Lower Bounds for the Multi-skill Project Scheduling Problem with Hierarchical Levels of Skills

In this paper, we introduce an extension of the classical Resource-Constrained Project Scheduling Problem: the Multi-skill Project Scheduling Problem. We consider a project made up of activities that must be implemented by a staff: every member of this staff masters one or more skill(s). An activity needs a given amount of each skill with a fixed minimum level of mastering. For each unit of a skill needed, we have to assign an employee who masters the required level of this skill during the whole processing time of the activity. The objective is to minimize the duration of the project, i.e. the makespan. We introduce here two lower bounds used to evaluate the minimum duration.

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