Ordonnancement stochastique avec impatience

In this thesis, production systems facing abandonments are studied. These problems are modeled as stochastic scheduling problems with due dates. In the literature, few results exist concerning the optimal control of such systems. This thesis aims at providing optimal control policies for systems with impatience. We consider a generic system with a single machine, on which jobs have to be processed. Processing times, due dates (or patience time) and release dates are random variables. A weight is associated to each job and the objective is to minimize the expected weighted number of late jobs. In our study, we use different models, taking into account the specific features of real life problems. For example, we make a difference between impatience, when a customer has been waiting for too long, and abandonment, when a customer leaves the system after getting impatient. In the class of static list scheduling policies, we provide optimal schedules for problems with impatience. In the class of preemptive dynamic policies, we specify conditions under which a strict priority rule is optimal and we give a new heuristic, both extending previous results from the literature. We study variants and extensions of these problems, when several machines are available or when preemption is not authorized.Le sujet de cette thèse est l'étude de systèmes de production avec impatience. Ces systèmes sont modélisés comme des problèmes d'ordonnancement stochastiques avec des dates d'échéance. Dans la littérature, peu de résultats existent sur le contrôle optimal de ce genre de systèmes. C'est dans ce cadre que s'inscrit cette thèse. Nous considérons un système générique avec une machine, sur laquelle des tâches sont à exécuter. Les durées d'exécution, les dates d'échéance (ou durées d'impatience) et les dates de disponibilité des tâches sont des variables aléatoires. À chaque tâche est associé un poids et l'objectif est de minimiser l'espérance du nombre pondéré de tâches en retard. Dans notre étude, nous utilisons différentes modélisations, rendant compte des différentes contraintes régissant des systèmes réels. Notamment, nous faisons la différence entre l'impatience, le fait d'avoir attendu trop longtemps, et l'abandon, le fait de quitter le système suite à l'impatience. Dans la classe des politiques statiques, nous donnons des ordonnancements optimaux pour des problèmes avec impatience. Dans la classe des politiques dynamiques avec préemption, nous donnons de nouvelles conditions garantissant l'optimalité d'une politique stricte pour des problèmes avec abandon et nous proposons une heuristique plus efficace que celles que l'on trouve dans la littérature. Enfin, nous explorons des variantes et des extensions de ces problèmes, lorsque le système comporte plusieurs machines et lorsque la préemption n'est pas autorisée

Optimal and Heuristic Lead-Time Quotation For an Integrated Steel Mill With a Minimum Batch Size

This paper presents a model of lead-time policies for a production system, such as an integrated steel mill, in which the bottleneck process requires a minimum batch size. An accurate understanding of internal lead-time quotations is necessary for making good customer delivery-date promises, which must take into account processing time, queueing time and time for arrival of the requisite volume of orders to complete the minimum batch size requirement. The problem is modeled as a stochastic dynamic program with a large state space. A computational study demonstrates that lead time for an arriving order should generally be a decreasing function of the amount of that product already on order (and waiting for minimum batch size to accumulate), which leads to a very fast and accurate heuristic. The computational study also provides insights into the relationship between lead-time quotation, arrival rate, and the sensitivity of customers to the length of delivery promises

Modification of fuzzy logic rule base in the optimization of traffic light control system

Road intersections, bad roads, accidents, road construction works, emergencies, etc. are some of the primary causes of high traffic congestions in urban areas. In an attempt to solve some of these problems, traffic wardens and traffic light control systems are employed at road intersections to ensure that deadlocks are avoided. However, the use of traffic warden is associated with weariness which can lead to poor judgement in allocating the right of way to motorist. An alternative approach is to employ the use of Traffic light control system in the management of the increased traffic congestion that is always experience in urban areas. The use of dynamic phase scheduling traffic control system has proven more efficient as compared to the static phase scheduling traffic control system. In this paper, an attempt was made to improve upon an earlier optimized traffic light control system developed using simulation of urban mobility (SUMO) in conjunction with fuzzy inference system which played the role of optimizing the traffic light control system. The modified fuzzy rule based gave a superior average waiting time of 72.07% improvement as compared to an earlier average waiting time improvement of 65.35%. This is an indication that amongst other factors, the size of the fuzzy rule base plays a significant role when fuzzy logic is employed in the optimization of traffic light control systems.Keywords: Fuzzy Logic Controller, Dynamic Automated Traffic Light System, Static Automated Traffic Light Syste

Convexity Properties and Comparative Statics for M/M/S Queues with Balking and Reneging

We use sample path arguments to derive convexity properties of an M/M/S queue with impatient customers that balk and renege. First, assuming that the balking probability and reneging rate are increasing and concave in the total number of customers in the system (head-count), we prove that the expected head-count is convex decreasing in the capacity (service rate). Second, with linear reneging and balking, we show that the expected lost sales rate is convex decreasing in the capacity. Finally, we employ a sample-path sub-modularity approach to comparative statics. That is, we employ sample path arguments to show how the optimal capacity changes as we vary the parameters of customer demand and impatience. We find that the optimal capacity increases in the demand rate and decreases with the balking probability, but is not monotone in the reneging rate. This means, surprisingly, that failure to account for customersâ reneging may result in over-investment in capacity. Finally, we show that a seemingly minor change in system structure, customer commitment during service, produces qualitatively different convexity properties and comparative statics.Operations Management Working Papers Serie