A hybrid genetic algorithm for a home health care routing problem with time window and fuzzy demand

Home Health Care (HHC) companies are widespread in European countries, and aim to serve patients at home to help them recover from illness and injury in a personal environment. Since transportation costs are among the biggest sources of expenditure in company activities, it is of great significance to optimize this in the Home Health Care industry. From the perspective of optimizing the cost of transportation, this paper studies the Vehicle Routing Scheduling problem as it applies to HHC companies. According to a survey of the HHC companies, during the process of delivering medication drugs, the quantity of drugs required for each patient is non-deterministic when the company makes planned routes. This paper considers uncertain demand as a fuzzy variable, which is closer to a potential real life scenario. A Home Health Care Scheduling Problem with fuzzy demand is considered and a fuzzy chance constraint model is designed. We propose a hybrid genetic algorithm integrated with stochastic simulation methods to solve the proposed model. Firstly, the problem is reduced to the classical vehicle routing problem within a time window. Experimental results for Solomon’s and Homberger’s benchmark instances show that the proposed algorithm performs efficiently. Then other experiments on the fuzzy version model are undertaken with the variable value of the Dispatcher Preference Index (DPI) parameter between [0, 1]. Finally, the influence of DPI on the final objective and the indicators of the problem are discussed using stochastic simulation, and the best value of DPI is obtained. This research will help HHC companies to make appropriate decisions when arranging their vehicle scheduling routes.