A hybrid model of integer programming and variable neighbourhood search for highly-constrained nurse rostering problems

This paper presents a hybrid multi-objective model that combines Integer Programming (IP) and Variable Neighbourhood Search (VNS) to deal with highly constrained nurse rostering problems in modern hospital environments. An IP is first used to solve the subproblem which includes the full set of hard constraints and a subset of soft constrains. A basic VNS then follows as a postprocessing procedure to further improve the IP’s resulting solutions, and the satisfaction of the excluded constraints from the preceding IP model is the VNS’s major concern in its search. Very promising results are reported compared with a commercial genetic algorithm and a hybrid VNS approach on real instances arising in a Dutch hospital. The comparison results demonstrate that our hybrid approach does combine advantages of both the IP and the VNS to beat pure metaheuristics in solving this type of problems. We also believe that the proposed approach can be applied to other resource allocation problems with a large number of constraints.