a new mathematical model for multi period multi depot home health care routing scheduling problem

background & aim: nowadays, home health care services play significant roles in modern societies. such services allow the elderly and needy people to pass their treatment process at their own houses in a friendly environment. in this paper, weekly routing and scheduling problem of home health care personnel was investigated. methods & materials: insufficient number of expert personnel or overlapping time windows of some patients would result in delayed beginning of the service time for patients. this paper attempted to solve multi-period multi-depot routing-scheduling problem with regard to the delay in giving services to patients, simultaneously. presented model is solved by gams software in small scale and hybrid genetic-imperialist competitive algorithm in large scale. results: for planning and managing the home health care institutions’ activity, it must be determined that which personnel will visit the patient and when the visit is met. this paper, considering the probable delay in giving services to the patients, would determine the best plan for personnel visit. starting time of each visit, number of patients that would be assigned to each personnel, occurred delay in patients’ visits, and each personnel’s overtime are the results of the proposed paper. conclusion: proposed model will minimize home health care institution’s total cost and increase the satisfaction of patients through minimizing the occurred delay. also, the hybrid algorithm indicates good performance for the model of this paper.