Health care systems The foremost rostering focus in health systems has been in nurse scheduling, usually in acute care hospital wards. There are both clinical and cost imperatives associated with providing appropriate levels of staff in the different medical wards in a hospital. The rosters must provide suitably qualified nurses to cover the demand arising from the numbers of patients in the wards while observing work regulations, distinguishing between permanent and casual staff, ensuring that night and weekend shifts are distributed fairly, allowing for leave and days off, and accommodating a range of employee preferences. The resulting rostering problems are, in most cases, over-constrained. Approaches in the 1970s and 1980s addressed a number of problem formulations and solution techniques. A goal in many studies was to provide support tools to reduce the need for manual construction of nurse rosters. Some studies addressed the problem of determining staff levels and skills based on the numbers of patients and their medical needs. Others adopted mathematical programming, branch and bound techniques, or goal programming, approaches in which the objective contains weighted coverage and shift satisfaction terms and the constraints enforce hard rules such as the ratios of nurse grades that must be observed on shifts. Others used iterative algorithms to generate cyclic rosters in which fairness is achieved by having each nurse work the same sequence of shifts with individual shift sequences offset so as to provide the required coverage and skill mix within wards. In the 1990s a number of papers provided classifications of nurse rostering systems and reviews of methods for solving different classes of problems. Further advances were made in applying linear and/or mixed integer programming and network optimization techniques for developing nurse rosters. Constraint programming (CP) methods were also used to model the complicated rules associated with nurse rosters. The methods were applied to problems involving cyclic and non-cyclic rosters. Typically, the problems contained roster rules applicable to a particular hospital. As such, these approaches may require substantial reformulation for use in a different hospital.
A number of approaches have included a mix of heuristic and simulation techniques in an attempt to deal with more complex nurse rostering and clinical service problems. A simulation model augmented by AI methods is used to incorporate nurse training into rosters. A decision support system based on a shift pattern generating heuristic is used to provide an interactive system for developing weekly work schedules. A simulated annealing (SA) algorithm for solving a large set covering integer programming formulation is used to develop rosters for a mix of permanent and casual staff with demand specified in half hourly intervals over a 10 day period. Day to day nurse scheduling based on decisions arising from stochastic models of patient acuity, assessed via simulation modeling, is considered .An attempt to develop a knowledge based system for generating weekly nurse rosters and then adjusting the rosters so as to react to daily changes in demand and staff availability is discussed .More recently, a mix of tabu search (TS) and integer program sub problems is used to generate weekly ward rosters while satisfying a complex set of shift rules, cost restriction, nurse grade, and employee preference constraints. A hybrid TS algorithm is used to obtain solutions within a reasonable timeframe for a commercial nurse rostering system. The algorithms incorporate various tabu and hybrid TS procedures within a genetic algorithm (GA). These algorithms are designed to overcome one of the basic problems associated with using heuristics for complex nurse rostering problems, namely that, as indicated by the authors, ‘‘the quality of a solution is not necessarily a sum or combination of the partial solutions’’. A number of other aspects of health system rostering systems have been studied by different researchers. Models for developing rosters for nurses serving home care and regional clinics, in which travel between different locations is an important factor, have been developed. A queuing model is used to determine the staffing levels needed to handle call arrivals for inpatient, outpatient and other hospital generated appointments. Simulation modeling is used to consider operational management policies for providing maintenance staff in a large hospital. The use of a simple relational database system to manage work schedules for radiologists is discussed.