Robust positioning of service units

In this paper, we address the problem of locating mobile service units to cover random incidents. The model does not assume complete knowledge of the probability distribution of the location of the incident to be covered. Instead, only the mean value of that distribution is known. We propose the minimization of the maximum expected response time as an effectiveness measure for the model. Thus, the solution obtained is robust with respect to any probability distribution. The cases of one and two service units under the nearest allocation rule are studied in the paper. For both problems, the optimal solutions are shown to be degenerate distributions for the servers

On the exponential cardinality of FDS for the ordered p-median problem

We study finite dominating sets (FDS) for the ordered median problem. This kind of problems allows to deal simultaneously with a large number of models. We show that there is no valid polynomial size FDS for the general multifacility version of this problem even on path networks

Modelos de localización continua

En este trabajo se revisan tres modelos de problemas de localización continua: (1) un problema general de localización con respecto a regiones de demanda; (2) el problema de la mediana ordenada y (3) un problema de localización multiobjetivo. Con ellos se pretende dar una amplia muestra de los problemas que aparecen en el ámbito de la Teoría de Localización continua, así como estudiar propiedades que permitan caracterizar los conjuntos de soluciones. El trabajo incluye una larga lista de referencias que facilitarán al lector adentrarse más profundamente en éstos y otros modelos de la Teoría de Localización.Ministerio de Ciencia y Tecnologí

New results on minimax regret single facility ordered median location problems on networks

We consider the single facility ordered median location problem with uncertainty in the parameters (weights) defining the objective function. We study two cases. In the first case the uncertain weights belong to a region with a finite number of extreme points, and in the second case they must also satisfy some order constraints and belong to some box, (convex case). To deal with the uncertainty we apply the minimax regret approach, providing strongly polynomial time algorithms to solve these problems

Robust mean absolute deviation problems on networks with linear vertex weights

This article deals with incorporating the mean absolute deviation objective function in several robust single facility location models on networks with dynamic evolution of node weights, which are modeled by means of linear functions of a parameter. Specifically, we have considered two robustness criteria applied to the mean absolute deviation problem: the MinMax criterion, and the MinMax regret criterion. For solving the corresponding optimization problems, exact algorithms have been proposed and their complexities have been also analyzed.Ministerio de Ciencia e Innovación MTM2007-67433-C02-(01,02)Ministerio de Ciencia e Innovación MTM2009-14243Ministerio de Ciencia e Innovación MTM2010-19576-C02-(01,02)Ministerio de Ciencia e Innovación DE2009-0057Junta de Andalucía P09-TEP-5022Junta de Andalucía FQM-584

Reformulated acyclic partitioning for rail-rail containers transshipment

Many rail terminals have loading areas that are properly equipped to move containers between trains. With the growing throughput of these terminals all the trains involved in a sequence of such movements may not ¿t in the loading area simultaneously, and storage areas are needed to place containers waiting for their destination train, although this storage increases the cost of the transshipment. This increases the complexity of the planning decisions concerning these activities, since now trains need to be packed in groups that ¿t in the loading area, in such a way that the number of containers moved to the storage area is minimized. Additionally, each train is only allowed to enter the loading area once. Similarly to previous authors, we model this situation as an acyclic graph partitioning problem for which we present a new formulation, and several valid inequalities based on its theoretical properties. Our computational experiments show that the new formulation outperforms the previously existing ones, providing results that improve even on the best exact algorithm designed so far for this problem.Peer ReviewedPostprint (author's final draft

The probabilistic p-center problem: Planning service for potential customers

This work deals with the probabilistic p-center problem, which aims at minimizing the expected maximum distance between any site with demand and its center, considering that each site has demand with a specific probability. The problem is of interest when emergencies may occur at predefined sites with known probabilities. For this problem we propose and analyze different formulations as well as a Variable Neighborhood Search heuristic. Computational tests are reported, showing the potentials and limits of each formulation, the impact of their enhancements, and the effectiveness of the heuristic.Peer ReviewedPostprint (author's final draft

A mathematical programming approach to overlapping community detection

We propose a new optimization model to detect overlapping communities in networks. The model elaborates suggestions contained in Zhang et al. (2007), in which overlapping communities were identified through the use of a fuzzy membership function, calculated as the outcome of a mathematical programming problem. In our approach, we retain the idea of using both mathematical programming and fuzzy membership to detect overlapping communities, but we replace the fuzzy objective function proposed there with another one, based on the Newman and Girvan's definition of modularity. Next, we formulate a new mixed-integer linear programming model to calculate optimal overlapping communities. After some computational tests, we provide some evidence that our new proposal can fix some biases of the previous model, that is, its tendency of calculating communities composed of almost all nodes. Conversely, our new model can reveal other structural properties, such as nodes or communities acting as bridges between communities. Finally, as mathematical programming can be used only for moderate size networks due to its computation time, we proposed two heuristic algorithms to solve the largest instances, that compare favourably to other methodologies. (c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Upgrading edges in the maximal covering location problem

We study the upgrading version of the maximal covering location problem with edge length modifications on networks. This problem aims at locating p facilities on the vertices (of the network) so as to maximise coverage, considering that the length of the edges can be reduced at a cost, subject to a given budget. Hence, we have to decide on: the optimal location of p facilities and the optimal edge length reductions. This problem is NP-hard on general graphs. To solve it, we propose three different mixed-integer formulations and a preprocessing phase for fixing variables and removing some of the constraints. Moreover, we strengthen the proposed formulations including valid inequalities. Finally, we compare the three formulations and their corresponding improvements by testing their performance over different datasets. © 2022 The Author(s