Integrated home health care optimization via genetic algorithms and mathematical programming

This study is a novel contribution to the field of optimization in home health care services, both model and solution approach. We address an integration of interrelated optimization problems: rostering, assignment, routing, and scheduling in multi-period workforce planning under uncertainty in nurse availability. Our model explicitly handles the constraints related to workload balancing and multi-period planning, and the principles of robust optimization approach are followed to find a robust solution. We introduce a matheuristic algorithm that works based on a genetic algorithm mechanism to tackle four optimization problems sequentially but interactively. Two nested genetic algorithms are integrated. Steady-state reproduction is applied to both the inner and outer ones to reduce computational time/memory requirements. Two replacement strategies are carried out: replacing solutions at random and replacing the worst solutions. Experiments are conducted on instances based on real historical data from a company operating in Lugano, Switzerland. The obtained results show that, in genetic algorithm, the strategy of replacing solutions at random outperforms the strategy of replacing the worst solutions in our case. Addressing the four optimization problems in a unified approach results in a more efficient solution. In addition, the proposed algorithm: i) is able to handle large instances and to provide a weekly workforce planning solution in a reasonable time, which is reliable against uncertainty in nurse availability; ii) can be used to efficiently support managers in evaluating the trade off between the robustness and the operational cost of a solution.