arXiv subjects

Justo Puerto

Publications and source records attributed to Justo Puerto.

At least 19 recordsLinked to original sources

arXiv2026

Cooperation in Conic Programming with Applications to Control, Production, and Portfolio

We introduce the class of cooperative conic games, a new family of transferable utility games whose characteristic function can be computed by solving a conic optimization problem. This framework unifies a broad range of optimization-based cooperative games within a common mathematical formulation, encompassing linear, second-order cone, semidefinite, and other convex nonlinear optimization problems admitting conic representations. Exploiting the structural properties of conic programs and conic duality theory, we derive general conditions ensuring the existence of core payoff allocations (or cost shares) and show how such allocations can be computed directly from optimal dual solutions. In particular, the proposed methodology replaces combinatorial verification procedures for core nonemptiness with tractable optimization-based criteria. The expressive power of the framework is illustrated through several representative applications. We show that it models cooperation in multi-agent optimal control, generalizes linear production games to nonlinear production settings such as Cobb--Douglas models, introduces cooperative formulations for portfolio selection under Markowitz, conditional value-at-risk, and entropic risk measures, and unifies a broad class of combinatorial optimization games through exact conic reformulations. These examples involve the most relevant cones in modern convex optimization, highlighting both the versatility of the proposed framework and its potential to strengthen the interaction between mathematical programming and cooperative game theory.

math.OC↗

arXiv2026

Optimal Embedding of Wiring Diagrams in Constrained Three-Dimensional Spaces

This paper investigates the \emph{Wiring Diagram Problem} (WDP), a three-dimensional layout design problem arising in industrial applications such as cable harness design and pipeline routing in constrained environments. In these settings, hierarchical tree-like systems composed of supply units, intermediate devices (e.g., valves or junctions), and terminal components must be spatially arranged and interconnected while satisfying stringent engineering requirements, including safety separation distances, obstacle avoidance, geometric feasibility, and constructibility constraints. We develop an optimization-based framework that formulates the WDP as a mixed-integer linear programming model capturing both topological and spatial design requirements within a unified formulation. To address the combinatorial and geometric complexity of three-dimensional routing, the feasible design space is discretized into structured network graphs that preserve engineering constraints while reducing dimensionality. The resulting model minimizes total cable or pipeline length while ensuring compliance with all technical specifications. Computational experiments on representative industrial instances demonstrate the robustness and practical applicability of the proposed approach for automated layout generation.

math.OC↗

arXiv2026

Exponential Conic Optimization for Multi-Regime Service System Design under Congestion and Tail-Risk Control

We study the design of single-facility service systems operating under multiple recurring regimes with service-level constraints on response times. Regime-dependent arrival and service rates induce hyperexponential response-time distributions, and the design problem selects regime-specific capacities to balance cost, congestion, fairness, and reliability. We propose a mixed-integer exponential conic optimization framework integrating SLA chance constraints, conflict-graph design restrictions, and CVaR-based tail-risk control. Although NP-hard, the problem admits an efficient decomposition scheme and tractable special cases. Computational experiments and a large-scale urban case study show substantial improvements over the current system, quantifying explicit trade-offs between efficiency, congestion control, fairness, and robustness. The framework provides a practical tool for congestion-aware and tail-control service system design.

math.OC↗

arXiv2026

Revisiting transportation problems under Monge costs with applications to location problems

We investigate the transportation problem under a Monge cost structure and derive compact formulas for optimal dual solutions based on the northwest-corner rule. As an application illustrating how these formulas yield structural insight while enhancing computational performance, we consider a broad class of facility location problems. In particular, the expressions are used within a Benders decomposition framework to derive novel formulations for the Discrete Ordered Median Problem with non-increasing weights. Numerical experiments validate that the resulting formulations achieve state-of-the-art performance and exhibit strong robustness across a wide range of instances.

math.OC↗

arXiv2025

Augmentation approaches for Mixed Integer Programming

This paper analyses the feasible sets structure of general mixed integer linear programs (MIPs) and its relationship with the existence of a finite cardinality test set which can be applied in augmentation algorithms. We derive and characterize a computable, finite test set for MIPs which can be embedded in a finite augmentation algorithm. Several examples illustrate the structure of this set and its relationship with previous approaches in the literature.

math.OC↗

arXiv2025

Exact Matrix Seriation through Mathematical Optimization: Stress and Effectiveness-Based Models

Matrix seriation, the problem of permuting the rows and columns of a matrix to uncover latent structure, is a fundamental technique in data science, particularly in the visualization and analysis of relational data. Applications span clustering, anomaly detection, and beyond. In this work, we present a unified framework grounded in mathematical optimization to address matrix seriation from a rigorous, model-based perspective. Our approach leverages combinatorial and mixed-integer optimization to represent seriation objectives and constraints with high fidelity, bridging the gap between traditional heuristic methods and exact solution techniques. We introduce new mathematical programming models for neighborhood-based stress criteria, including nonlinear formulations and their linearized counterparts. For structured settings such as Moore and von Neumann neighborhoods, we develop a novel Hamiltonian path-based reformulation that enables effective control over spatial arrangement and interpretability in the reordered matrix. To assess the practical impact of our models, we carry out an extensive set of experiments on synthetic and real-world datasets, as well as on a newly curated benchmark based on a coauthorship network from the matrix seriation literature. Our results show that these optimization-based formulations not only enhance solution quality and interpretability but also provide a versatile foundation for extending matrix seriation to new domains in data science.

math.OC↗

arXiv2025

Linear, nested, and quadratic ordered measures: Computation and incorporation into optimization problems

In this paper we address a unified mathematical optimization framework to compute a wide range of measures used in most operations research and data science contexts. The goal is to embed such metrics within general optimization models allowing their efficient computation. We assess the usefulness of this approach applying it to three different families of measures, namely linear, nested, and quadratic ordered measures. Computational results are reported showing the efficiency and accuracy of our methods as compared with standard implementations in numerical software packages. Finally, we illustrate this methodology by computing a number of optimal solutions with respect to different metrics on three well-known linear and combinatorial optimization problems: scenario analysis in linear programming, the traveling salesman and the weighted multicover set problem.

math.OC↗

arXiv2024

Optimal probabilistic feature shifts for reclassification in tree ensembles

In this paper we provide a novel mathematical optimization based methodology to perturb the features of a given observation to be re-classified, by a tree ensemble classification rule, to a certain desired class. The method is based on these facts: the most viable changes for an observation to reach the desired class do not always coincide with the closest distance point (in the feature space) of the target class; individuals put effort on a few number of features to reach the desired class; and each individual is endowed with a probability to change each of its features to a given value, which determines the overall probability of changing to the target class. Putting all together, we provide different methods to find the features where the individuals must exert effort to maximize the probability to reach the target class. Our method also allows us to rank the most important features in the tree-ensemble. The proposed methodology is tested on a real dataset, validating the proposal.

math.OC↗

arXiv2024

A fresh view on Least Quantile of Squares Regression based on new optimization approaches

Regression analysis is an important instrument to determine the effect of the explanatory variables on response variables. When outliers and bias errors are present, the standard weighted least squares estimator may perform poorly. For this reason, many alternative robust techniques have been studied in literature. In these terms, the Least Squares Quantile (LQS), and in particular the Least Squares Median, are among the regression estimators that exhibit better robustness properties. However, the accurate computation of this estimators is computationally demanding, resulting in a difficult estimator to obtain. In this paper, new novel approaches to compute a global optimal solution for the LQS estimator based on single-level and bilevel optimization methods are proposed. An extensive computational study is provided to support the efficiency of the methods considered, and an ad hoc procedure to address the scalability of the problem to larger instances is proposed.

stat.CO↗

arXiv2024

Fixed Topology Minimum-Length Trees with Neighborhoods

In this paper, we introduce the Fixed Topology Minimum-Length Tree with Neighborhood Problem, which aims to embed a rooted tree-shaped graph into a $d$-dimensional metric space while minimizing its total length provided that the nodes must be embedded to some restricted areas. This problem has significant applications in efficiently routing cables or pipelines in engineering designs. We propose novel mathematical optimization-based approaches to solve different versions of the problem based on the domain for the embedding. In cases where the embedding maps to a continuous space, we provide several Mixed Integer Nonlinear Optimization formulations. If the embedding is to a network, we derive a mixed integer linear programming formulation as well as a dimensionality reduction methodology that allows for solving larger problems in less CPU time. A data-driven methodology is also proposed to construct a proper network based on the instance of the problem. We report the results of a battery of computational experiments that validate our proposal.

math.OC↗

arXiv2024

Constraint relaxation for the Discrete Ordered Median Problem

This paper compares different exact approaches to solve the Discrete Ordered Median Problem (DOMP). In recent years, DOMP has been formulated using set packing constraints giving rise to one of its most promising formulations. The use of this family of constraints, known as strong order constraints (SOC), has been validated in the literature by its theoretical properties and because their linear relaxation provides very good lower bounds. Furthermore, embedded in branch-and-cut or branch-price-and-cut procedures as valid inequalities, they allow one to improve computational aspects of solution methods such as CPU time and use of memory. In spite of that, the above mentioned formulations require to include another family of order constraints, e.g., the weak order constraints (WOC), which leads to coefficient matrices with elements other than {0,1}. In this work, we develop a new approach that does not consider extra families of order constraints and furthermore relaxes SOC -- in a branch-and-cut procedure that does not start with a complete formulation -- to add them iteratively using row generation techniques to certify feasibility and optimality. Exhaustive computational experiments show that it is advisable to use row generation techniques in order to only consider {0,1}-coefficient matrices modeling the DOMP. Moreover, we test how to exploit the problem structure. Implementing an efficient separation of SOC using callbacks improves the solution performance. This allows us to deal with bigger instances than using fixed cuts/constraints pools automatically added by the solver in the branch-and-cut for SOC, concerning both the formulation based on WOC and the row generation procedure.

math.OC↗

arXiv2024

Dynamic Realization Games in Newsvendor Inventory Centralization

Consider a set N of n (>1) stores with single-item and single-period nondeterministic demands like in a classic newsvendor setting with holding and penalty costs only. Assume a risk-pooling single-warehouse centralized inventory ordering option. Allocation of costs in the centralized inventory ordering corresponds to modelling it as a cooperative cost game whose players are the stores. It has been shown that when holding and penalty costs are identical for all subsets of stores, the game based on optimal expected costs has a non empty core (Hartman et. al., 2000, Muller \textit{et. al.}, 2002). In this paper we examine a related inventory centralization game based on demand realizations that has, in general, an empty core even with identical penalty and holding costs (Hartman and Dror, 2005). We propose a repeated cost allocation scheme for dynamic realization games based on allocation processes introduced by Lehrer (2002a). We prove that the cost subsequences of the dynamic realization game process, based on Lehrer's rules, converge almost surely to either a least square value or the core of the expected game. We extend the above results to more general dynamic cost games and relax the independence hypothesis of the sequence of players' demands at different stages.

cs.GT↗

arXiv2024

Production-Inventory games: a new class of totally balanced combinatorial optimization games

In this paper we introduce a new class of cooperative games that arise from production-inventory problems. Several agents have to cover their demand over a finite time horizon and shortages are allowed. Each agent has its own unit production, inventory-holding and backlogging cost. Cooperation among agents is given by sharing production processes and warehouse facilities: agents in a coalition produce with \ the cheapest production cost and store with the cheapest inventory cost. We prove that the resulting cooperative game is totally balanced and the Owen set reduces to a singleton: the Owen point. Based on this type of allocation we find a population monotonic allocation scheme for this class of games. Finally, we point out the relationship of the Owen point with other well-known allocation rules such as the nucleolus and the Shapley value.

cs.GT↗

arXiv2024

Production-inventory games and pmas games: characterizations of the Owen point

Production-inventory games were introduced in Guardiola et al. (2007) as a new class of totally balanced combinatorial optimization games. From among all core-allocations, the Owen point was proposed as a specifically appealing solution. In this paper we study some relationships of the class of production-inventory games and other classes of new and known games. In addition, we propose three axiomatic characterizations of the Owen point. We use eight axioms for these characterizations, among those, inessentiality and additivity of players' demands are used for the first time in this paper.

cs.GT↗

arXiv2024

Unitary Owen points in cooperative lot-sizing models with backlogging

Cooperative lot-sizing models with backlogging and heterogeneous costs are studied in Guardiola et al. (2020). In this model several firms participate in a consortium aiming at satisfying their demand over the planing horizon with minimal operation cost. Each firm uses the best ordering channel and holding technology provided by the participants in the consortium. The authors show that there are always fair allocations of the overall operation cost among the firms so that no group of agents profit from leaving the consortium. This paper revisits those cooperative lot-sizing models and presents a new family of cost allocations, the unitary Owen points. This family is an extension of the Owen set which enjoys very good properties in production-inventory proble, introduced by Guardiola et al. (2008). Necessary and sufficient conditions are provided for the unitary Owen points to be fair allocations. In addition, we provide empirical evidence, throughout simulation, showing that the above condition is fulfilled in most cases. Additionally, a relationship between lot-sizing games and a certain family of production-inventory games, through Owen's points of the latter, is described. This interesting relationship enables to easily construct a variety of fair allocations for cooperative lot-sizing models.

cs.GT↗

arXiv2024

New approximate stochastic dominance approaches for Enhanced Indexation models

In this paper, we discuss portfolio selection strategies for Enhanced Indexation (EI), which are based on stochastic dominance relations. The goal is to select portfolios that stochastically dominate a given benchmark but that, at the same time, must generate some excess return with respect to a benchmark index. To achieve this goal, we propose a new methodology that selects portfolios using the ordered weighted average (OWA) operator, which generalizes previous approaches based on minimax selection rules and still leads to solving linear programming models. We also introduce a new type of approximate stochastic dominance rule and show that it implies the almost Second-order Stochastic Dominance (SSD) criterion proposed by Lizyayev and Ruszczynski (2012). We prove that our EI model based on OWA selects portfolios that dominate a given benchmark through this new form of stochastic dominance criterion. We test the performance of the obtained portfolios in an extensive empirical analysis based on real-world datasets. The computational results show that our proposed approach outperforms several SSD-based strategies widely used in the literature, as well as the global minimum variance portfolio.

q-fin.PM↗

arXiv2023

Budget-constrained cut problems

The minimum and maximum cuts of an undirected edge-weighted graph are classic problems in graph theory. While the Min-Cut Problem can be solved in P, the Max-Cut Problem is NP-Complete. Exact and heuristic methods have been developed for solving them. For both problems, we introduce a natural extension in which cutting an edge induces a cost. Our goal is to find a cut that minimizes the sum of the cut weights but, at the same time, restricts its total cut cost to a given budget. We prove that both restricted problems are NPComplete and we also study some of its properties. Finally, we develop exact algorithms to solve both as well as a non-exact algorithm for the min-cut case based on a Lagreangean relaxation that generally provides optimal solutions. Their performance is reported by an extensive computational experience.

math.CO↗

arXiv2023

Allocating the surplus induced by cooperation in distribution chains with multiple suppliers and retailers

The coordination of actions and the allocation of profit in supply chains under decentralized control play an important role in improving the profits of retailers and suppliers in the chain. We focus on supply chains under decentralized control in which noncompeting retailers can order from multiple suppliers to replenish their stocks. Suppliers' production capacity is bounded. The goal of the firms in the chain is to maximize their individual profits. As the outcome under decentralized control is inefficient, coordination of actions between cooperating agents can improve individual profits. Cooperative game theory is used to analyze cooperation between agents. We define multi-retailer-supplier games and show that agents can always achieve together an optimal profit and they have incentives to cooperate and to form the grand coalition. Moreover, we show that there always exist stable allocations of the total profit among the firms upon which no coalition can improve. Then we propose and characterize a stable allocation of the total surplus induced by cooperation.

cs.GT↗