Optimizing cost-effectiveness in a stochastic Markov manpower planning system under control by recruitment

The present paper proposes a mathematical model and algorithm for optimizing cost‐effectiveness in a stochastic manpower planning system under control by recruitment. More specifically, we suggest a multi‐objective model that simultaneously addresses two objectives, namely minimizing the cost and maximizing the desirability degree of the attained personnel structure. In a stochastic environment, the uncontrollable parameters of the manpower model (i.e. internal transitions and wastage) are random variables. We suggest a scenario approach in order to cope with this uncertainty. The optimization problem under study is formulated as a mixed integer program. Further, in order to decrease the computing time in solving the optimization problem, we show that the optimal recruitment strategy has some properties that enable narrowing the solution space.