A new mathematical model for designing and improving the performance of a home health care logistics network

To provide better care for the elderly, health trustees establish home health care centers in cities. These centers offer services at homes, and a logistics network is essential for providing these services. An integrated framework is developed to design such a network by which various logistical decisions are made under inherent epistemic uncertainty of the travel and service times. A new mixed integer linear programming model is developed, and its equivalent deterministic formulation is obtained using a well-applied possibilistic programming approach. An improved genetic algorithm is also devised to solve large-sized instances and various sensitivity analyses are performed on key factors. Finally, a case study is presented to validate the developed model and its solution method. The numerical results demonstrate 20% reduction in the total time of employing care givers at almost 3.5% cost savings.