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

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

On a general approach to the formal cohomology of quadratic Poisson structures

We propose a general approach to the formal Poisson cohomology of $r$-matrix induced quadratic structures, we apply this device to compute the cohomology of structure 2 of the Dufour-Haraki classification, and provide complete results also for the cohomology of structure 7.Comment: 19 page