Robust home health care services: an enhanced matheuristic optimization

During the last decades, optimization for home health care services has become increas- ingly important. In this study, we model a home health care model which is close to reality by taking uncertainty in nurse availability (e.g. they might call sick on a short notice) into account. Different features arising from the home health care services in the reality are also stated. A mixed integer linear programming formulation is developed to present the deter- ministic case of the studied problem in which uncertainty is ignored. A nonlinear formulation formulated based on the principles of robust optimization is also developed to represent the robust home health care model in which uncertainty is taken into account. An algorithm based on the integration of mathematical models, genetic algorithm, and robust optimization is proposed. Experimental results on real historical data from a company operating in Lugano Switzerland show that the method we propose is efficient to provide a weekly operational plan.