Project scheduling under uncertainty using fuzzy modelling and solving techniques

In the real world, projects are subject to numerous uncertainties at different levels of planning. Fuzzy project scheduling is one of the approaches that deal with uncertainties in project scheduling problem. In this paper, we provide a new technique that keeps uncertainty at all steps of the modelling and solving procedure by considering a fuzzy modelling of the workload inspired from the fuzzy/possibilistic approach. Based on this modelling, two project scheduling techniques, Resource Constrained Scheduling and Resource Leveling, are considered and generalized to handle fuzzy parameters. We refer to these problems as the Fuzzy Resource Constrained Project Scheduling Problem (FRCPSP) and the Fuzzy Resource Leveling Problem (FRLP). A Greedy Algorithm and a Genetic Algorithm are provided to solve FRCPSP and FRLP respectively, and are applied to civil helicopter maintenance within the framework of a French industrial project called Helimaintenance

Asymptotic stability for the Couette flow in the 2D Euler equations

In this expository note we discuss our recent work [arXiv:1306.5028] on the nonlinear asymptotic stability of shear flows in the 2D Euler equations of ideal, incompressible flow. In that work it is proved that perturbations to the Couette flow which are small in a suitable regularity class converge strongly in $L^2$ to a shear flow which is close to the Couette flow. Enstrophy is mixed to small scales by an almost linear evolution and is generally lost in the weak limit as t -> +/- infinity. In this note we discuss the most important physical and mathematical aspects of the result and the key ideas of the proof.Comment: Short, expository summary of the preprint J. Bedrossian, N. Masmoudi "Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations", arXiv:1306.502

Fuzzy uncertainty modelling for project planning; application to helicopter maintenance

Maintenance is an activity of growing interest specially for critical systems. Particularly, aircraft maintenance costs are becoming an important issue in the aeronautical industry. Managing an aircraft maintenance center is a complex activity. One of the difficulties comes from the numerous uncertainties that affect the activity and disturb the plans at short and medium term. Based on a helicopter maintenance planning and scheduling problem, we study in this paper the integration of uncertainties into tactical and operational multiresource, multi-project planning (respectively Rough Cut Capacity Planning and Resource Constraint Project Scheduling Problem). Our main contributions are in modelling the periodic workload on tactical level considering uncertainties in macro-tasks work contents, and modelling the continuous workload on operational level considering uncertainties in tasks durations. We model uncertainties by a fuzzy/possibilistic approach instead of a stochastic approach since very limited data are available. We refer to the problems as the Fuzzy RoughCut Capacity Problem (FRCCP) and the Fuzzy Resource Constraint Project Scheduling Problem (RCPSP).We apply our models to helicopter maintenance activity within the frame of the Helimaintenance project, an industrial project approved by the French Aerospace Valley cluster which aims at building a center for civil helicopter maintenance

Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations

We prove asymptotic stability of shear flows close to the planar Couette flow in the 2D inviscid Euler equations on \Torus \times \Real. That is, given an initial perturbation of the Couette flow small in a suitable regularity class, specifically Gevrey space of class smaller than 2, the velocity converges strongly in L^2 to a shear flow which is also close to the Couette flow. The vorticity is asymptotically driven to small scales by a linear evolution and weakly converges as $t \rightarrow \pm\infty$. The strong convergence of the velocity field is sometimes referred to as inviscid damping, due to the relationship with Landau damping in the Vlasov equations. This convergence was formally derived at the linear level by Kelvin in 1887 and it occurs at an algebraic rate first computed by Orr in 1907; our work appears to be the first rigorous confirmation of this behavior on the nonlinear level.Comment: 78 page