A MILP model for an integrated project scheduling and multi-skilled workforce allocation with flexible working hours

In this paper, we integrate two decision problems arising in various applications such as production planning and project management: the project scheduling problem, which consists in scheduling a set of precedence-constrained tasks, where each task requires executing a set of skills to be performed, and the workforce allocation problem which includes assigning workers as scarce resources to the skills of each task. These two problems are interrelated as the tasks durations are not predefined, but depend on the number of workers assigned to that task as well as their skill levels. We here present a mixed integer linear programming model that considers important real life aspects related to the flexibility in the use of human resources, such as multi-skilled workers whose skill levels are different and measured by their efficiencies. Hence, execution times of the same workload by different workers vary according to these efficiencies. Moreover, the model considers the flexible working time of employees; i.e. the daily and weekly workload of a given worker may vary from one period to another according to the work required. Furthermore, efficient team building is incorporated in this model; i.e. assigning an expert worker and one or more apprentice worker(s) together with the purpose of skill development thanks to knowledge transfer. A numerical example is provided to check the performance of the model.