The nurse rerostering problem: Strategies for reconstructing disrupted schedules

Abstract

The nurse rostering problem is a well-known optimization problem within the field of operational research which seeks to assign nurses to shifts during a scheduling horizon subject to a set of hard and soft constraints. The nurse rerostering problem, meanwhile, occurs when one or more nurses already scheduled to work cannot be present due to unforeseen events such as, for example, illness. Such absences may render an existing solution infeasible and thus a fast method is required to recreate the roster. The present research explores several novel strategies for rerostering based on relaxations of different problem parameters, including soft constraints and the rescheduling horizon. A general integer programming formulation is developed considering multi-skilled nurses and various constraints commonly found in real-world problems. Secondly, the nurse rerostering problem is explored by rescheduling both the entire scheduling horizon and only a limited part. Additionally, the impact of considering both the soft constraints from the original nurse rostering problem and a relaxation of them is evaluated when solving the nurse rerostering problem. Finally, a variable neighborhood descent heuristic is developed to address the problem without the use of a solver. A computational study on instances adapted from the Second International Nurse Rostering Competition and on real-world instances from a Lisbon hospital demonstrates that the proposed strategies solve realistic large-scale rerostering problems to (near-)optimality in limited computation time.