A Multi-objective Approach to Nurse Scheduling with both Hard and Soft Constraints

-Solving the nurse scheduling problem properly has a great impact on nurses' working conditions which are strongly related to the level of quality of health care and recruiting of qualified personnel. In this paper, a multi-objective approach is shown to be a very flexible tool for modeling this problem. Hence, it could be used in several specific contexts. Three different solution techniques are also summarized. The approach is illustrated with an example, and numerical results are reported. Copyright © 1996 Elsevier Science Ltd INTRODUCTION Solving properly the nurse scheduling problem has a great impact on nurses' working conditions which are strongly related to the level of quality of health care and recruiting of qualified personnel. To improve nurses' level of satisfaction, schedules are generated individually for each hospital unit by the head-nurse. Unfortunately, this operation requires a large amount of time and effort from the head-nurses. The nurse scheduling problem involves generating a schedule of working days and days off for each nurse. There are three daily 8-h shifts: day shift (08:00-16:00), evening shift (16:00--24:00), and night shift (00:00-08:00). In this paper, we assume that each nurse always works during the same shift (i.e. there is no rotation). Hence, each shift corresponds to a separate problem. Three different approaches exist for dealing with this problem. The first provides a straightforward computer decision support system to assist head-nurses in handling their data [14, 18]. Mathematical programming models are used in the second approach. They can be divided into three different categories. The first type includes a single objective (in general, the objective is to maximize the overall level of satisfaction) subject to constraints related to the workforce requirements and to administrative and union contract specifications [2, 3, 6, 20]. In general, these models deal with very specific problems, and they require large amounts of computation time. In [21], Warner proposes a heuristic exchange procedure to select each worker's schedule among a set of schedules generated a priori and satisfying administrative and union contract constraints. The objective is to maximize the overall workers' satisfaction given workforce requirements constraints. Several other models [7, 9, 12, 16] are offsprings of Warner's formulation, while other authors [1, 13, 15] prefer using multi-objective mathematical programming. These models appear to be more realistic and have more flexibility in modifying the relative priority of the objectives. Finally, the third approach generates a tandem [11] or hybrid [8] expert system embedding mathematical programming techniques. Chen and Yeung introduce a system of this type in [8] using a zero-one goal programming module to generate appropriate schedules within each shift while using an expert system module to deal with shift rotation. In this paper, we deal with the nurse scheduling problem with a multi-objective mathematical programming approach. Our model includes several objectives found in other models (see [8] for instance): limiting the number of consecutive working days to prevent long stretches, preventing 010 situations where nurses must work for a single day between 2 days off, and allowing nurses'