Nurse scheduling problem

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. Solutions to the nurse scheduling problem can be applied to constrained scheduling problems in other fields.
The nurse scheduling problem has been studied since before 1969, and is known to have NP-hard complexity.
General description.
The nurse scheduling problem involves the assignment of shifts and holidays to nurses. Each nurse has their own wishes and restrictions, as does the hospital. The problem is described as finding a schedule that both respects the constraints of the nurses and fulfills the objectives of the hospital. Conventionally, a nurse can work 3 shifts because nursing is shift work:
In this problem we must search for a solution satisfying as many wishes as possible while not compromising the needs of the hospital.
Constraints.
There are two types of constraints:
Some examples of constraints are:
Hard constraints typically include a specification of shifts (e.g. morning, afternoon, and night), that each nurse should work no more than one shift per day, and that all patients should have nursing coverage. Differences in qualifications between nurses also create hard constraints. 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. The shift preferences of individual nurses may be treated as a soft constraint, or as a hard constraint.
Solutions.
Solutions to the problem use a variety of techniques, including both mathematically exact solutions and a variety of heuristic solutions using decomposition, parallel computing, stochastic optimization, genetic algorithms, colony optimization, simulated annealing, quantum annealing Tabu search, and coordinate descent.
Burke "et al". (2004) summarised the state of art of academic research to the nurse rostering problem, including brief introductions of various then published solutions.