Characterisation and Generation of Nurse Scheduling Problem Instances

In this paper, we propose different complexity indicators for the well-known nurse scheduling problem (NSP). The NSP assigns nurses to shifts per day taking both hard and soft constraints into account. The objective is to maximize the nurses’ preferences and to minimize the total penalty cost from violations of the soft constraints. The problem is known to be NP-hard. Due to its complexity and relevance in practice, the operations research literature has been overwhelmed by different procedures to solve the problem. The complexity has resulted in the development of several (meta-)heuristic procedures, able to solve a NSP instance heuristically in an acceptable time limit. The practical relevance has resulted in a never-ending amount of different NSP versions, taking practical, case-specific constraints into account. The contribution of this paper is threefold. First, we describe our complexity indicators to characterize a nurse scheduling problem instance. Secondly, we develop a NSP generator to generate benchmark instances to facilitate the evaluation of existing and future research techniques. Finally, we perform some preliminary tests on a simple IP model to illustrate that the proposed indicators can be used as predictors of problem complexity.