The Nurse Rostering Problem (NRP) is defined as assigning a number of nurses to different shifts during a specified planning period, considering some regulations and preferences. This is often very difficult to solve in practice particularly by applying a sole approach. In this paper, we propose a novel hybrid algorithm combining the strengths of Integer Programming (IP) and Variable Neighbourhood Search (VNS) algorithms to design a hybrid method for solving the NRP. After generating the initial solution using a greedy heuristic, the solution is further improved by employing a Variable Neighbourhood Descent algorithm. Then IP, deeply embedded in the VNS algorithm, is employed within a ruin-and-recreate framework to assist the search process. Finally, IP is called again to further refine the solution during the remaining time. We utilize the strength of IP not only to diversify the search process, but also to intensify the search efforts. To identify the quality of the current solution, we use a new generic scoring scheme to mark the low-penalty parts of the solution. Based on the computational tests with 24 instances recently introduced in the literature, we obtain better results with our proposed algorithm, where the hybrid algorithm outperforms two state-of-the-art algorithms and Gurobi in most of the instances. Furthermore, we introduce 11 randomly generated instances to further evaluate the efficiency of the hybrid algorithm, and we make these computationally challenging instances publicly available to other researchers for benchmarking purposes.
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 in- stances 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
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