Fairness bei Crew-Scheduling unter Einsatz von Integer Linear Programming (ILP)

The shortage of skilled workers changes the requirements for personnel scheduling. In addition to cost efficiency, fairness has increasingly become a key consideration. This study therefore investigates how incorporating fairness into a crew scheduling problem affects total costs. To this end, several optimization strategies are compared: fairness optimization with a cost constraint, cost optimization with a fairness constraint, and simultaneous multi-objective optimization using a weighted objective function. Furthermore, it is examined whether optimization over multiple periods leads to improved fairness outcomes on average. An Integer Linear Program (ILP) is formulated and tested using various instances based on the literature. The results show that substantial improvements in fairness can be achieved at relatively small increases in cost when fairness is taken into account. The choice of an appropriate optimization strategy depends strongly on the planning horizon considered: in single-period optimization, fairness optimization under a cost constraint yields the best results, whereas in multi-period optimization, simultaneous cost and fairness optimization proves superior. Moreover, multi-period optimization, on average, leads to smaller deviations in working hours per crew. However, the increased computational effort of models with explicit fairness optimization constitutes a limitation, particularly for larger instances; nevertheless, it can be expected that significantly larger models will be solvable efficiently in the future.