The bilevel optimisation of a multi-agent project scheduling and staffing problem

In this paper, we study a multi-agent project staffing problem involving single project, which has to be scheduled under resource constraints. We consider functional organisational structure where team leader and manager are together responsible for the operational execution of project. The leader, formal authority over resources, is standing at top hierarchy determines number mix (additional) employees tries level workload planning period in order avoid idle times. scheduling activities his/her objective minimise duration. interaction between both agents decision-making process is, on one hand, hierarchical, i.e. imposes decision manager. On other taken by should comply such that plan schedule agreed parties. propose bilevel optimisation model embeds nested inner problem, as constraint outer leader. algorithm mathematical programming method thriving generation additional lazy constraints via feasibility callbacks so respect requirements formulated problem. computational experiments, compare solution approach alternative classical approaches validate design choices related proposed speed-up mechanisms parameter settings.