The proper balancing of geographically distributed task schedules and the associated workforce distributions are critical determinants of productivity in any people-centric production environment. The paper has investigated the cross-trained workers scheduling problem considering the qualified personal allocation and temporally cooperation of engineers simultaneously. A 0-1 programming model is developed and the non-dominated sorting genetic algorithm-II (NSGA-II) is adopted to deal with the NP-hard problem. In order to enforce the NSGA-II, significant improvements are made to function the approach in a more efficient way. It is observed that the improved NSGA-II outperforms the original NSGA-II in the experimental test. The promising outcomes of the formulation in the experiment make its implementation easily customisable and transferable for solving other intricate problems in the context of skilled workforce scheduling. Furthermore, the modified NSGA II can be used as an efficient and effective tool for other multiobjective optimisation problems.