Dynamic resource constrained multi-project scheduling problem with weighted earliness/tardiness costs

In this study, a conceptual framework is given for the dynamic multi-project scheduling problem with weighted earliness/tardiness costs (DRCMPSPWET) and a mathematical programming formulation of the problem is provided. In DRCMPSPWET, a project arrives on top of an existing project portfolio and a due date has to be quoted for the new project while minimizing the costs of schedule changes. The objective function consists of the weighted earliness tardiness costs of the activities of the existing projects in the current baseline schedule plus a term that increases linearly with the anticipated completion time of the new project. An iterated local search based approach is developed for large instances of this problem. In order to analyze the performance and behavior of the proposed method, a new multi-project data set is created by controlling the total number of activities, the due date tightness, the due date range, the number of resource types, and the completion time factor in an instance. A series of computational experiments are carried out to test the performance of the local search approach. Exact solutions are provided for the small instances. The results indicate that the local search heuristic performs well in terms of both solution quality and solution time

Price of Anarchy in Bernoulli Congestion Games with Affine Costs

We consider an atomic congestion game in which each player participates in the game with an exogenous and known probability $p_{i}\in[0,1]$, independently of everybody else, or stays out and incurs no cost. We first prove that the resulting game is potential. Then, we compute the parameterized price of anarchy to characterize the impact of demand uncertainty on the efficiency of selfish behavior. It turns out that the price of anarchy as a function of the maximum participation probability $p=\max_{i} p_{i}$ is a nondecreasing function. The worst case is attained when players have the same participation probabilities $p_{i}\equiv p$. For the case of affine costs, we provide an analytic expression for the parameterized price of anarchy as a function of $p$. This function is continuous on $(0,1]$, is equal to $4/3$ for $0<p\leq 1/4$, and increases towards $5/2$ when $p\to 1$. Our work can be interpreted as providing a continuous transition between the price of anarchy of nonatomic and atomic games, which are the extremes of the price of anarchy function we characterize. We show that these bounds are tight and are attained on routing games -- as opposed to general congestion games -- with purely linear costs (i.e., with no constant terms).Comment: 29 pages, 6 figure

Convergence of Large Atomic Congestion Games

We consider the question of whether, and in what sense, Wardrop equilibria provide a good approximation for Nash equilibria in atomic unsplittable congestion games with a large number of small players. We examine two different definitions of small players. In the first setting, we consider a sequence of games with an increasing number of players where each player's weight tends to zero. We prove that all (mixed) Nash equilibria of the finite games converge to the set of Wardrop equilibria of the corresponding nonatomic limit game. In the second setting, we consider again an increasing number of players but now each player has a unit weight and participates in the game with a probability tending to zero. In this case, the Nash equilibria converge to the set of Wardrop equilibria of a different nonatomic game with suitably defined costs. The latter can also be seen as a Poisson game in the sense of Myerson (1998), establishing a precise connection between the Wardrop model and the empirical flows observed in real traffic networks that exhibit stochastic fluctuations well described by Poisson distributions. In both settings we give explicit upper bounds on the rates of convergence, from which we also derive the convergence of the price of anarchy. Beyond the case of congestion games, we establish a general result on the convergence of large games with random players towards Poisson games.Comment: 34 pages, 3 figure

A three-phase approach for robust project scheduling: an application for R&D project scheduling

During project execution, especially in a multi-project environment unforeseen events arise that disrupt the project process resulting in deviations of project plans and budgets due to missed due dates and deadlines, resource idleness, higher work-in-process inventory and increased system nervousness. In this thesis, we consider the preemptive resource constrained multi-project scheduling problem with generalized precedence relations in a stochastic and dynamic environment and develop a three-phase model incorporating data mining and project scheduling techniques to schedule the R&D projects of a leading home appliances company in Turkey. In Phase I, models classifying the projects with respect to their resource usage deviation levels and an activity deviation assignment procedure are developed using data mining techniques. Phase II, proactive project scheduling phase, proposes two scheduling approaches using a bi-objective genetic algorithm (GA). The objectives of the bi-objective GA are the minimization of the overall completion time of projects and the minimization of the total sum of absolute deviations for starting times for possible realizations leading to solution robust baseline schedules. Phase II uses the output of the first phase to generate a set of non-dominated solutions. Phase III, called the reactive phase, revises the baseline schedule when a disruptive event occurs and enables the project managers to make “what-if analysis” and thus to generate a set of contingency plans for better preparation

Conception et application d'une méthodologie multicritère floue de sélection de logiciels de planification et d'ordonnancement avancé (APS)

Avec la mondialisation, la croissance des entreprises et les besoins de plus en plus exigeants des clients, les défis en termes de planification et d’ordonnancement des opérations en environnement manufacturier ne cessent de croitre. Face à cette situation, les entreprises manufacturières sont dans l’obligation de mettre à jour leurs politiques de planification et d’ordonnancement en adoptant des systèmes et des approches de planifications nouvelles telles que la planification et l’ordonnancement avancés (POA). Dans cet exercice, les entreprises désirant implanter des approches de POA ont généralement deux possibilités. Elles peuvent choisir de développer une solution personnalisée ou alors d’implanter des logiciels commerciaux de POA. La deuxième piste est plus courue de nos jours. L’objectif de ce travail est d’accompagner les entreprises désirant améliorer la planification et l’ordonnancement de leurs opérations par la sélection et l’implantation d’un logiciel commercial de POA. Plus précisément, le but de ce travail est d’évaluer et de sélectionner parmi les logiciels commerciaux de POA disponibles sur le marché celui qui satisfait au mieux les besoins de l’entreprise. Trois sous objectifs ont été identifiés : la cartographie des processus de planification et d’ordonnancement de l’entreprise, la capture des besoins de l’entreprise et la conception d’une nouvelle méthodologie de sélection intégrant sous incertitude à la fois les besoins de l’entreprise et les critères et sous critères de sélection. La méthodologie adoptée pour cette étude est celle dictée par la science de la conception, qui permet l’itération du processus de conception afin de perfectionner et de valider les résultats ou les livrables obtenus. Des données sont recueillies auprès d’experts et des preneurs de décisions internes à l’entreprise à l’aide d’entrevues individuelles et de groupes. Par ailleurs, en guise de contributions de cette recherche, trois méthodes ont été conçues. La première méthode permet de cartographier les processus de l’entreprise. La deuxième méthode est destinée à la capture des besoins de l’entreprise tandis que la troisième méthode intègre le déploiement de la fonction qualité (DFQ), l’analyse hiérarchique des processus (AHP) et la méthode VIKOR pour la sélection du logiciel qui satisfait au mieux les besoins de l’entreprise. Cette intégration est rendue possible en mettant en place une version modifiée du DFQ. L’incertitude sur les données provenant des enquêtes adressées aux experts et aux preneurs de décision est considérée par l’utilisation de la logique floue et des variables linguistiques. L’approche globale de l’étude est appliquée à un cas réel d’entreprise manufacturière. Les résultats montrent la pertinence des méthodes développées face au problème de selection d’un logiciel de POA