A Multi-Machine Scheduling Problem with Global Non Idling Constraint

International audienceWe deal here with a multi-machine scheduling problem with non idling constraints, i.e constraints which forbids the interruption of the use of the processors. We reformulate the problem, while using specific pyramidal profile functions, next get a min-max feasibility criterion and finally derive exact polynomial algorithms for both the feasibility problem and the makespan optimization problem

Approches par horizon roulant pour un problème de planification stochastique

International audienceStochastic planning problems are common in many application areas: supply chain, production management, reservation system (reservations for vacations, TV spots, ...), patient allocation in surgical unit, satellites launching for example. While exact stochastic dynamic programming approaches could solve these problems, the curse of dimensionality makes such approaches practically inefficient, and there is actually no unified treatment for such problems . Among the many stochastic optimization methods in the literature, those with a rolling horizon turn out to be well suited to this multi-step stochastic problem. We present such a method for a stochastic planning problem.Les problèmes de planification stochastique sont courants dans de nombreux domaines d’application : chaîne logistique, gestion de production, système de réservation (réservations de centres de vacances, de spots télévisés,...), affectation des patients à un bloc chirurgical, lancement de satellites par exemple. Si les approches exactes de programmation dynamique stochastique pourraient en théorie résoudre ces problèmes, l’explosion combinatoire rend de telles approches inopérantes en pratique et il n’existe pas de nos jours une méthode unifiée de résolution. Parmi les multiples méthodes d’optimisation stochastique de la littérature, celles à horizon roulant se révèlent bien adaptées à ce problème stochastique multi-étapes.Nous présentons une telle méthode pour un problème de planification stochastique

Ordonnancement réactif sur une machine conservant un nombre maximum de dates de début,

National audienc

Single Machine Scheduling with no Intermediate Delays

International audienc

Minimizing the Earliness and Tardiness Cost of a Sequence of Tasks on a Single Machine

Assume that n tasks must be processed by one machine in a fixed sequence. The processing time, the preferred starting time and the earliness and tardiness costs per time unit are known for each task. The problem is to allocate each task a starting time such that the total cost incurred by the early and tardy tasks is minimum. Garey et al. have proposed a nice O(nlogn) algorithm for the special case of symmetric and task-independent costs. In this paper we first extend that algorithm to the case of asymmetric and task-independent cost without increasing its worst-case complexity. For the general case of asymmetric and task-dependent costs, we propose an O(n3logn) algorithm based on a strong dominance property that yields to model the scheduling problem as a minimum cost path in a valued directed acyclic graph