In this dissertation, we study the single machine scheduling problem with an objective of minimizing the total completion time subject to release dates. The problem, denoted 1|rj £UCj ,was known to be strongly NP-hard and both theoretically and practically important. The focus of the research in this dissertation is to develop the efficient algorithms for solving the 1|rj|£UCj problem. This thesis contains two parts. In the first part, the theme concerns the approximation approach. We derive a necessary and sufficient condition for local optimality, which can be implemented as a priority rule and be used to construct three heuristic algorithms with running times of O(n log n). By ¡¨local optimality¡¨, we mean the optimality of all candidates whenever a job is selected in a schedule, without considering the other jobs preceding or following. This is the most broadly considered concepts of locally optimal rule. We also identify a dominant subset which is strictly contained in each of all known dominant subsets, where a dominant subset is a set of solutions containing all optimal schedules. In the second part, we develop our optimality algorithms for the 1|rj |£UCj problem. First, we present a lemma for estimating the sum of delay times of the rest jobs, if the starting time is delayed a period of time in a schedule. Then, using the lemma, partially, we proceed to develop a new partition property and three dominance theorems, that will be used and have improved the branch-and-bound algorithms for our optimization approach. By exploiting the insights gained from our heuristics as a branching scheme and by exploiting our heuristics as an upper bounding procedure, we propose three branch-and-bound algorithms. Our algorithms can optimally solve the problem up to 120 jobs, which is known to be the best till now.

Nous adaptons une heuristique de recherche à voisinage variable pour traiter le problème du voyageur de commerce avec fenêtres de temps (TSPTW) lorsque l'objectif est la minimisation du temps d'arrivée au dépôt de destination. Nous utilisons des méthodes efficientes pour la vérification de la réalisabilité et de la rentabilité d'un mouvement. Nous explorons les voisinages dans des ordres permettant de réduire l'espace de recherche. La méthode résultante est compétitive avec l'état de l'art. Nous améliorons les meilleures solutions connues pour deux classes d'instances et nous fournissons les résultats de plusieurs instances du TSPTW pour la première fois. / We adapt a general variable neighborhood search heuristic to solve the traveling salesman problem with time windows (TSPTW) where the objective is to minimize the completion time. We use efficient methods to check the feasibility and the profitability of a movement. We use a specific order to reduce the search space while exploring the neighborhoods. The resulting method is competitive with the state-of-the-art. We improve the best known solutions for two classes of instances and provide the results of multiple instances of TSPTW for the first time.