A polynomial time algorithm for makespan minimization on one machine with forbidden start and completion times

International audienceWe consider the problem of scheduling independent jobs on a single resource under a special unavailability constraint: a set of forbidden instants is given, where no job is allowed to start or complete. We show that a schedule without idle time always exists if the number of forbidden instants is less than the number of distinct processing times appearing in the instance. We derive quite a fast algorithm to find such a schedule, based on an hybridization between a list algorithm and local exchange. As a corollary minimizing the makespan for a fixed number of forbidden instants is polynomia

Minimisation des conflits aériens par des modulations de vitesse

Afin de pouvoir subvenir aux futurs besoins en matière de transport aérien il est nécessaire d'augmenter la capacité de l'espace aérien. Les contrôleurs aériens, qui occupent une place centrale dans la gestion du trafic, doivent quotidiennement faire face à des situations conflictuelles (conflits) lors desquelles deux vols risquent de violer les normes de séparation en vigueur si aucune modification de trajectoire n'est envisagée. La détection et la résolution des conflits potentiels contribuent à augmenter la charge de travail des contrôleurs et peuvent potentiellement les conduire à diriger les vols vers des zones moins denses de l'espace aérien, induisant a posteriori un retard pour les vols. Le problème de la capacité de l'espace aérien peut donc être abordé en régulant les flux de trafic de façon réduire la quantité de conflits aériens. L'objectif de cette thèse est de mettre au point une méthodologie destinée à minimiser les risques de conflits aériens en modifiant légèrement les vitesses des appareils. Cette approche est principalement motivée par les conclusions du projet ERASMUS portant sur la régulation de vitesse subliminale. Ce type de régulation a été conçu de façon à ne pas perturber les contrôleurs aériens dans leur tâche. En utilisant de faibles modulations de vitesse, imperceptibles par les contrôleurs aériens, les trajectoires des vols peuvent être modifiées pour minimiser la quantité totale de conflits et ainsi faciliter l'écoulement du trafic dans le réseau aérien. La méthode retenue pour mettre en œuvre ce type de régulation est l'optimisation sous contrainte. Dans cette thèse, nous développons un modèle d'optimisation déterministe pour traiter les conflits à deux avions. Ce modèle est par la suite adapté à la résolution de grandes instances de trafic en formulant le modèle comme un Programme Linéaire en Nombres Entiers. Pour reproduire des conditions de trafic réalistes, nous introduisons une perturbation sur la vitesse des vols, destinée à représenter l'impact de l'incertitude en prévision de trajectoire dans la gestion du trafic aérien. Pour valider notre approche, nous utilisons un outil de simulation capable de rejouer des journées entières de trafic au dessus de l'espace aérien européen. Les principaux résultats de ce travail démontrent les performances du modèle de détection et de résolution de conflits et soulignent la robustesse de la formulation face à l'incertitude en prévision de trajectoire. Enfin, l'impact de notre approche est évalué à travers divers indicateurs propres à la gestion du trafic aérien et valide la méthodologie développée.As global air traffic volume is continuously increasing, it has become a priority to improve air traffic control in order to deal with future air traffic demand. One of the current challenges regarding air traffic management is the airspace capacity problem, which is acknowledged to be correlated to air traffic controllers' workload. Air traffic controllers stand at the core of the traffic monitoring system and one of their main objective is to ensure the separation of aircraft by anticipating potential conflicts. Conflict detection and resolution are likely to increase workload and may lead them to reroute aircrafts to less dense areas, triggering off flight delay. The airspace capacity problem can hence be tackled by regulating air traffic flow in order to reduce the global conflict quantity. The objective of this thesis is to develop a methodology aiming at minimizing potential conflicts quantity by slightly adjusting aircraft speeds in real time. This approach is mainly motivated by conclusions of the ERASMUS project on subliminal speed control, which was designed to keep air traffic controllers unaware of the ongoing regulation process. By focusing on low magnitude speed modulations, aircraft trajectories can be modified to reduce the quantity of conflicts and smoothen air traffic flow in the airspace network. The method used to carry out this type of regulation is constraint optimization. In this thesis, we develop a deterministic optimization model for two-aircraft conflicts which is then adapted to large scale instances using Mixed-Integer Linear Programming. In order to reproduce realistic navigation conditions, uncertainty on aircraft speeds is introduced with the goal of modeling the impact of trajectory prediction uncertainty in air traffic management. To validate our approach, a simulation device capable of simulating real air traffic data over the European airspace is used. Main results of this work reveal a significant conflict quantity reduction and demonstrate the robustness of the developed model to the uncertainty in trajectory prediction. Finally, the impact of our model on air traffic flow is measured through several air traffic management indicators and validates the proposed methodology.SAVOIE-SCD - Bib.électronique (730659901) / SudocGRENOBLE1/INP-Bib.électronique (384210012) / SudocGRENOBLE2/3-Bib.électronique (384219901) / SudocSudocFranceF

Algorithmes d'approximation pour la gestion de stock

Nous considérons des problèmes de gestion des stocks multi-échelon à temps périodique avec des demandes non stationnaires. Ces hypothèses sur la demande apparaissent notamment lorsque des prévisions sur la demande sont utilisées dynamiquement (de nouvelles prévisions sont fournies à chaque période). La structure des coûts comprend des coûts fixes et variables d approvisionnement, des coûts de stockage et des coûts de mise en attente des demandes. Le délai d approvisionnement est supposé constant. Le problème consistant à déterminer la politique optimale qui minimise les coûts sur un horizon fini peut être formulé grâce à un programme dynamique. Dans le cadre déterministe, les problèmes auxquels nous nous intéressons sont le plus souvent NP-difficiles, ce qui fait rapidement exploser l espace d état. Il devient alors nécessaire de recourir à des heuristiques. Nous nous orientons vers la recherche d'algorithmes d'approximation combinatoires pour le problème One Warehouse Multi Retailers et plus généralement pour des systèmes de distribution divergents. Nous nous intéresserons dans un premier temps à des systèmes de distribution à deux étages avec un entrepôt central et des entrepôts secondaires qui voient la demande finale. Dans un deuxième temps, des structures logistiques plus complexes pourront être considérées. L objectif sera de proposer des heuristiques originales, basées sur des techniques de répartition des coûts, de les comparer numériquement à la politique optimale sur de petites instances et, si possible, d établir des garanties de performance.Inventory management has always been a major component of the field of operations research and numerous models derived from the industry aroused the interest of both the researchers and the practitioners. Within this framework, our work focuses on several classical inventory problems, for which no tractable method is known to compute an optimal solution. Specifically, we study deterministic models, in which the demands of the customers are known in advance, and we propose approximation techniques for each of the corresponding problems that build feasible approximate solutions while remaining computationally tractable. We first consider continuous-time models with a single facility when demand and holding costs are time-dependent. We present a simple technique that balances the different costs incurred by the system and we use this concept to build approximation methods for a large class of such problems. The second part of our work focuses on a discrete time model, in which a central warehouse supplies several retailers facing the final customers demands. This problem is known to be NP-hard, thus finding an optimal solution in polynomial time is unrealistic unless P=NP. We introduce a new decomposition of the system into simple subproblems and a method to recombine the solutions to these subproblems into a feasible solution to the original problem. The resulting algorithm has a constant performance guarantee and can be extended to several generalizations of the system, including more general cost structures and problems with backlogging or lost-sales.SAVOIE-SCD - Bib.électronique (730659901) / SudocGRENOBLE1/INP-Bib.électronique (384210012) / SudocGRENOBLE2/3-Bib.électronique (384219901) / SudocSudocFranceF

Adaptive and Hybrid Algorithms: classification and illustration on triangular system solving

International audienceWe propose in this article a classification of the different notions of hybridization and a generic framework for the automatic hybridization of algorithms. Then, we detail the results of this generic framework on the example of the parallel solution of multiple linear systems

An efficient algorithm for the 2-level capacitated lot-sizing problem with identical capacities at both levels

International audienc

Graph decomposition into paths under length constraints

Given 2 integers a and b, we define an (a,b)-decomposition of a graph G =(V,E) as a partition of E into paths where the length of each path lies between a and b. In this definition paths are requested to be simple but not necessarily elementary. In other words an (a,b)-decomposition corresponds to a partition E1,...,Ek of E with a = 3, we identify 2 classes of graphs, trees and Eulerian graphs, for which the (a,b)-decomposition problem remains polynomial. However we prove that the (3,3)-decomposition problem is NP-complete, even on bipartite graphs. We give some evidence to conjecture that the more general H-decomposition problem into a given family H = H1,...,Hn of connected graphs is NP-complete if and only if all Hi-decomposition problems are NP-complete

Polynomial time algorithms for constant capacitated lot sizing problems with equal length step-wise linear costs

This paper presents polynomial time algorithms for three extensions of the classical capacitated lot sizing problem (CLSP). We consider a constant batch size production with a fixed cost associated to each batch, additionally to the production setup cost and a unit holding cost. The production cost can then be considered as a step-wise function where the step length corresponds to the batch size. We can no more use the efficient methods proposed for the CLSP with concave costs in order to solve the CLSP with step-wise costs. We propose several properties of optimal solutions. Based on these properties, three polynomial time algorithms are provided under the assumptions of constant production capacity and constant batch sizes, as well as linear and non-increasing production costs over time. The uncapacitated case is solved in time complexity O(T^3). For the constant capacitated case, with a production capacity multiple of the batch size, the algorithm has a time complexity in O(T^4). The final algorithm concerns the general constant capacitated case, and has a time complexity in O(T^6)

Ordonnancement sur une machine avec instants interdits de début et de fin des tâches

National audienc

Polynomial time algorithm for multi-level in series capacitated lot-sizing problems with constant batch size

International audienceWe consider a multi-level lot-sizing problem in a serial distribution network. Customers demands are to be satisfied at the last level of the network. At each level, units can be carried in stock, and the inventory is replenished from the upstream level using batch deliveries, where a fixed cost is incurred for each batch ordered. In addition, we also consider a limitation on the number of batches that can be ordered at any period. As far as we know, the status of this multi-level lot-sizing problem with batch deliveries and capacities on the size of the orders is open. Assuming stationary and identical batch sizes and capacities for all the levels, we derive some structural properties on the optimal policy, and propose a polynomial time algorithm based on a decomposition of the problem into induced connected components. Our algorithm is polynomial both in the length of the planning horizon and in the number of levels