A shift-based model to solve the integrated staff rostering and task assignment problem with real-world requirements

Due to the computational complexity, the staff scheduling problem is generally decomposed into two subproblems, i.e. staff rostering and task assignment problems. Very often, this could result in suboptimal solutions. Thus, we study an integrated staff rostering and task assignment (ISRTA) problem in this paper. Previous studies formulate this problem as task- and roster-based ISRTA models, which can only solve small-scale problems. To overcome this limitation, this paper proposes a novel shift-based ISRTA model, which exhibits less symmetry and greatly reduces the number of variables and constraints. We extend the shift-based ISRTA model to six real-world requirements, i.e., shift flexibility, qualification, travel time, contractual rules, task connection preference, and fairness, which ensure the applicability of the result schedule. To efficiently solve the shift-based ISRTA model, we propose a clique-based aggregated model that enhances the performance of the basic shift model. Further, two heuristics, i.e., rolling horizon algorithm and iterative shift selection algorithm, are proposed to speed up the solution process. Based on randomly generated 24 benchmark instances and 16 real-world instances from a major airline, computational results show that the shift-based ISRTA model outperforms the task- and roster-based ISRTA models. For small- and mid-scale problems, the shift-based ISRTA model can be solved optimally or near-optimally directly using a commercial solver, and the rolling horizon algorithm and iterative shift selection algorithm can solve large-scale problems and obtain high-quality solutions.