Modeling and solving simultaneous delivery and pick-up problem with stochastic travel and service times in home health care

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 constitute one of the largest forms of expenditure in the HHC industry, it is of importance to research the optimization of the HHC logistics. This paper considers an HHC routing problem with stochastic travel and service times, which comes from the logistics practice of HHC companies. A Stochastic Programming model with Recourse (SPR model) is proposed based on the specific structure of the supply chain. Three series of experiments are carried out to evaluate the model. Firstly, the SPR model is reduced to the deterministic one, and five approaches (Gurobi Solver, Hybrid Genetic Algorithm, Simulated Annealing, Bat Algorithm and Firefly Algorithm) are respectively implemented to solve the deterministic model. The SPR model is finally solved by the proposed SA-based heuristic algorithm. Evaluation of the solutions achieved by the two models highlights the advantages of considering stochastic travel and service times. Finally, a case study is given to explain how the SPR model works for an HHC company. This research will help HHC companies to make appropriate decisions when planning their vehicle routes.