A Lagrangian Relaxation-based Algorithm to Solve a Home Health Care Routing Problem

Nowadays, a rapid growth in the rate of life expectancy can be seen especially in the developed countries. Accordingly, the population of elderlies has been increased. By another point of view, the number of hospitals, retirement homes along with medical staffs has not been grown with a same rate. Hence, Home Health Care (HHC) operations including a set of nurses and patients have been developed recently by both academia and health practitioners to consider elderlies’ preferences willing to receive their cares at their homes instead of hospitals or retirement homes. To alleviate the drawbacks of pervious works and make HHC more practical, this paper introduces not only a new mathematical formulation considering new suppositions in this research area but also a solution approach based on Lagrangian relaxation theory has been employed for the first time. The main strategy of used algorithm aims to fill the gap between the lower bound and upper bound of problem and finds a solution which has both optimality and feasibility properties. By generating a number of numerical examples, results show the performance of the proposed algorithm analyzed by different criteria as well as the efficiency of developed formulation through a set of sensitivity analyses.