We present a framework to obtain valid inequalities for optimization problems constrained by a reverse convex set, which is defined as the set of points in a polyhedron that lie outside a given open convex set. We are particularly interested in cases where the closure of the convex set is either non-polyhedral, or is defined … Read more
In this paper, we first present a new extended formulation of the Capacitated Concentrator Location Problem (CCLP) using the notion of cardinality of terminals assigned to a concentrator location. The disaggregated formulation consists of O(mn2) variables and constraints, where m denotes the number of concentrators and n the number of terminals. An immediate benefit of … Read more
We propose a new class of valid inequalities for mixed-integer nonlinear optimization problems with indicator variables. The inequalities are obtained by lifting polymatroid inequalities in the space of the 0–1 variables into conic inequalities in the original space of variables. The proposed inequalities are shown to describe the convex hull of the set under study … Read more
We consider an uncapacitated multi-item multi-echelon lot-sizing problem within a remanufacturing system involving three production echelons: disassembly, refurbishing and reassembly. We seek to plan the production activities on this system over a multi-period horizon. We consider a stochastic environment, in which the input data of the optimization problem are subject to uncertainty. We propose a … Read more
The classic version of the Inventory Routing Problem considers a system with one supplier that manages the stock level of a set of customers. The supplier defines when and how much products to supply and how to combine customers in routes while minimizing storage and transportation costs. We present a new version of this problem … Read more
We investigate a mixed 0-1 conic quadratic optimization problem with indicator variables arising in mean-risk optimization. The indicator variables are often used to model non-convexities such as fixed charges or cardinality constraints. Observing that the problem reduces to a submodular function minimization for its binary restriction, we derive three classes of strong convex valid inequalities … Read more
This paper deals with a variant of the well-known Cluster Editing Problem (CEP), more precisely, the \textit{p}-CEP, in which a given input graph should be edited by adding and/or removing edges in such a way that \textit{p} vertex-disjoint cliques (clusters) are generated with the minimum number of editions. We introduce several valid inequalities where some … Read more
As the modern transmission control and relay technologies evolve, transmission line switching has become an important option in power system operators’ toolkits to reduce operational cost and improve system reliability. Most recent research has relied on the DC approximation of the power flow model in the optimal transmission switching problem. However, it is known that … Read more
In this article, six different mixed integer programming (MIP) formulations are proposed and analyzed. These formulations are based on the knowledge of four different paradigms for single machine scheduling problems (SMSP) with sequence dependent setup times and release dates. Each formulation reflects a specific concept on how the variables and parameters are defined, requiring particular … Read more
The planning of chemical production often involves the optimization of the size of the tasks to be performed subject to unit capacity constraints, as well as inventory constraints for intermediate materials. While several mixed-integer programming (MIP) models have been proposed that account for these features, the development of tightening methods for these formulations has received … Read more