Local and global constraint consistency in personnel rostering

Personnel rostering is a challenging combinatorial optimization problem in which shifts are assigned to employees over a scheduling period while subject to organizational, legislative, and personal constraints. Academic models for personnel rostering typically abstractly conceptualize complex real‐world problem characteristics. Often only one isolated scheduling period is considered, contradicting common practice where personnel rostering inherently spans multiple dependent periods. The state of the art offers no systematic approach to address this modeling challenge, and consequently, few models capture the requirements imposed by practice. The present paper introduces the concepts of local and global consistency in constraint evaluation processes and proposes a general methodology to address these challenges in integer programming approaches. The impact of inconsistent constraint evaluation is analyzed in a case study concerning rostering nurses in a hospital ward, of which the data have been made publicly available. The results demonstrate that the proposed methodology approximates the optimal solution.