Home health care routing and scheduling problem: A preventive approach

Abstract

Due to several challenges in hospital service caused by the increasing demand for hospitalization, Home Health Care Service (HHCS) has become the best alternative for hospitals to provide a delivery service system that allows patients to be cared at their place of residence. The HHCS offers benefits because it helps hospitals to reduce costs, prevent contagiousinfections and give some emotional and psychological benefits to the patients. In this paper, a tactical and operational solution is proposed to the Home Health Care Routing and Scheduling Problem (HHCRSP) applied in the study case presented by Instituto Roosevelt (IR). IR manually defines the daily routes, and it generates the monthly staffing and workforce scheduling based on the HHCS head’s experience. This causes additional workload and human errors in routing assignments, staffing, and demand forecasting. This project integrates a single-objective Mixed Integer Linear Programming (MILP) model to tackle the monthly staffing and scheduling decisions, and a multi-objective MILP model to the scheduling and routing problem. The aim is to minimize the tactical costs associated with doctor's hiring and monthly assignment, and to minimize the operative costs and the gap differences between the maximum and minimum workload of the doctor’s routes assignment. Due to the high computation times of the routing MILP, a Non-dominated Sorting Genetic Algorithm (NSGA II) metaheuristic is applied. The final aim of the project is to design a tool that builds the daily route and the monthly staffing and workforce scheduling of the HHCS offered by the Instituto Roosevelt. Additionally, the tool will consider different stochastic components (demand and travel time) with a series of constraints associated with the Instituto Roosevelt’s case study. The methodology to deal with the stochastic parameters is through simulation and a Genetic Algorithm sim-heuristic that hybridizes the NSGA II with Monte Carlo Simulation. These methodologies and the MLPI’s proposed are carried out on a set of instances and their efficiencies are compared to test their performance. In the deterministic routing solution, the GA shows a competitive result by giving an average difference of 16% of the optimal costs and 0.4% on the optimal workload balance. In the stochastic routing component, it is evident that the results obtained by deterministic genetics with NSGA II are good, since approximately 70% of the time they obtain better results than the Institute's proposal. According to the literature review, the combined tactical and operational decisions with stochastic parameters have been little applied and discussed on HHCRSP (Home Health Care Routing and Scheduling Problem). That is the added value of this work.