Multi-depot home health care routing and scheduling problem with multimodal transportation: Mathematical model and solution methods

Abstract Providing appropriate home health care is one of the increasing concerns in the health care organizations. Home Health Care provides various services for disabled or elderly individuals at their homes. Also, deal with the current critical situation of the coronavirus disease (COVID-19) due to the limited capacity of hospitals and the feeling of insecurity in crowded places, home health care is more recommended. This paper addresses a Home Health Care Routing and Scheduling Problem (HHCRSP) with two modes of transportations including public and private modes. Also, multi-depot version of the problem is studied to enhance the service delivery in scattered points. In this study, a mathematical model is presented based on a Mixed Integer Linear P‌rogramming (MILP) whose objective function is minimization of the sum of the travel distance and overtime costs. Furthermore, three meta-heuristic algorithms including Invasive Weed Optimization (IWO), Grasshopper Optimization Algorithm (GOA) and Simulated Annealing (SA) are presented for solving the large-sized problems. Since the performance of meta-heuristic algorithms depends on setting the parameters, Taguchi method is used to statistically set parameters of the developed algorithms. The computational results have shown that the proposed IWO has worked better than the other two proposed algorithms statistically.