Robust DEA efficiency scores: A probabilistic/combinatorial approach

In this paper we propose robust efficiency scores for the scenario in which the specification of the inputs/outputs to be included in the DEA model is modelled with a probability distribution. This proba- bilistic approach allows us to obtain three different robust efficiency scores: the Conditional Expected Score, the Unconditional Expected Score and the Expected score under the assumption of Maximum Entropy principle. The calculation of the three efficiency scores involves the resolution of an exponential number of linear problems. The algorithm presented in this paper allows to solve over 200 millions of linear problems in an affordable time when considering up 20 inputs/outputs and 200 DMUs. The approach proposed is illustrated with an application to the assessment of professional tennis players

Hicieron historia Martine Labbé

Martine Labbé es una matemática belga conocida por sustrabajos en investigación operativa. A día de hoy, es profesorahonoraria del Departamento de Ciencia Computacional de laUniversidad Libre de Brusela

Formulations and valid inequalities for the capacitated dispersion problem

This work focuses on the capacitated dispersion problem for which we study several mathematical formulations in different spaces using variables associated with nodes, edges, and costs. The relationships among the presented formulations are investigated by comparing the projections of the feasible sets of the LP relaxations onto the subspace of natural variables. These formulations are then strengthened with families of valid inequalities and variable-fixing procedures. The separation problems associated with the valid inequalities that are exponential in number are shown to be polynomially solvable by reducing them to longest path problems in acyclic graphs. The dual bounds obtained from stronger but larger formulations are used to improve the strength of weaker but smaller formulations. Several sets of computational experiments are conducted to illustrate the usefulness of the findings, as well as the aptness of the formulations for different types of instances

An exact approach for the reliable fixed-charge location problem with capacity constraints

Introducing capacities in the reliable fixed charge location problem is a complex task since successive failures might yield in high facility overloads. Ideally, the goal consists in minimizing the total cost while keeping the expected facility overloads under a given threshold. Several heuristic approaches have been proposed in the literature for dealing with this goal. In this paper, we present the first exact approach for this problem, which is based on a cutting planes algorithm. Computational results illustrate its good performancePostprint (published version

Introducing capacitaties in the location of unreliable facilities

The goal of this paper is to introduce facility capacities into the Reliability Fixed-Charge Location Problem in a sensible way. To this end, we develop and compare different models, which represent a tradeoff between the extreme models currently available in the literature, where a priori assignments are either fixed, or can be fully modified after failures occur. In a series of computational experiments we analyze the obtained solutions and study the price of introducing capacity constraints according to the alternative models both, in terms of computational burden and of solution cost.Peer ReviewedPostprint (author's final draft

Rank aggregation in cyclic sequences

In this paper we propose the problem of finding the cyclic sequence which best represents a set of cyclic sequences. Given a set of elements and a precedence cost matrix we look for the cyclic sequence of the elements which is at minimum distance from all the ranks when the permutation metric distance is the Kendall Tau distance. In other words, the problem consists of finding a robust cyclic rank with respect to a set of elements. This problem originates from the Rank Aggregation Problem for combining different linear ranks of elements. Later we define a probability measure based on dissimilarity between cyclic sequences based on the Kendall Tau distance. Next, we also introduce the problem of finding the cyclic sequence with minimum expected cost with respect to that probability measure. Finally, we establish certain relationships among some classical problems and the new problems that we have proposed.Ministerio de Economía y CompetitividadJunta de AndalucíaFondo Europeo de Desarrollo Regiona

SARS-CoV-2 Infection in Multiple Sclerosis

To understand COVID-19 characteristics in people with multiple sclerosis (MS) and identify high-risk individuals due to their immunocompromised state resulting from the use of disease-modifying treatments. Retrospective and multicenter registry in patients with MS with suspected or confirmed COVID-19 diagnosis and available disease course (mild = ambulatory; severe = hospitalization; and critical = intensive care unit/death). Cases were analyzed for associations between MS characteristics and COVID-19 course and for identifying risk factors for a fatal outcome. Of the 326 patients analyzed, 120 were cases confirmed by real-time PCR, 34 by a serologic test, and 205 were suspected. Sixty-nine patients (21.3%) developed severe infection, 10 (3%) critical, and 7 (2.1%) died. Ambulatory patients were higher in relapsing MS forms, treated with injectables and oral first-line agents, whereas more severe cases were observed in patients on pulsed immunosuppressors and critical cases among patients with no therapy. Severe and critical infections were more likely to affect older males with comorbidities, with progressive MS forms, a longer disease course, and higher disability. Fifteen of 33 patients treated with rituximab were hospitalized. Four deceased patients have progressive MS, 5 were not receiving MS therapy, and 2 were treated (natalizumab and rituximab). Multivariate analysis showed age (OR 1.09, 95% CI, 1.04-1.17) as the only independent risk factor for a fatal outcome. This study has not demonstrated the presumed critical role of MS therapy in the course of COVID-19 but evidenced that people with MS with advanced age and disease, in progressive course, and those who are more disabled have a higher probability of severe and even fatal diseas

Obtención de facetas de poliedros asociados a problemas de empaquetamientos / Mercedes Landete Ruiz ; directores Alfredo Marín Pérez, Lázaro Cánovas Martínez.

Tesis-Universidad de Murcia.Consulte la tesis en: BCA. GENERAL. DEPOSITO. T.M-2169

The Domatic Partition Problem in Separable Graphs

The domatic partition problem consists of partitioning a given graph into a maximum number of disjoint dominating sets. This problem is related with the domatic number problem, which consists of quantifying this maximum number of disjoint dominating sets. Both problems were proved to be NP-complete. In this paper, we present a decomposition algorithm for finding a domatic partition on separable graphs, that is, on graphs with blocks, and as a consequence, its domatic number, highly reducing the computational complexity. Computational results illustrate the benefits of the block decomposition algorithm