Papers by Laurent Houssin
In this paper, we focus on exact methods to solve the preemptive Flexible Job-Shop Scheduling Pro... more In this paper, we focus on exact methods to solve the preemptive Flexible Job-Shop Scheduling Problem with makespan and total completion time minimisation objective functions. Mathematical and constraint programming models enable the resolution of this problem for small instances. However, as an NP-hard problem, the cost of solving grows rapidly when considering larger instances. In this regard, we propose a logic-based Benders decomposition that relies on an efficient branch-and-bound procedure to solve the subproblem representing a pure (non-flexible) preemptive job-shop scheduling problem. Computational experiments are carried out and show the very good performance of our proposals.
l'expression de ma reconnaissance. Je remercie très chaleureusement mes parents et mes frères pou... more l'expression de ma reconnaissance. Je remercie très chaleureusement mes parents et mes frères pour le soutien considérable qu'ils m'ont apporté et la confiance dont ils m'ont toujours témoigné. Enfin et surtout, mille fois merci à Daphné. Conclusion Annexes A Détails des exemples A.
Étude Des Systèmes De Transport À Travers L'Algèbre Des Dioïdes
HAL (Le Centre pour la Communication Scientifique Directe), 2004
Ordonnancement cyclique : nouveaux résultats sur la théorie des tas
HAL (Le Centre pour la Communication Scientifique Directe), Feb 26, 2014
International audienceLes problèmes de Job-Shop peuvent souvent être simplifiés en les considéran... more International audienceLes problèmes de Job-Shop peuvent souvent être simplifiés en les considérant comme des problèmes cycliques. L'ordonnancement des tâches devient ainsi cyclique et son objectifest d'organiser les activités de production en répétant un cycle de base que l'on a optimisé. De nombreux paramètres entrent en jeu dans l'optimisation du cycle de base tels que lapériode du cycle choisie, l'ordre des opérations élémentaires pour réaliser un travail, la durée de ces opérations, le nombre de produits à réaliser par cycle, etc.Plusieurs approches ont été utilisées pour résoudre ce problème. Parmi elles, nouspouvons citer l'approche par réseaux de Petri et plus particulièrement par graphes d'événementstemporisés, l'approche par les graphes, l'approche par la programmation linéaireet l'approche par la théorie des tas.Concernant l'approche par la théorie des tas, le sous-problème de l'évaluation d'unesolution peut être résolu aisément avec l'aide de la théorie des tas. En effet, en traduisantle problème dans une structure mathématique adaptée, l'évaluation du taux de productiondu cycle revient au calcul d'une valeur propre d'un produit de matrices dans lequel chacunedes matrices représente une opération élémentaire. Cette propriété s'avère particulièrementintéressante dans le cas de l'évaluation successive d'un grand nombre d'ordonnancement. En outre, la théorie des tas permet une représentation très intuitive d'un ordonnancement,puisque celui-ci s'illustre comme un empilement de plusieurs briques (en fait, un " tas "de briques) dont le contour supérieur correspond aux dates de fin des dernières opérationsdes machines. Dans ce papier nous présentons les derniers résultats concerant l'application de cette théorie à l'ordonnancement cyclique. Plus particulièrement, nous montrons que le problème du nombre d' "en cours" à l'intérieur du motif peut être résolu au prix d'une extension du tas. </p
IFAC Proceedings Volumes, May 1, 2012
The topic of this paper is the cyclic job shop problem which aims at minimizing the cycle time un... more The topic of this paper is the cyclic job shop problem which aims at minimizing the cycle time under precedence and resource constraints. Based on graph theory, we propose a new branch and bound enumeration procedure to solve this problem. We compare the new procedure with other exact methods and present numerical test results.
IFAC Proceedings Volumes, 2011
In this paper, we focus on the cyclic job-shop problem. This problem consists in determining the ... more In this paper, we focus on the cyclic job-shop problem. This problem consists in determining the order of a set of generic tasks on machines in order to minimize the cycle time of the sequence. We propose an exact method to solve this problem. For each solution, a linear max-plus model (possibly non causal) is obtained. To evaluate the performance of a considered schedule, we build the causal max-plus representation and compute the eigenvalue of the evolution matrix. A branch and bound procedure is presented.
Computers & Operations Research, Apr 1, 2023
In this paper, we focus on exact methods to solve the preemptive Flexible Job-Shop Scheduling Pro... more In this paper, we focus on exact methods to solve the preemptive Flexible Job-Shop Scheduling Problem with makespan and total completion time minimisation objective functions. Mathematical and constraint programming models enable the resolution of this problem for small instances. However, as an NP-hard problem, the cost of solving grows rapidly when considering larger instances. In this regard, we propose a logic-based Benders decomposition that relies on an efficient branch-and-bound procedure to solve the subproblem representing a pure (non-flexible) preemptive job-shop scheduling problem. Computational experiments are carried out and show the very good performance of our proposals.
HAL (Le Centre pour la Communication Scientifique Directe), Mar 30, 2014
HAL (Le Centre pour la Communication Scientifique Directe), Feb 23, 2022
On s'intéresse au problème d'ordonnancement de production du type job-shop flexible préemptif (pr... more On s'intéresse au problème d'ordonnancement de production du type job-shop flexible préemptif (preemptive flexible job-shop scheduling problem, pFJSSP). Trois approches sont proposées pour le résoudre : la programmation linéaire en nombres entiers (MILP), la programmation par contraintes (CP), la décomposition de Benders basée sur la logique (LBBD). Dans le problème de job-shop (JSSP), on a un ensemble de jobs composés d'opérations et chacune d'elles doit être traitée sur une machine prédéterminée. Pour l'objectif de minimisation de la durée totale que l'on considère ici, le problème est NP-difficile. Le problème du job-shop flexible (FJSSP) est une extension du problème de job-shop classique dans lequel plusieurs machines sont en capacité d'exécuter une même opération, cette flexibilité permet alors de s'adapter aux variations du marché. Un grand nombre de méthodes, exactes et heuristiques, ont été proposées pour résoudre le FJSSP (voir [5] pour un travail récent). Ici, nous considérons une version préemptive de ce problème. Quand elle est possible, la préemption d'opérations en cours de traitement peut permettre de réduire les durées de fabrication. Cependant, les problèmes de job-shop préemptif ont reçu peu d'attention [2], et, à notre connaissance, personne ne s'est encore intéressé à la résolution du problème de job-shop flexible et préemptif.
HAL (Le Centre pour la Communication Scientifique Directe), Apr 17, 2018
A robust optimization approach for the cyclic job shop problem
HAL (Le Centre pour la Communication Scientifique Directe), Jul 8, 2018
International audienc
This paper deals with feedback controller synthesis for (max,+)-linear systems. We attempt to com... more This paper deals with feedback controller synthesis for (max,+)-linear systems. We attempt to compute a feedback which ensures some given constraints while delaying as less as possible the system. The controller synthesis presented here is based on fixed points results of antitone mappings.
Lecture Notes in Computer Science, 2023
This paper addresses the robust two-machine permutation flow-shop scheduling problem considering ... more This paper addresses the robust two-machine permutation flow-shop scheduling problem considering non-deterministic operation processing times associated with an uncertainty budget. The objective is to minimize the makespan of the schedule. Exact solution methods incorporated within the framework of a twostage robust optimization are proposed to solve the problem. We first prove that under particular conditions the robust two-machine permutation flow-shop scheduling problem can be solved in polynomial time by the well-known Johnson's algorithm usually dedicated to the deterministic version. Then we tackle the general problem, for which we propose a column and constraint generation algorithm. We compare two versions of the algorithm. In the first version, a mixed-integer linear programming formulation is used for the master problem. In the second version, we use a constraint programming model for the master problem. To the best of our knowledge, the use of constraint programming for a master problem in a two-stage robust optimization problem is innovative. The experimental results show the very good performance of the method based on the constraint programming formulation. We also notice that Johnson's algorithm is surprisingly efficient for the robust version of the general problem.
Génération de tables d'horaires à l'aide de la théorie des dioïdes
HAL (Le Centre pour la Communication Scientifique Directe), 2005
Springer eBooks, 2018
This paper deals with the cyclic job shop problem where the task durations are uncertain and belo... more This paper deals with the cyclic job shop problem where the task durations are uncertain and belong to a polyhedral uncertainty set. We formulate the cyclic job shop problem as a two-stage robust optimization model. The cycle time and the execution order of tasks executed on the same machines correspond to the here-and-now decisions and have to be decided before the realization of the uncertainty. The starting times of tasks corresponding to the wait-and-see decisions are delayed and can be adjusted after the uncertain parameters are known. In the last decades, different solution approaches have been developed for two-stage robust optimization problems. Among them, the use of affine policies, column generation algorithms, row and row-and-column generation algorithms. In this paper, we propose a Branch-and-Bound algorithm to tackle the robust cyclic job shop problem with cycle time minimization. The algorithm uses, at each node of the search tree, a robust version of the Howard's algorithm to derive a lower bound on the optimal cycle time. We also develop a heuristic method that permits to compute an initial upper bound for the cycle time. Finally, encouraging preliminary results on numerical experiments performed on randomly generated instances are presented.
IFAC-PapersOnLine, Jul 1, 2017
In this paper, we consider a cyclic job shop problem where a subset of tasks have varying process... more In this paper, we consider a cyclic job shop problem where a subset of tasks have varying processing times. The minimum processing times and maximum processing times of these tasks are known. We propose a branch and bound method that finds the schedule which minimizes the mean cycle time with respect to variations. We show that the evaluation of a schedule can be considered as a volume calculus of some polytopes. Indeed, for each schedule we can associate a set of polytopes whose volumes provide information on the variation effect on the considered schedule.
EURO journal on computational optimization, Sep 1, 2018
This paper addresses the Basic Cyclic Scheduling Problem where the processing times are affected ... more This paper addresses the Basic Cyclic Scheduling Problem where the processing times are affected by uncertainties. We formulate the problem as a twostage robust optimization problem with polyhedral uncertainty set. We propose three exact algorithms for solving the problem. Two of them use a negative circuit detection algorithm as a subroutine and the last one is an Howard's algorithm adaptation. Results of numerical experiments on randomly generated instances show that the Howard's algorithm adaptation yields efficient results and opens perspectives on more difficult robust cyclic scheduling problems.
Annals of Operations Research, Oct 16, 2019
This paper addresses the Cyclic Jobshop Problem in a flexible context. The flexibility feature me... more This paper addresses the Cyclic Jobshop Problem in a flexible context. The flexibility feature means that machines are able to perform several kinds of tasks. Hence, a solution of the scheduling problem does not only concern the starting times of the elementary tasks, but also the assignment of these tasks to a unique machine. The objective considered in this paper is the minimisation of the cycle time of a periodic schedule. We formulate the problem as a Mixed Integer Linear Problem and propose a Benders decomposition method along with a heuristic procedure to speed up the solving of large instances. It consists in reducing the number of machines available for each task. Results of numerical experiments on randomly generated instances show that the MILP modelling has trouble solving difficult instances, while our decomposition method is more efficient for solving such instances. Our heuristic procedure provides good estimates for difficult instances.
HAL (Le Centre pour la Communication Scientifique Directe), Apr 6, 2022
HAL (Le Centre pour la Communication Scientifique Directe), Dec 10, 2008
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Papers by Laurent Houssin