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.^[1] Solutions to the nurse scheduling problem can be applied to constrained scheduling problems in other fields.^[2][3][4]
The nurse scheduling problem has been studied since before 1969,^[5] and is known to be NP-hard.^[1]

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:

• day shift
• night shift
• late night shift

In this problem we must search for a solution satisfying as many wishes as possible while not compromising the needs of the hospital. Some examples of constraints are:

• A nurse doesn't work the day shift, night shift and late night shift on the same day (for obvious reasons).
• A nurse may go on a holiday and will not work shifts during this time.
• A nurse doesn't do a late night shift followed by a day shift the next day.

Constraints

There are two types of constraints:

• hard constraints: if this constraint fails then the entire schedule is invalid.
• soft constraints: it is desirable that these constraints are met but not meeting them doesn't make the schedule invalid.

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.^[1] Differences in qualifications between nurses also create hard constraints.^[6] 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.^[1] The shift preferences of individual nurses may be treated as a soft constraint, ^[7] or as a hard constraint. ^[8]

Solutions

Solutions to the problem use a variety of techniques, including both mathematically exact solutions^[7] and a variety of heuristic solutions using decomposition,^[5] parallel computing,^[5] stochastic optimization,^[1] genetic algorithms,^[7] colony optimization,^[7] simulated annealing,^[7] Tabu search,^[7] and coordinate descent. ^[9]

See also

• Assignment problem
• Constraint programming

References

External links

• A study on how to solve the NSP using CGA