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Ricardo Gázquez

Publications and source records attributed to Ricardo Gázquez.

10 recordsLinked to original sources
arXiv2026

Constructing Nested Self-Amplifying Multiperiod Hypergraphs through Mathematical Optimization

This paper proposes an optimization-based framework for the analysis of multiperiod directed multihypergraphs aimed at identifying self-amplifying structures that sustain endogenous growth in complex systems. The approach captures the progressive and nested activation of nodes and hyperarcs, providing a dynamic representation of evolving production and reaction networks. We formulate the problem as a mixed integer optimization model. First, we introduce a tractable linear formulation that captures structural amplification. We then extend this model to a mixed integer nonlinear setting that incorporates a synergistic flow law that generalizes mass-action kinetics in Chemical Reaction Networks and that accounts for interaction effects. This nonlinear formulation is handled through logarithmic transformations and piecewise-linear outer approximations. The framework unifies combinatorial structure selection and flow dynamics, bridging Mathematical Optimization with applications in Economics and Chemistry, including autocatalytic systems related to the Origin of Life. Computational experiments on synthetic instances demonstrate scalability, while an input--output case study illustrates the ability of the model to identify growth-enabling sectors, interdependencies, and structural bottlenecks across different periods, providing actionable insights for the analysis and management of complex systems.

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arXiv2024

Insights into Efficiency and Satisfaction Trade-offs in Facility Location Problems with Regional Preferences

This paper studies a practical regional demand continuous multifacility location problems whose main goal is to locate a given number of services and entry points in each region to distribute certain products to the users at minimum transportation cost. Additionally, a minimum satisfaction level is required for the customers in each region. This satisfaction is measured through continuous preference functions that reflect the satisfaction degree of each location in the region. We provide a mathematical optimization-based framework for the problem and derive suitable Mixed Integer Second Order Cone optimization models for some interesting situations: norm-based transportation costs for the services to the entry points, and different families of preference functions. Among these preference functions, we highlight those derived from economic production models and distance-based preferences. We conduct an extensive computational study along two main lines: a computational approach, where we provide optimal solutions for up to 500 demand regions in the single-facility case and up to $50$ for the p-facility case; and a qualitative approach, where we analyze whether the incorporation of preferences is statistically significant compared to the case without preferences.

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arXiv2024

The Cooperative Maximal Covering Location Problem with ordered partial attractions

The Maximal Covering Location Problem (MCLP) is a classical location problem where a company maximizes the demand covered by placing a given number of facilities, and each demand node is covered if the closest facility is within a predetermined radius. In the cooperative version of the problem (CMCLP), it is assumed that the facilities of the decision maker act cooperatively to increase the customersz' attraction towards the company. In this sense, a demand node is covered if the aggregated partial attractions (or partial coverings) of open facilities exceed a threshold. In this work, we generalize the CMCLP introducing an Ordered Median function (OMf), a function that assigns importance weights to the sorted partial attractions of each customer and then aggregates the weighted attractions to provide the total level of attraction. We name this problem the Ordered Cooperative Maximum Covering Location Problem (OCMCLP). The OMf serves as a means to compute the total attraction of each customer to the company as an aggregation of ordered partial attractions and constitutes a unifying framework for CMCLP models. We introduce a multiperiod stochastic non-linear formulation for the CMCLP with an embedded assignment problem characterizing the ordered cooperative covering. For this model, two exact solution approaches are presented: a MILP reformulation with valid inequalities and an effective approach based on Generalized Benders' cuts. Extensive computational experiments are provided to test our results with randomly generated data and the problem is illustrated with a case study of locating charging stations for electric vehicles in the city of Trois-Rivières, Québec (Canada).

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arXiv2023

Proceedings of the XII International Workshop on Locational Analysis and Related Problems

The International Workshop on Locational Analysis and Related Problems will take place during September 7-8, 2023 in Edinburgh (United Kingdom). It is organized by the Spanish Location Network and the Location Group GELOCA from the Spanish Society of Statistics and Operations Research (SEIO). The Spanish Location Network is a group of more than 140 researchers from several Spanish universities organized into 7 thematic groups. The Network has been funded by the Spanish Government since 2003. The current project is RED2022-134149-T. One of the main activities of the Network is a yearly meeting aimed at promoting the communication among its members and between them and other researchers, and to contribute to the development of the location field and related problems. As a proof of the internationalization of this research group, this will be the first time that the meeting is held out of Spain. The topics of interest are location analysis and related problems. This includes location models, networks, transportation, logistics, exact and heuristic solution methods, and computational geometry, among others.

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arXiv2022

Fairness in Maximal Covering Location Problems

This paper provides a general mathematical optimization based framework to incorporate fairness measures from the facilities' perspective to Discrete and Continuous Maximal Covering Location Problems. The main ingredients to construct a function measuring fairness in this problem are the use of: (1) ordered weighted averaging operators, a family of aggregation criteria very popular to solve multiobjective combinatorial optimization problems; and (2) $α$-fairness operators which allow to generalize most of the equity measures. A general mathematical optimization model is derived which captures the notion of fairness in maximal covering location problems. The models are firstly formulated as mixed integer non-linear optimization problems for both the discrete and the continuous location spaces. Suitable mixed integer second order cone optimization reformulations are derived using geometric properties of the problem. Finally, the paper concludes with the results obtained on an extensive battery of computational experiments on real datasets. The obtained results support the convenience of the proposed approach.

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arXiv2021

Multitype Maximal Covering Location Problems: Hybridizing discrete and continuous problems

This paper introduces a general modeling framework for a multi-type maximal covering location problem in which the position of facilities in different metric spaces are simultaneously decided to maximize the demand generated by a set of points. From the need of intertwining location decisions in discrete and in continuous sets, a general hybridized problem is considered in which some types of facilities are to be located in finite sets and the others in continuous metric spaces. A natural non-linear model is proposed for which an integer linear programming reformulation is derived. A branch-and-cut algorithm is developed for better tackling the problem. The study proceeds considering the particular case in which the continuous facilities are to be located in the Euclidean plane. In this case, taking advantage from some geometrical properties it is possible to propose an alternative integer linear programming model. The results of an extensive battery of computational experiments performed to assess the methodological contribution of this work is reported on. The data consists of up to 920 demand nodes using real geographical and demographic data.

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arXiv2021

A Branch-and-Price approach for the Continuous Multifacility Monotone Ordered Median Problem

In this paper, we address the Continuous Multifacility Monotone Ordered Median Problem. This problem minimizes a monotone ordered weighted median function of the distances between given demand points in $\mathbb{R}^d$ and its closest facility among the $p$ selected, also in a continuous space. We propose a new branch-and-price procedure for this problem, and two mathehuristics. One of them is a decomposition-based procedure and the other an aggregation-based heuristic. We give detailed discussions of the validity of the exact formulations and also specify the implementation details of all the solution procedures. Besides, we assess their performance in an extensive computational experience that shows the superiority of the branch-and-price approach over the compact formulation in medium-sized instances. To handle larger instances it is advisable to resort to the matheuristics that also report rather good results.

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arXiv2020

Reallocating and Sharing Health Equipments in Sanitary Emergency Situations: The COVID-19 Case in Spain

In this paper we provide a mathematical programming based decision tool to optimally reallocate and share equipments between different units in emergency situations under lack of resources. The approach is motivated by the COVID-19 pandemic in which many Heath National Systems were not able to satisfy the demand of ventilators, sanitary individual protection equipments or different human resources. Our tool is based in two main principles: (1) Part of the stock of equipments at a unit that is not needed (in near future) could be shared to other units; and (2) extra stock to be shared among the units in a region can be efficiently distributed taking into account the demand of the units. The decisions are taken with the aim of minimizing certain measures of the non-covered demand in a region where a given network structured set of units is given. The mathematical programming models that we provide are stochastic and multiperiod and we provide different robust objective functions. Since the proposed models are computationally hard to solve, we provide a divide-et-conquer math-heuristic approach. We report the results of applying our approach to the data of the COVID-19 case in different regions of Spain, highlighting some interesting conclusions of our analysis, such as the great increase of treated patients if the proposed redistribution tool is applied.

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arXiv2020

Continuous maximal covering location problems with interconnected facilities

In this paper we analyze a continuous version of the maximal covering location problem, in which the facilities are required to be interconnected by means of a graph structure in which two facilities are allowed to be linked if a given distance is not exceed. We provide a mathematical programming framework for the problem and different resolution strategies. First, we propose a Mixed Integer Non Linear Programming formulation, and derive properties of the problem that allow us to project the continuous variables out avoiding the nonlinear constraints, resulting in an equivalent pure integer programming formulation. Since the number of constraints in the integer programming formulation is large and the constraints are, in general, difficult to handle, we propose two branch-&-cut approaches that avoid the complete enumeration of the constraints resulting in more efficient procedures. We report the results of an extensive battery of computational experiments comparing the performance of the different approaches.

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