The multivariate non-homogeneous Markov manpower system in a departmental mobility framework

► We model a non-homogeneous multivariate Markov manpower system. ► Horizontal and vertical mobility between and within departments is considered. ► Functional relationships using multivariate Markov chains are provided. ► A minmax fuzzy goal-programming optimization and control framework is given. ► The framework enables mild-mannered control in mathematical manpower planning.