Job assignment with multivariate skills and the Peter Principle

This paper analyzes the job assignment problem faced by a firm when workers' skills are distributed along several dimensions and jobs require different skills to varying extent. I derive optimal assignment rules with and without slot constraints, and show that under certain circumstances workers may get promoted although they are expected to be less productive in their new job than in their old job. This can be interpreted as a version of the Peter Principle which states that workers get promoted up to their level of incompetence.