The nurse scheduling problem (NSP), also called the nurse rostering problem (NRP), is the operations research problem of finding an optimal way to assign nurses to shifts, typically with a set of hard constraints which all valid solutions must follow, and a set of soft constraints which define the relative quality of valid solutions.
The problem is described as finding a schedule that both respects the constraints of the nurses and fulfills the objectives of the hospital.
[7] Soft constraints may include minimum and maximum numbers of shifts assigned to a given nurse in a given week, of hours worked per week, of days worked consecutively, of days off consecutively, and so on.
[9] Solutions to the problem use a variety of techniques, including both mathematically exact solutions[8] and a variety of heuristic solutions using decomposition,[10] parallel computing,[10][11] stochastic optimization,[1] genetic algorithms,[8] colony optimization,[8] simulated annealing,[8] quantum annealing,[12] Tabu search,[8] and coordinate descent.
[11][13] Burke et al. (2004)[14] summarised the state of art of academic research to the nurse rostering problem, including brief introductions of various then published solutions.