Workload Equity in Vehicle Routing Problems: A Survey and Analysis

Over the past two decades, equity aspects have been considered in a growing number of models and methods for vehicle routing problems (VRPs). Equity concerns most often relate to fairly allocating workloads and to balancing the utilization of resources, and many practical applications have been reported in the literature. However, there has been only limited discussion about how workload equity should be modeled in VRPs, and various measures for optimizing such objectives have been proposed and implemented without a critical evaluation of their respective merits and consequences. This article addresses this gap with an analysis of classical and alternative equity functions for biobjective VRP models. In our survey, we review and categorize the existing literature on equitable VRPs. In the analysis, we identify a set of axiomatic properties that an ideal equity measure should satisfy, collect six common measures, and point out important connections between their properties and those of the resulting Pareto-optimal solutions. To gauge the extent of these implications, we also conduct a numerical study on small biobjective VRP instances solvable to optimality. Our study reveals two undesirable consequences when optimizing equity with nonmonotonic functions: Pareto-optimal solutions can consist of non-TSP-optimal tours, and even if all tours are TSP optimal, Pareto-optimal solutions can be workload inconsistent, i.e. composed of tours whose workloads are all equal to or longer than those of other Pareto-optimal solutions. We show that the extent of these phenomena should not be underestimated. The results of our biobjective analysis are valid also for weighted sum, constraint-based, or single-objective models. Based on this analysis, we conclude that monotonic equity functions are more appropriate for certain types of VRP models, and suggest promising avenues for further research.Comment: Accepted Manuscrip

Pattern-based decompositions for human resource planning in home health care services

Home health care services play acrucial role in reducing the hospitalization costs due to the increase of chronic diseases of elderly people. At the same time, they allow us to improve the quality of life for those patients that receive treatments at their home. Optimization tools are therefore necessary to plan service delivery at patients' homes. Recently, solution methods that jointly address the assignment of the patient to the caregiver (assignment), the definition of the days (pattern) in which caregivers visit the assigned patients (scheduling), and the sequence of visits for each caregiver (routing) have been proposed in the scientific literature. However, the joint consideration of these three level of decisions may be not affordable for large providers, due to the required computational time. In order to combine the strength and the flexibility guaranteed by a joint assignment, scheduling and routing solution approach with the computational efficiency required for large providers, in this study we propose a new family of two-phase methods that decompose the joint approach by incrementally incorporating some decisions into the first phase.The concept of pattern is crucial to perform such a decomposition in a clever way. Several scenarios are analyzed by changing the way in which resource skills are managed and the optimization criteria adopted to guide the provider decisions. The proposed methods are tested on realistic instances. The numerical experiments help us to identify the combinations of decomposition techniques, skill management policies and optimization criteria that best fit with problem instances of different size

Gestión logística de sistemas de hospitalización domiciliaria: una revisión crítica de modelos y métodos

RESUMEN: Los servicios de Hospitalización Domiciliaria (HD) se basan en una red de distribución, en la cual los pacientes son hospitalizados en sus casas y los prestadores de servicios de salud deben entregar cuidados médicos coordinados a los pacientes. La demanda de estos servicios está creciendo rápidamente y los gobiernos y proveedores de servicios de salud enfrentan el reto de tomar un conjunto de decisiones complejas en un sector con un componente logístico importante. En este artículo se presenta una revisión crítica de los modelos y métodos utilizados para darle soporte a las decisiones logísticas en HD. Para esto se presenta primero un marco de referencia, con el objetivo de identificar las oportunidades de investigación en el campo. Con base en dicho marco, se presenta la revisión de la literatura y la identificación de brechas en la investigación. En particular, se hace énfasis en la necesidad de desarrollar e implementar metodologías más integradas para dar soporte a las decisiones estratégicas y tácticas y de considerar puntos clave de los sistemas reales.ABSTRACT: Home Health Care (HHC) services are based on a delivery network in which patients are hospitalized at their homes and health care providers must deliver coordinated medical care to patients. Demand for HHC services is rapidly growing and governments and health care providers face the challenge to make a set of complex decisions in a medical service business that has an important component of logistics problems. The objective of this paper is to provide a critical review of models and methods used to support logistics decisions in HHC. For this purpose, a reference framework is proposed first in order to identify research perspectives in the field. Based on this framework, a literature review is presented and research gaps are identified. In particular, the literature review reveals that more emphasizes is needed to develop and implement more integrated methodologies to support decisions at tactical and strategic planning levels and to consider key features from real systems

Efficient Duration-Based Workload Balancing for Interdependent Vehicle Routes

Vehicle routing and scheduling problems with interdependent routes arise when some services must be performed by at least two vehicles and temporal synchronization is thus required between the starting times of these services. These problems are often coupled with time window constraints in order to model various real-world applications such as pickup and delivery with transfers, cross-docking and home care scheduling. Interdependent routes in these applications can lead to large idle times for some drivers, unnecessarily lengthening their working hours. To remedy this unfairness, it is necessary to balance the duration of the drivers\u27 routes. However, quickly evaluating duration-based equity functions for interdependent vehicle routes with time windows poses a significant computational challenge, particularly when the departure time of routes is flexible. This paper introduces models and algorithms to compute two well-known equity functions in flexible departure time settings: min-max and range minimization. We explore the challenges and algorithmic complexities of evaluating these functions both from a theoretical and an experimental viewpoint. The results of this paper enable the development of new heuristic methods to balance the workload of interdependent vehicle routes with time windows

The sustainable home health care process based on multi-criteria decision-dupport

The increase in life expectancy has led to a growing demand for Home Health Care (HHC) services. However, some problems can arise in the management of these services, leading to high computational complexity and time-consuming to obtain an exact and/or optimal solution. This study intends to contribute to an automatic multi-criteria decision-support system that allows the optimization of several objective functions simultaneously, which are often conflicting, such as costs related to travel (distance and/or time) and available resources (health professionals and vehicles) to visit the patients. In this work, the HHC scheduling and routing problem is formulated as a multi objective approach, aiming to minimize the travel distance, the travel time and the number of vehicles, taking into account specific constraints, such as the needs of patients, allocation variables, the health professionals and the transport availability. Thus, the multi-objective genetic algorithm, based on the NSGA-II, is applied to a real-world problem of HHC visits from a Health Unit in Bragança (Portugal), to identify and examine the different compromises between the objectives using a Pareto-based approach to operational planning. Moreover, this work provides several efficient end-user solutions, which were standardized and evaluated in terms of the proposed policy and compared with current practice. The outcomes demonstrate the significance of a multi-criteria approach to HHC services.The authors are grateful to the Foundation for Science and Technology (FCT, Portugal) for financial support through national funds FCT/MCTES (PIDDAC) to CeDRI (UIDB/05757/2020 and UIDP/05757/2020), SusTEC (LA/P/0007/2021) and ALGORITMI Research Centre / LASI (UIDB/00319/2020). Filipe Alves thanks the FCT for supporting its research with the Ph.D. grant SFRH/BD/143745/2019.info:eu-repo/semantics/publishedVersio

Planning and Scheduling Optimization

Although planning and scheduling optimization have been explored in the literature for many years now, it still remains a hot topic in the current scientific research. The changing market trends, globalization, technical and technological progress, and sustainability considerations make it necessary to deal with new optimization challenges in modern manufacturing, engineering, and healthcare systems. This book provides an overview of the recent advances in different areas connected with operations research models and other applications of intelligent computing techniques used for planning and scheduling optimization. The wide range of theoretical and practical research findings reported in this book confirms that the planning and scheduling problem is a complex issue that is present in different industrial sectors and organizations and opens promising and dynamic perspectives of research and development

Resource constrained routing and scheduling: Review and research prospects

In the service industry, it is crucial to efficiently allocate scarce resources to perform tasks and meet particular service requirements. What considerably complicates matters is when these resources, for example skilled technicians, nurses, and home carers have to visit different customer locations. This paper provides a comprehensive survey on resource constrained routing and scheduling that unveils the problem characteristics with respect to resource qualifications, service requirements and problem objectives. It also identifies the most effective exact and heuristic algorithms for this class of problems. The paper closes with several research prospects

Modelling and (re-)planning periodic home social care services with loyalty and non-loyalty features

This work was partially supported by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the project UID/MAT/00297/2019 (Centro de Matematica e Aplicacees).The aging population alongside little availability of informal care are two of the several factors leading to an increased need for assisted living support. In this work, we tackle a home social care service problem, motivated by two real case studies where a new loyalty scheme must be considered: within a week, patient-caregiver loyalty should be pursued but, between weeks, the caregivers must rotate among patients (non-loyalty). In addition, a common situation in this kind of service is also addressed: the need of a constant re-planning caused by the leaving of patients and the arrival of new ones. This new plan should be such that minimum disturbance is caused to the visiting hours of current patients, the caregivers’ travelling time between visits is minimized, and the workload is balanced among caregivers. A multi-objective optimization approach based on mixed-integer models is developed. Results on the two real case studies show that both institutions can efficiently re-plan their activities without much disturbance on the visits of their patients, and with a patient-caregiver loyalty scheme suiting their needs.authorsversionpublishe