural optimization field is the Truss Topology Design Problem (TTDP) which deals with the selection of optimal configuration for structural systems for applications in mechanical, civil, aerospace engineering, among others. In this paper we consider a TTDP where the goal is to find the stiffest truss, under a given load and with a bound on the total volume. The design variables are the cross-section areas of the truss bars that must be chosen from a given finite set. This results in a large-scale non-convex problem with discrete variables. This problem can be formulated as a Semidefinite Programming Problem (SDP problem) with binary variables. We propose a branch and bound algorithm to solve this problem. In this paper it is considered a binary formulation of the problem, to take advantage of its structure, which admits a Knapsack problem as subproblem. Thus, trying to improve the performance of the Branch and Bound, at each step, some valid inequalities for the Knapsack problem are included.

Abstract
We consider a real production planning problem occurring in a glass container manufacturing company. The goal is to minimise the average stock level during a planning horizon of one year, maintaining customers satisfaction and keeping the production at its maximum rate. Besides the production capacity, the main constraints considered are related to the number of setup changes in machines, which is restricted in each factory. The main goal is to find the best balance between the number of setups and the average stock level. We propose a decomposition of the problem into two interrelated problems: a lot-sizing problem and a scheduling problem. For each problem we propose a mathematical model that can be solved using a commercial solver package. To be an efficient managerial tool, the method should provide quickly good solutions. Therefore we solve the lot-sizing problem through a relax-and-fix heuristic and discuss the results. Copyright © 2011 Inderscience Enterprises Ltd.

Abstract
We consider the Weight-constrained Minimum Spanning Tree problem (WMST). The WMST aims at finding a minimum spanning tree such that the overall tree weight does not exceed a specified limit on a graph with costs and weights associated with each edge. We present and compare, from the computational point of view, several formulations for the WMST. From preliminary computational results we propose a model that combines a formulation similar to the well known Miller-Tucker-Zemlin formulation with the cut-set inequalities.

Abstract
We consider the weight-constrained minimum spanning tree problem which has important applications in telecommunication networks design. We discuss and compare several formulations. In order to strengthen these formulations, new classes of valid inequalities are introduced. They adapt the well-known cover, extended cover and lifted cover inequalities. They incorporate information from the two subsets: the set of spanning trees and the knapsack set. We report computational experiments where the best performance of a standard optimization package was obtained when using a formulation based on the well-known Miller-Tucker-Zemlin variables combined with separation of cut-set inequalities.

Abstract
One of the classical problems in the structural optimization field is to find the stiffest truss, under a given load and with a bound on the total volume. This is a well-studied problem for continuous cross sectional areas. Generally, the optimal solutions obtained for this problem contain bars with many different cross sectional areas. However, in real life, only a finite set of possible values for those cross sectional areas can be considered. We propose a Semidefinite Programming with discrete variables for this problem. In order to solve the problem we derive and compare two exact algorithms. The first one is a branch and bound algorithm where the branching is done only on the bar-areas. The second algorithm has two stages. In the first stage a branch and bound on the nodes of the structure is performed. In the second stage, considering the nodes in the structure from the first stage, a branch and bound algorithm on the bar-areas is performed.

Abstract
Currently, there is increasing implementation of renewable energy communities, where consumers and producers come together to form energy cooperatives. This growing trend has been accompanied by several studies aiming to optimize energy exchanges and sharing inside the community, always taking into account the most favorable tariff regimes for community members. This paper presents an analysis that, based on applying a linear programming model, optimizes energy transactions in a renewable energy community with the integration of storage systems. The results show the developed model's effectiveness, presenting substantial profits for the community.