https://hdl.handle.net/11000/459 2026-07-24T12:10:37Z https://hdl.handle.net/11000/40207 Título : Under-capacitated p-median location problem Autor : Martín Melero, Iñigo; Gonçalves Dosantos, Juan Carlos; Landete, Mercedes; Sánchez Soriano, Joaquín Resumen : In many Location Science applications, a key challenge is the fair allocation of scarce resources among clients, especially in contexts such as disaster response, transportation planning, and healthcare systems. This challenge becomes particularly critical under severe capacity shortages, where not all demand can be satisfied, an aspect that has received limited attention in the existing literature. This paper studies the joint problem of locating p facilities from a set of candidates with heterogeneous, limited capacities and allocating indivisible resources (e.g., hospital beds) among clients. We propose a generalized capacitated p-median model that integrates location decisions with a fair allocation of insufficient capacity. Fairness is defined using concepts from bankruptcy theory in cooperative game theory, which are adapted to explicitly represent capacity scarcity. Several optimization models based on bankruptcy-inspired allocation rules are introduced and their theoretical properties are analyzed. We examine how different weights in the objective function affect the trade-offs between efficiency, equity, and network costs, and we compare bankruptcy-based allocations with alternative fairness rules. Extensions to divisible resources (e.g., water) are also discussed, and computational experiments are used to assess the impact of the proposed models on location decisions. The proposed framework is well suited for strategic and tactical planning under static and deterministic settings in which total capacity is insufficient to meet demand. Relative to classical p-median formulations and existing fairness-based benchmarks, the model explicitly represents demand shortfalls through bankruptcy-based allocation rules, leading to substantially fairer allocations while preserving high capacity utilization and competitive network costs. From a managerial perspective, the approach allows decision-makers to embed equity considerations directly into the planning stage, rather than relying on ad hoc rationing after facility locations are fixed. The practical relevance of the framework is illustrated through a real-world case study on food insecurity in Todd County, South Dakota, demonstrating its effectiveness in designing fair and efficient service networks under severe capacity shortages. 2026-07-16T08:51:24Z https://hdl.handle.net/11000/40206 Título : Assessments in public procurement procedures Autor : Martínez, Ricardo; Sánchez Soriano, Joaquín; Llorca, Natividad Resumen : In this paper we study how to assess the performance of a group of individuals according to their achievements in several attributes or categories by means of a scoring system. Such an assessment is the composition of two steps. First, each individual obtains a partial score in each category (that may potentially depend on her opponents’ performance). And second, those partial scores are combined into a global assessment. The partial score in each attribute is upper bounded by an exogenous threshold or cap. Each problem is determined by four elements: a set of agents (or tenders), a set of attributes to be evaluated, a matrix of achievements that specified the score each agent has obtained in each attribute, and a vector of caps. By means of the axiomatic methodology, we identify the families of assessment functions that satisfy some natural requirements (anonymity, continuity, monotonicity, null contribution, additivity, and separability). Our findings state that these families are weighted averages of the attribute assessments. Finally, as an illustration, we analyze a public tender whose purpose was to carry out an accounts auditing of a public company. As a practical implication of our theoretical results, we show that truncation presents significant advantages with respect to other methods. Particularly, it avoids the exclusion paradox. 2026-07-16T08:50:49Z https://hdl.handle.net/11000/40205 Título : Revenue distribution in streaming Autor : Gonçalves Dosantos, Juan Carlos; Martínez, Ricardo; Sánchez Soriano, Joaquín Resumen : The streaming industry has experienced exponential growth over the past decade. Streaming platforms provide subscribers with unlimited access to a diverse range of services, including movies, TV shows, and music, in exchange for a subscription fee. We take an axiomatic approach to the problem of how to share the overall revenue obtained from subscription sales among services or content producers. In doing so, we provide normative justifications for several distribution rules. We formulate several axioms that convey ethical and operational principles. In the first group, we consider properties that guarantee equal and impartial treatment of services and subscribers. In the second group, we introduce requirements designed to safeguard allocation schemes from inconvenient alterations, namely, changes in the units of measurement of inputs, subscription sharing, or group decomposition. Our analysis reveals that different combinations of these axioms define two classes of rules that strike a balance between three focal schemes, each representing distinct perspectives on the egalitarian and proportional principles. To illustrate the practical implications of our theoretical model, we explore its potential application by assessing how various types of content impact the revenues of some of the most well-known Twitch streamers. 2026-07-16T08:50:13Z https://hdl.handle.net/11000/40204 Título : Apportionment when seats are allocated in lots. The D’Hondt method case and political implications Autor : Gonçalves Dosantos, Juan Carlos; Sánchez Soriano, Joaquín Resumen : The apportionment problem involves determining how to distribute a given (non-negative) integer number among a group of individuals based on their respective sizes. In electoral systems with proportional representation, this problem arises in two situations: assigning seats to constituencies, if applicable, and distributing seats to political parties within each constituency. This paper addresses the scenario where seats are grouped into lots, extending the standard apportionment problem. We propose and analyze various apportionment methods based on the D’Hondt method for this new problem. Additionally, we examine the political implications of allocating seats not individually but in groups of varying sizes. 2026-07-16T08:49:30Z https://hdl.handle.net/11000/40203 Título : Families of sequential priority rules and random arrival rules with withdrawal limits Autor : Sánchez Soriano, Joaquín Resumen : This paper deals with extensions of the family of sequential priority rules and the random arrival rule for bankruptcy problems when withdrawal limits are fixed by an arbitrator. We assume two approaches to limit withdrawals. The first is based on the principle that agents can only obtain at most a fixed part of the endowment each time they qualify for an award, and the second that agents can only receive at most a proportion of their claims each time they are attended. For each approach we introduce two pairs of families, each consisting of a sequential priority rule-like family and a random arrival rule-like family. Applying the first approach, we show that the constrained equal awards rule belongs to each of the families. In the second, we prove the same for the proportional rule. We study in detail one pair of families for each approach, and the others are examined in relation to them. 2026-07-16T08:48:54Z https://hdl.handle.net/11000/40202 Título : Incremental Decision Rules Algorithm: A Probabilistic and Dynamic Approach to Decisional Data Stream Problems Autor : Mollá, Nuria; Rabasa, Alejandro; Rodríguez Sala, Jesús J.; Sánchez Soriano, Joaquín; Ferrándiz, Antonio Resumen : Data science is currently one of the most promising fields used to support the decision-making process. Particularly, data streams can give these supportive systems an updated base of knowledge that allows experts to make decisions with updated models. Incremental Decision Rules Algorithm (IDRA) proposes a new incremental decision-rule method based on the classical ID3 approach to generating and updating a rule set. This algorithm is a novel approach designed to fit a Decision Support System (DSS) whose motivation is to give accurate responses in an affordable time for a decision situation. This work includes several experiments that compare IDRA with the classical static but optimized ID3 (CREA) and the adaptive method VFDR. A battery of scenarios with different error types and rates are proposed to compare these three algorithms. IDRA improves the accuracies of VFDR and CREA in most common cases for the simulated data streams used in this work. In particular, the proposed technique has proven to perform better in those scenarios with no error, low noise, or high-impact concept drifts. 2026-07-16T08:47:02Z https://hdl.handle.net/11000/40192 Título : Mathematical indices for the influence of risk factors on the lethality of a disease Autor : Martínez, Ricardo; Sánchez Soriano, Joaquín Resumen : We develop a theoretical model to measure the relative relevance of different pathologies of the lethality of a disease in society. This approach allows a ranking of diseases to be determined, which can assist in establishing priorities for vaccination campaigns or prevention strategies. Among all possible measurements, we identify three families of rules that satisfy a combination of relevant properties: neutrality, irrelevance, and one of three composition concepts. One of these families includes, for instance, the Shapley value of the associated cooperative game. The other two families also include simple and intuitive indices. As an illustration, we measure the relative relevance of several pathologies in lethality due to COVID-19. 2026-07-14T08:22:08Z https://hdl.handle.net/11000/40191 Título : Measuring success in streaming platforms Autor : Gonçalves Dosantos, Juan Carlos; Martínez, Ricardo; Sánchez Soriano, Joaquín Resumen : Digital streaming platforms , including Twitch, Spotify, Netflix, Disney+, and Kindle, have emerged as major sources of entertainment with significant growth potential. Many of these platforms distribute royalties among streamers, artists, producers, or writers based on their impact. In this paper, we measure the relevance of each of these contributors to the overall success of the platform, which can play a key role in revenue allocation. We perform an axiomatic analysis to provide normative foundations for four relevance metrics: the uniform, the subscriber-uniform, the proportional, and the subscriber-proportional indicators. The last two indicators implement the so-called pro-rata and user-centric models, which are extensively applied to distribute revenues in the music streaming market. The axioms we propose formalize different principles of fairness, stability, and non-manipulability, and are tailor-made for the streaming context. We complete our analysis with a case study that measures the influence of the 19 most-followed streamers worldwide on the Twitch platform. 2026-07-14T08:21:05Z https://hdl.handle.net/11000/40190 Título : The museum pass problem with consortia Autor : Gonçalves Dosantos, Juan Carlos; Martínez, Ricardo; Sánchez Soriano, Joaquín Resumen : In this paper, we extend the museum pass problem to incorporate the market structure. To be more precise, we consider that museums are organized into several pass programs or consortia. Within this framework, we propose four allocation mechanisms based on the market structure and the principles of proportionality and egalitarianism. Each mechanism satisfies a distinct set of reasonable properties related to fairness and stability, which serve to axiomatically characterize them. 2026-07-14T08:20:22Z https://hdl.handle.net/11000/40189 Título : Benchmarking Analysis of the Accuracy of Classification Methods Related to Entropy Autor : Orenes, Yolanda; Rabasa, Alejandro; Rodríguez Sala, Jesús Javier; Sánchez Soriano, Joaquín Resumen : In the machine learning literature we can find numerous methods to solve classification problems. We propose two new performance measures to analyze such methods. These measures are defined by using the concept of proportional reduction of classification error with respect to three benchmark classifiers, the random and two intuitive classifiers which are based on how a non-expert person could realize classification simply by applying a frequentist approach. We show that these three simple methods are closely related to different aspects of the entropy of the dataset. Therefore, these measures account somewhat for entropy in the dataset when evaluating the performance of classifiers. This allows us to measure the improvement in the classification results compared to simple methods, and at the same time how entropy affects classification capacity. To illustrate how these new performance measures can be used to analyze classifiers taking into account the entropy of the dataset, we carry out an intensive experiment in which we use the well-known J48 algorithm, and a UCI repository dataset on which we have previously selected a subset of the most relevant attributes. Then we carry out an extensive experiment in which we consider four heuristic classifiers, and 11 datasets. 2026-07-14T08:19:39Z