Joint Optimization of Service Routing and Scheduling in Home Health Care

TL;DR

The paper introduces VRASP, a joint optimization framework for home health care that simultaneously schedules service start times and caregiver routes under uncertainty. It advances deterministic ($P_0$) and stochastic ($P_1$) formulations, the latter solved via Sample Average Approximation (SAA), and develops a Variable Neighborhood Search (VNS) heuristic to efficiently obtain high-quality solutions. Computational results show the stochastic model improves performance over the deterministic one, and the VNS delivers near-optimal solutions for small instances with superior scalability for larger problems compared to CPLEX. Practically, the approach provides HHC providers with a decision-support tool that reduces waiting, improves punctuality, and enhances utilization under travel and service-time variability.

Abstract

The growing aging population has significantly increased demand for efficient home health care (HHC) services. This study introduces a Vehicle Routing and Appointment Scheduling Problem (VRASP) to simultaneously optimize caregiver routes and appointment times, minimizing costs while improving service quality. We first develop a deterministic VRASP model and then extend it to a stochastic version using sample average approximation to account for travel and service time uncertainty. A tailored Variable Neighborhood Search (VNS) heuristic is proposed, combining regret-based insertion and Tabu Search to efficiently solve both problem variants. Computational experiments show that the stochastic model outperforms the deterministic approach, while VNS achieves near-optimal solutions for small instances and demonstrates superior scalability for larger problems compared to CPLEX. This work provides HHC providers with a practical decision-making tool to enhance operational efficiency under uncertainty.

Figures (1)

• Figure 1: Overlap Area