Solving a multi-depot vehicle routing problem with time windows and fuzzy demands using metaheuristic algorithms in home health care services

Todays, meeting the healthcare needs of patients at home has many benefits. By providing regular and timely healthcare servicing, in addition to reducing costs, the patient's recovery process also speeds up. In this paper, a multi-depot vehicle routing problem is considered with regard to time windows and fuzzy demands. This paper attempts to optimize provided mathematical formulation in such a way that the distance traveled, total travel time, the number of transportation vehicles and transportation cost be minimized; also by taking the hard time window to meet patients , patient satisfaction rate will increase. This is a complex and difficult problem, and it takes a long time to solve it through linear programming and existing software. Therefore, in this paper, two general approaches including genetic algorithm and particle swarm optimization are used to tackle the problem. The response surface methodology (RSM) has been used to set parameters for meta-algorithms. To illustrate the efficiency of proposed algorithms, a number of test problems are solved and computational results are compared with the solutions obtained with the GAMS software.