arXiv subjects

Juan de Dios Jaime-Alcántara

Publications and source records attributed to Juan de Dios Jaime-Alcántara.

3 recordsLinked to original sources

arXiv2026

An optimization-based approach to ranking aggregation with weak order outputs

Rank aggregation problems combine conflicting rankings of items into a single consensus ranking. In many applications, forcing all items into a strict order is too restrictive, since some items may be tied and placed in the same ordered group. This paper presents an optimization framework for rank aggregation problems in which the final ranking is a weak order, or bucket order. The framework uses binary variables to indicate whether one item is ranked before another or tied with it, and allows additional requirements to be added through linear constraints. We consider settings with an exact number of buckets, given bucket sizes, a ranking of the top items with the remaining items grouped in a final bucket, and fairness requirements for predefined groups in the upper part of the ranking. As a case study, we apply the framework to the Optimal Bucket Order Problem (OBOP), which we formulate for the first time as a mixed-integer linear programming problem. Experiments on benchmark instances derived from PrefLib and MovieLens evaluate the proposed formulation and its constrained versions. They also show that the new OBOP formulation allows us to confirm the optimality of most best-known heuristic solutions and improves some of them.

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arXiv2026

Uncovering latent consensus in heterogeneous populations: The Mixture Linear Ordering Problem

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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arXiv2025

Stable formulations for the Capacitated Facility Location Problem with Customer Preferences

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 the 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. For this setting, 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 provide extensive computational experiments and compare the quality of our allocations with previous ones defined in the literature. As an additional result, we present a novel formulation that provides Pareto optimal matchings in the Capacitated House Allocation problem of maximum cardinality.

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