Loek van Montfort | Searcharxiv

arXiv2026

Task-splitting in home healthcare routing and scheduling

This paper introduces the concept of task-splitting into home healthcare (HHC) routing and scheduling. It focuses on the design of routes and timetables for caregivers providing services at patients' homes. Task-splitting is the division of a (lengthy) patient visit into separate visits that can be performed by different caregivers at different times. The resulting split parts may have reduced caregiver qualification requirements, relaxed visiting time windows, or a shorter/longer combined duration. However, additional temporal dependencies can arise between them. To incorporate task-splitting decisions into the planning process, we introduce two different mixed integer linear programming formulations, a Miller-Tucker-Zemlin and a time-indexed variant. These formulations aim to minimize operational costs while simultaneously deciding which visits to split and imposing a potentially wide range of temporal dependencies. We also propose pre-processing routines for the time-indexed formulation and two heuristic procedures. These methods are embedded into the branch-and-bound approach as primal and improvement heuristics. The results of our computational study demonstrate the additional computational difficulty introduced by task-splitting possibilities and the associated additional synchronization, and the usefulness of the proposed heuristic procedures. From a planning perspective, our results indicate that integrating task-splitting decisions into the planning process reduces staff requirements, decreases HHC operational costs, and allows caregivers to spend relatively more time on tasks aligned with their qualifications.

math.OC↗

arXiv2026

An exact algorithm for vehicle routing problems with temporal dependency constraints

Temporal dependencies between customer visits, such as synchronization constraints, pose a fundamental challenge in vehicle routing. These dependencies, which arise in applications such as home healthcare routing, aircraft scheduling, and technician routing, introduce inter-route constraints that make the resulting problems significantly harder to solve. We present an exact solution method for vehicle routing problems with temporal dependencies capable of handling all types of temporal dependencies studied in the literature, unlike most existing approaches that target specific subclasses. Our approach is based on a fragment-based formulation in which routes are represented as sequences of a new type of fragment, designed to handle temporal dependency constraints. This formulation is solved via a price-cut-and-enumerate algorithm that computes a lower bound using alternating column-and-row generation, obtains an initial upper bound, and iteratively refines both bounds through fragment enumeration and branch-and-cut, supported by several new classes of valid inequalities. Computational experiments show that our method significantly outperforms state-of-the-art benchmark methods and is able to solve previously intractable instances while covering a wider range of temporal dependencies.

math.OC↗