arXiv subjects

Balbina Casas-Méndez

Publications and source records attributed to Balbina Casas-Méndez.

3 recordsLinked to original sources

arXiv2024

Two-stage heuristic algorithm for a new variant of the multi-compartment vehicle routing problem with stochastic demands

This paper presents a model for a vehicle routing problem in which customer demands are stochastic and vehicles are divided into compartments. The problem is motivated by the needs of certain agricultural cooperatives that produce various types of livestock food. The vehicles and their compartments have different capacities, and each compartment can only contain one type of feed. Additionally, certain farms can only be accessed by specific vehicles, and there may be urgency constraints. To solve the problem, a two-step heuristic algorithm is proposed. First, a constructive heuristic is applied, followed by an improvement phase based on iterated tabu search. The designed algorithm is tested on several instances, including an analysis of real-world datasets where the results are compared with those provided by the model. Furthermore, multiple benchmark instances are created for this problem and an extensive simulation study is conducted. Results are presented for different model parameters, and it is shown that, despite the problems' complexity, the algorithm performs efficiently. Finally, the proposed heuristic is compared to existing solution algorithms for similar problems using benchmark instances from the literature, achieving competitive results.

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arXiv2024

On the influence of dependent features in classification problems: a game-theoretic perspective

This paper deals with a new measure of the influence of each feature on the response variable in classification problems, accounting for potential dependencies among certain feature subsets. Within this framework, we consider a sample of individuals characterized by specific features, each feature encompassing a finite range of values, and classified based on a binary response variable. This measure turns out to be an influence measure explored in existing literature and related to cooperative game theory. We provide an axiomatic characterization of our proposed influence measure by tailoring properties from the cooperative game theory to our specific context. Furthermore, we demonstrate that our influence measure becomes a general characterization of the well-known Banzhaf-Owen value for games with a priori unions, from the perspective of classification problems. The definitions and results presented herein are illustrated through numerical examples and various applications, offering practical insights into our methodologies.

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arXiv2023

Cost allocation problems on highways with grouped users

One of the practical applications of cooperative transferable utility games involves determining the fee structure for users of a given facility, whose construction or maintenance costs need to be recouped. In this context, certain efficiency and equity criteria guide the considered solutions. This paper analyzes how to allocate the fixed costs of a highway among its users through tolls, considering that different classes of vehicles or travelers utilize the service. For this purpose, we make use of generalized highway games with a priori unions that represent distinct user groups, such as frequent travelers or truckers, who, due to enhanced bargaining power, often secure reductions in their fares in real-world scenarios. In particular, the Owen value, the coalitional Tijs value, and a new value termed the Shapley-Tijs value, are axiomatically characterized. Additionally, straightforward formulations for calculating these values are provided. Finally, the proposed methodology is applied to actual traffic data from the AP-9 highway in Spain.

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