Mid-term home health care planning problem with flexible departing way for caregivers

Abstract

Home Health Care (HHC) centers aim to deliver health care service to patients at their domiciles to help them recover in a convenient environment. Staffs planning in HHC centers have always been a challenging task because this issue not only just dispatches suitable caregivers to serve patients with considering many peculiar constraints, such as, time window of patients, qualification and mandatory break of caregivers, but also seeks optimal solution to achieve its objective, which is often taken to equivalent to minimize total operational cost, or to maximize satisfaction of patients or caregivers. This chapter formulates a mixed integer programming model for mid-term HHC planning problem, which aims at minimizing the total operational cost of HHC centers. We define the real-life constraints as follows: patients need to be visited once or for several times during the planning horizon by capable caregivers; patients must be served in their time window; each patient has specific preferences to caregivers for some personal reasons (e.g. gender); caregivers work in their contract working time with no more than daily maximum working time; a lunch break happens only if caregivers start to work before the lunch start time and finish working after the lunch end time. Specially, in real life, caregivers can use their own cars or rent cars from HHC center to complete their service tasks, and thus, this chapter firstly concerns a flexible departing way for caregivers, which means that each caregiver can either start working from their domiciles or from HHC center according to the transportation mode chosen though they must end their work at HHC center. We call this way of providing service by caregivers as Center and Domicile to Center (CDC). In addition, in order to discuss the relationship between caregivers’ geographical areas and optimal results, we put forward the other two scenarios, (1) each caregiver must only depart from and return to the HHC center, and this case is named as Center to Center (CC); (2) each caregiver departs from their own domicile and returns to HHC center, this scenario is named as Domicile to Center (DC). As the departing ways for caregivers keep the same in these two scenarios, they can be called fixed departing ways. All these models are solved by a commercial programming solver Gurobi through the two group modified classic Periodic Vehicle Routing Problem with Time Windows (PVRPTW) benchmark instances and the other two group instances generated randomly. In total, 21 instances with up to 12 caregivers, 20 patients and 47 demands during the planning horizon. Experimental results show that the model CDC is the best model as it can find optimal solution for 90% instances, and solve the problem with least computational time for 40% instances. Model CC gets the worst results with no optimal solution can be obtained for all instances. This work will help HHC centers planners make proper decision through managing the depart way of caregivers that satisfy the real life constraints, minimize the total operational cost as well as find the optimal solution efficiency.