A hybrid integer and constraint programming approach to solve nurse rostering problems

The Nurse Rostering Problem can be defined as assigning a series of shift sequences (schedules) to several nurses over a planning horizon according to some limitations and preferences. The inherent benefits of generating higher-quality schedules are a reduction in outsourcing costs and an increase in job satisfaction of employees. In this paper, we present a hybrid algorithm, which combines Integer Programming and Constraint Programming to efficiently solve the highly-constrained Nurse Rostering Problem. We exploit the strength of IP in obtaining lower-bounds and finding an optimal solution with the capability of CP in finding feasible solutions in a co-operative manner. To improve the performance of the algorithm, and therefore, to obtain high-quality solutions as well as strong lower-bounds for a relatively short time, we apply some innovative ways to extract useful information such as the computational difficulty of instances and constraints to adaptively set the search parameters. We test our algorithm using two different datasets consisting of various problem instances, and report competitive results benchmarked with the state-of-the-art algorithms from the recent literature as well as standard IP and CP solvers, showing that the proposed algorithm is able to solve a wide variety of instances effectively.