Robust Routing and Scheduling of Home Healthcare Workers: A Nested Branch-and-Price Approach

TL;DR

This paper presents a robust optimization approach for multi-day home healthcare worker routing and scheduling, addressing uncertainties and multiple criteria to improve patient care and operational efficiency.

Contribution

It introduces a novel nested branch-and-price method for robust, multi-criteria home healthcare routing and scheduling, considering uncertainty and complex constraints.

Findings

Instances can be solved to optimality within reasonable time

Robustness reduces patient load per caregiver

Geographical proximity is less critical in patient assignment

Abstract

The global home healthcare market is growing rapidly due to aging populations, advancements in healthcare technology, and patient preference for home-based care. In this paper, we study the multi-day planning problem of simultaneously deciding patient acceptance, assignment, routing, and scheduling under uncertain travel and service times. Our approach ensures cardinality-constrained robustness with respect to timely patient care and the prevention of overtime. We take into account a wide range of criteria including patient time windows, caregiver availability and compatibility, a minimum time interval between two visits of a patient, the total number of required visits, continuity of care, and profit. We use a novel systematic modeling scheme that prioritizes health-related criteria as hard constraints and optimizes cost and preference-related criteria as part of the objective function. We present a mixed-integer linear program formulation, along with a nested branch-and-price technique. Results from a case study in Austin, Texas demonstrate that instances of realistic size can be solved to optimality within reasonable runtimes. The price of robustness primarily results from reduced patient load per caregiver. Interestingly, the criterion of geographical proximity appears to be of secondary priority when selecting new patients and assigning them to caregivers.