A Bi-objective home health care routing and scheduling model with considering nurse downgrading costs

In recent years, the management of health systems is a main concern of governments and decision-makers. Home health care is one of the newest methods of providing services to patients in developed societies that can respond to the individual lifestyle of the modern age and the increase of life expectancy. The home health care routing and scheduling problem is a generalized version of the vehicle routing problem, which is extended to a complex problem by adding special features and constraints of health care problems. In this problem, there are multiple stakeholders, such as nurses, for which an increase in their satisfaction level is very important. In this study, a mathematical model is developed to expand traditional home health care routing and scheduling models to downgrading cost aspects by adding the objective of minimizing the difference between the actual and potential skills of the nurses. Downgrading can lead to nurse dissatisfaction. In addition, skillful nurses have higher salaries, and high-level services increase equipment costs and need more expensive training and nursing certificates. Therefore, downgrading can enforce huge hidden costs to the managers of a company. To solve the bi-objective model, an ε-constraint-based approach is suggested, and the model applicability and its ability to solve the problem in various sizes are discussed. A sensitivity analysis on the Epsilon parameter is conducted to analyze the effect of this parameter on the problem. Finally, some managerial insights are presented to help the managers in this field, and some directions for future studies are mentioned as well.