Matheuristic optimization for robust home health care services

In modern societies, home health care services are becoming increasingly important. Having optimized solutions on operational issues can play a potential role in offering patients high quality medical service as well as taking in better regard, the needs of care providers. An important issue to consider is the uncertainty on the problem data. In more details, an optimal solution that was obtained under the assumption that the collected problem data are accurate, can turn out to be infeasible when it is implemented in the reality, because the data encountered in the reality might differ from the assumed data in the optimization model. In this paper, we consider the uncertainty on the availability of the nurses (e.g. they might call sick on short notice), and we follow a robust optimization approach to handle the case when nurses are unexpectedly unable to operate. A matheuristic method based on a constructive heuristic combined with a genetic algorithm and mathematical programming is proposed to provide a near-optimal solution both in terms of nurse-patient assignment and nurse scheduling and routing.