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Jaime Alcántara, Juan de Dios

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Jaime Alcántara, Juan de Dios
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Estadística e Investigación Operativa
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    Uncovering latent consensus in heterogeneous populations: The Mixture Linear Ordering Problem
    (2026) Aledo, Juan A.; Landete, Mercedes; Domínguez Sánchez, Concepción; Jaime Alcántara, Juan de Dios; Estadística e Investigación Operativa; Facultades de la UMU::Facultad de Matemáticas
    The classical linear ordering problem seeks a single ranking representing a given preference matrix. While suitable for homogeneous populations, it fails when observed preferences arise from several latent groups with distinct ranking patterns. To address this limitation, we introduce an extension partitioning the population into latent groups, each characterized by its own linear order, relative size, and preference structure. The observed matrix is then explained as the aggregate outcome of these group-specific preferences. We develop mixed-integer programming formulations, including a compact reformulation yielding a geometric interpretation within the linear ordering polytope. Because exact solutions become computationally demanding for larger instances, we propose a multi-start alternating-direction matheuristic iteratively updating group rankings and weights. Computational experiments on synthetically generated instances, matching sizes typical in preference aggregation scenarios, demonstrate the effectiveness of the exact approach in successfully recovering the underlying groups. Furthermore, the proposed heuristic delivers high-quality solutions in substantially shorter times, occasionally improving upon the exact method's best incumbent in difficult instances within the imposed time limit.
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    Stable formulations for the Capacitated Facility Location Problem with Customer Preferences
    (2026) Domínguez Sánchez, Concepción; Jaime Alcántara, Juan de Dios; Estadística e Investigación Operativa; Facultades de la UMU::Facultad de Matemáticas
    In the Simple Plant Location Problem with Order (SPLPO), the aim is to open a subset of plants to assign every customer taking into account their preferences. Customers rank the plants in strict order and are assigned to their favorite open plant, and the objective is to minimize the location plus allocation costs. Here, we study a generalization of SPLPO named the Capacitated Facility Location Problem with Customer Preferences (CFLCP) where a limited number of customers can be allocated to each facility. We consider the global preference maximization setting, where the customers preferences are globally maximized. We define three new types of stable allocations, namely customer stable, pairwise stable and cyclic-coalition stable allocations, and we provide two mixed-integer linear formulations for each setting. In particular, our cyclic-coalition stable formulations are Pareto optimal in a global-preference maximization setting, in the sense that no customer can improve their allocation without making another one worse off. We assess the performance of the proposed formulations and the quality of the resulting stable allocations through extensive computational experiments. As an additional contribution, we present a novel formulation that provides maximum-cardinality Pareto-optimal matchings for the Capacitated House Allocation problem.
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    An optimization-based approach to ranking aggregation with weak order outputs
    (2026) Aledo, Juan A.; Landete, Mercedes; Domínguez Sánchez, Concepción; Jaime Alcántara, Juan de Dios; Estadística e Investigación Operativa; Facultades de la UMU::Facultad de Matemáticas
    Rank aggregation problems combine individual orderings of a common set of items into a consensus ranking reflecting collective preferences. This paper introduces a general Integer Linear Programming (ILP) framework to model and solve aggregation problems whose solutions are weak orders (bucket orders). The framework provides a flexible and tractable architecture that incorporates structural and normative constraints required in practice. Within this setting, we develop several ILP formulations embedding additional structural requirements on the consensus bucket order, including a fixed number of buckets, predefined bucket sizes, top-$k$ constraints, and group-based fairness conditions. The formulations are modular and adaptable to different aggregation contexts. A particularly relevant case is the Optimal Bucket Order Problem (OBOP), for which we present the first exact mixed-integer linear programming formulation. We evaluate the models through computational experiments, comparing optimal solutions with the heuristics of Aledo et al.\ (2018) and assessing scalability on benchmark instances from the PrefLib library. Finally, we present a real-world case study on Spanish universities, where the proposed models aggregate competing rankings under structural and fairness constraints.
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