ED Mathématiques et Informatique
Branch-cut-and-price methods for the Inventory Routing Problem
by Isaac BALSTER (IMB - Institut de Mathématiques de Bordeaux)
The defense will take place at 14h00 - 2 Institut de Mathématiques de Bordeaux UMR 5251 Université de Bordeaux 351, Cours de la Libération F-33405 TALENCE
in front of the jury composed of
- Francois CLAUTIAUX - Directeur de recherche - Université de Bordeaux - Directeur de these
- Frédéric SEMET - Full professor - Université de Lille - Examinateur
- Frédéric MEUNIER - Professeur - École nationale des ponts et chaussées - Examinateur
- Aurélien FROGER - Associate Professor - Université de Bordeaux - Examinateur
- Leandro COELHO - Full professor - Université Laval - Rapporteur
- Claudia ARCHETTI - Associate Professor - University of Brescia - Rapporteur
Vehicle routing problems (VRPs) are a fundamental piece of logistics planning. Exact methods for the classic capacitated VRP (CVRP) have seen significant advancements over the last ten years, pushing the boundaries of problem sizes that can be efficiently solved to optimality. Standard benchmark CVRP instances having hundreds of customers can be solved to proven optimality within seconds or a few minutes. Nevertheless, the picture is far less promising for other CVRP variants, especially variants that embed delivery decisions in the modelling. For some of these problems, instances with fewer than one hundred – or even a few dozen – customers can be challenging enough. We develop Branch-cut-and-price (BCP) algorithms, the current state-of-the-art approach for solving CVRP problems exactly, for two VRP variants with delivery decisions, namely the split delivery VRP with (SDVRPTW) or without time windows (SDVRP), and the inventory routing problem (IRP). For these problems, the best performing approaches in the literature are mainly Branch-and-cut (B&C) algorithms. Thus, we aim at designing BCP algorithms, adapting state-of-the-art BCP algorithmic components designed for the CVRP to these problems, to assess whether these algorithms can solve large instances and be competitive with tailored B&C for these problems. For the SDVRP, we propose a family of partially discretised formulations representing different delivery quantities to customers. For these formulations, the delivery quantities are not explicitly known, and validity is ensured by an exponential set of non-robust constraints. Only for the fully discretised formulation, where each delivery quantity is represented, the addition of non-robust inequalities is optional. We propose new variants of non-robust cutting planes that strengthen the formulations, namely limited-memory subset-row covering inequalities and limited-memory strong $k$-path inequalities. We show how to effectively manage the non-robust cuts when solving the pricing problem, generating route variables dynamically. Numerical results indicate that our formulations and BCP algorithm establish a new state-of-the-art for the SDVRPTW, as many benchmark instances with 50 and 100 customers are solved to optimality for the first time. We also show competitive results for the SDVRP, proving optimality for the first time for several instances as well. For the IRP, we present theoretical findings: a fully discretised formulation with sub-deliveries information, and the description of a BCP algorithm to solve it. A new family of inequalities for the IRP is presented, which generalises known families of inequalities for the problem and is comparable with the rounded capacity cuts adapted for the problem. Computational tests are left to future work. Results for the split delivery variants show that carefully crafted BCP algorithms can be competitive – often dominant – over B&C codes for a very relevant class of VRP problems. Future work will extend these ideas to computational testing on IRP benchmarks.
ED Sociétés, Politique, Santé Publique
Factors and Markers of Tuberculosis Severity in HIV-infected Adults
by Robert AKPATA (Bordeaux Population Health Research Center)
The defense will take place at 14h00 - Salle de visioconférence n°4 Université de Bordeaux - Campus Carreire, 146 Rue Léo Saignat, 33000 Bordeaux
in front of the jury composed of
- Olivier MARCY - Directeur de recherche - Université de Bordeaux - Directeur de these
- Maryline BONNET - Directrice de recherche - TransVIHMI (IRD, Inserm & Montpellier University), Institut de Recherche pour le Développement (IRD) - Rapporteur
- Prudence WACHINOU - Professeur des universités - praticien hospitalier - Université d'Abomey-Calavi - Rapporteur
- Xavier ANGLARET - Directeur de recherche émérite - Université de Bordeaux - Examinateur
- Alima BAKAYOKO-YEO - Professeur des universités - praticien hospitalier - Université Félix-Houphouët-Boigny - Examinateur
- Lorenzo GUGLIELMETTI - Docteur - Sorbonne Université - Examinateur
- Nathalie DE CASTRO - Praticienne hospitalière - Université de Bordeaux - Examinateur
- Marcel ZANNOU - Professeur des universités - praticien hospitalier - Université d'Abomey-Calavi - CoDirecteur de these
Tuberculosis is the leading opportunistic infection and the leading cause of early mortality among people living with HIV (PLHIV). Early identification of PLHIV with severe TB disease could help improve their care. However, existing tuberculosis severity scores may not be optimal when applied to PLHIV because only a small proportion were specifically developed for this population, and the available ones do not include key disease features such as dissemination, extent of pulmonary involvement, and bacillary load. Our primary objective was to propose a consensual multifactorial tuberculosis severity score specifically tailored for PLHIV that includes all these features. Using data from the ANRS 12300 Reflate TB2 trial and the Global TB Sentinel Research Network (TB-SRN) cohort, and the RAND/UCLA Appropriateness Method combining the best available scientific evidence in the literature with the collective judgment of a multidisciplinary panel of international experts from high and low HIV and tuberculosis prevalence settings following a modified Delphi process, we developed a consensual Multifactorial Tuberculosis Severity Score (MTSS) that integrates 15 parameters: proportion of pulmonary involvement, number of cavitations, urinary LAM, extrapulmonary involvement, microscopy positivity level, hemoptysis, dyspnea, respiratory rate, pulse oxygen saturation, body mass index, functional status, hemoglobin, CD4 count, number of concomitant opportunistic infections, and comorbidities. The MTSS could simplify the rapid detection of the most serious patients and improve their management, particularly through closer medical monitoring or differentiated treatment options, thus contributing to a significant reduction in tuberculosis mortality among PLHIV. From an epidemiological perspective, the MTSS could also allow for better classification of tuberculosis severity and its comparison between different studies. However, further validation studies are needed before it can be recommended for routine use. Keywords : Tuberculosis, HIV, severity