The papers reviewed in this chapter have focussed on nurse rostering problems and the methods used to solve them. There are, however, many other publications that examine some of the other Operations Research problems related to nurse scheduling. For example, Kwak and Lee [153] use goal programming to solve a staffing problem involving physicians, nurses and technicians in three different hospital departments. Nooriafshar [196] developed a decision support system for solving a trainee nurse staffing problem. Staffing requirements must be met in different wards while giving different trainee nurses the required experience and training from working in the various departments. Wright et al. [248] investigate how different policies such as nurse to patient ratios affect total wage costs and work schedule quality. Punnakitikashem et al. [209] developed a stochastic
integer programming model for the problem of assigning nurses to patients before a shift starts so as to minimise excess workloads for nurses. Al-Zubaidi and Christer [16] use simulations to predict the effect of different management and operational policies on maintenance manpower requirements in a UK hospital. Moz and Vaz Pato [188-190] developed a number of methods for solving the nurse rerostering problem. Re-rostering involves adjusting rosters to cope with unexpected absences when there is no reserve pool of nurses available. Gutjahr and Rauner [126] use an ant colony optimisation approach to assign a pool of nurses to a number of hospitals within the Vienna region, Austria. The hospitals make requests for extra nurses on certain days due to excess demand. The nurses are then allocated to the hospitals, taking into consideration the nurses’ working preferences, the hospitals’ requirements and cost constraints. Beliën and Demeulemeester [35] combine a nurse rostering and surgery scheduling problem and successfully solve it using column generation.
Blake and Carter [40] used goal programming to determine patient level targets at a hospital that was about to experience a significant reduction in funding. Patient requirements, operating costs and doctors’ preferred incomes and level and type of workload all needed to be considered.
Abernathy et al. [7] present a stochastic programming model for solving staffing problems in hospitals which have highly variable personnel demands. The three planning stages that the process can be decomposed into are: policy decisions such as the number of nurses allocated to each ward over a scheduling period, staff planning such as the number of nurses needed in employment and short term scheduling using the decisions from the previous stages.
Trivedi and Warner [234] describe a method for optimally allocating float nurses among nursing units at the start of shifts. A model for representing the head nurse’s perception on the need for additional nurses at specific units is used to form the objective of a problem which is then solved using a branch and bound algorithm. Factors considered for describing the shortage severity include patient load, patient classifications and staff absences.
Musliu et al. [193] handle weekly shift scheduling problems using local search techniques. Thompson [231] solves a general employee shift scheduling problem using a simulated annealing based approach. Glover et al. [122] outline local search ideas for solving a week long employee scheduling problem in which employee availability and cover requirements fluctuate. Baker et al. [24] present an optimal constructive approach to a very simplified rostering problem.
Easton et al. [94] observe that in order to retain higher numbers of nurses and reduce nurse turnover and the associated costs, some hospitals are providing more attractive work schedules. Some of these scheduling policies include preferable shift rotations, less weekend assignments and higher wages for undesirable shifts. To examine the effects of some of these scheduling rules on the changes to total nurse wage costs and workforce sizes required, the authors conduct simulations and solve nurse scheduling problems using these new scheduling rules. The results suggest that although more restrictive scheduling policies may be more attractive to the nurses, the costs incurred to the hospital through higher total wages and larger workforces should perhaps be considered too.
There are also a number of papers which do not present a specific method for nurse rostering but discuss different ways of modelling problems or ideas which
may be applicable to a number of approaches. For example in [55], Burke et al. suggest an alternative approach to the evaluation function which reduces the knowledge required by the user of the system when setting weights for soft constraints. In [53], Burke et al. describe a fast implementation of the evaluation function for a nurse rostering problem. Due to the large number of complex constraints which are typical in nurse rostering problems, the evaluation function is often a bottleneck. Therefore any gain in the speed of evaluation functions will increase the efficiency of the algorithms. Instead of writing individual evaluation functions for each soft constraint, they developed a single evaluation function. This function accepts certain data structures (called numberings and counters) which are cleverly initialised for each constraint. Performance gains occur due to the fact that certain soft constraints are able to share these data structures, hence reducing the number of evaluation function calls. For instances in which these data structures are significantly shared, this method is very efficient. De Causmaecker and Vanden Berghe [86] present algorithms for improving roster quality by manipulating coverage constraints. The algorithms mimic the way expert human planners sometimes alter coverage constraints in order to increase the quality of the nurses’ work patterns.
Blöchliger [42] provides a tutorial on modelling a nurse scheduling problem with three objectives: minimize employment costs, maximize fairness by evenly distributing unpopular shifts and minimize soft constraint violations. No method for solving the problem is given but potential general approaches are suggested.
It is worth mentioning that there is also a very large body of research around the effects of different nurse scheduling policies. Examples include:
̇ The health risks of shift work, such as the disruption of circadian rhythms and sleep disorders [207].
̇ The benefit of providing flexible working in order to encourage commitment to nursing [45].
̇ The effect of longer shifts on performance [103]. ̇ Stress due to shift working [171] and so on.
Finally, the publications reviewed in this chapter have primarily focussed on nurse rostering. It is worth noting though that the physician scheduling problem can be very similar and methods which are effective for this problem may also have applications in nurse rostering. See for example [29, 72, 110, 150, 218].