Consistent home health care routing and scheduling problem under time uncertainty

• We tackle consistent home health care routing under travel and service time uncertainty. • Scenario-based and extreme value theory-based (EVT) stochastic models are introduced. • We propose a decomposition algorithm that effectively handles nonlinear constraints in EVT-based model. • We comprehensively demonstrate the value of the stochastic models against the model in the literature. This study addresses the challenge of routing and scheduling care workers for home health care logistics in a stochastic environment, where consistency in service delivery is crucial. The primary research question focuses on determining reliable schedules while ensuring timely care despite the uncertainty of travel and service times (TST). The objective is to maximize the number of new patients care workers can attend to while ensuring feasible and consistent schedules. To tackle this challenge, we propose a chance-constrained optimization modeling framework that ensures a likelihood of on-time arrivals, with arrival time distributions at patients estimated empirically and analytically via a discrete scenario set and an extreme value theory-based (EVT-based) approach, respectively. The EVT-based approximation incorporates nonlinear constraints that link patient visit times with the probability of on-time arrivals. The problem is decomposed into a master problem, which optimizes patient assignments, and subproblems, which generate feasible schedules and routes. To solve this problem, we propose a branch-and-check (B&Ch) algorithm, where the subproblems are solved efficiently via constraint programming. Computational results demonstrate that our solution approach, particularly with the EVT-based approximation, can efficiently handle practical benchmark instances while producing schedules with significantly higher service levels than the deterministic model in the literature.