Robust meal delivery service for the elderly: a case study in Hong Kong

Service providers in a community center in Hong Kong deliver meals to community-dwelling elderly, first from a central kitchen to intermediate depots by a van and then to the homes of the elderly via walking. We propose a modified two-echelon vehicle routing model with concerns of both delivery efficiency and workload fairness among workers, incorporating important practical aspects, such as continuity of care and unique features of buildings and served elderly. Notably, we employ robust optimization to address service time uncertainties that differentiate between frail and ordinary elderly. The robust model can be transformed into a mixed integer program, for which we provide two decomposition-based approaches to accelerate computation. Through a real-data case study, we verify the effectiveness of the proposed models. We show that robust solutions can protect against service time variations and achieve better performance while incurring a small additional cost over deterministic ones. We provide insights into choosing the level of conservatism and human resource planning for practitioners.