Job assignment with multivariate skills

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 in their new job they are expected to be less productive 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.