On two-echelon inventory systems with Poisson demand and lost sales

We derive approximations for the service levels of two-echelon inventory systems with lost sales and Poisson demand. Our method is simple and accurate for a very broad range of problem instances, including cases with both high and low service levels. In contrast, existing methods only perform well for limited problem settings, or under restrictive assumptions.\u

Ambulance Emergency Response Optimization in Developing Countries

The lack of emergency medical transportation is viewed as the main barrier to the access of emergency medical care in low and middle-income countries (LMICs). In this paper, we present a robust optimization approach to optimize both the location and routing of emergency response vehicles, accounting for uncertainty in travel times and spatial demand characteristic of LMICs. We traveled to Dhaka, Bangladesh, the sixth largest and third most densely populated city in the world, to conduct field research resulting in the collection of two unique datasets that inform our approach. This data is leveraged to develop machine learning methodologies to estimate demand for emergency medical services in a LMIC setting and to predict the travel time between any two locations in the road network for different times of day and days of the week. We combine our robust optimization and machine learning frameworks with real data to provide an in-depth investigation into three policy-related questions. First, we demonstrate that outpost locations optimized for weekday rush hour lead to good performance for all times of day and days of the week. Second, we find that significant improvements in emergency response times can be achieved by re-locating a small number of outposts and that the performance of the current system could be replicated using only 30% of the resources. Lastly, we show that a fleet of small motorcycle-based ambulances has the potential to significantly outperform traditional ambulance vans. In particular, they are able to capture three times more demand while reducing the median response time by 42% due to increased routing flexibility offered by nimble vehicles on a larger road network. Our results provide practical insights for emergency response optimization that can be leveraged by hospital-based and private ambulance providers in Dhaka and other urban centers in LMICs

Planning the delivery of home-based long-term care: A mathematical programming-based tool to support routes' planning

The adequate planning of home-based long-term care (HBLTC) is essential in the current European setting where long-term care (LTC) demand is increasing rapidly, and where home-based care represents a potential cost-saving alternative from traditional inpatient care. Particularly, this planning should involve proper route planning to ensure visits of health professionals to patients’ homes. Nevertheless, literature in the specific area of HBLTC planning is still scarce. Accordingly, this paper proposes a tool based on a mathematical programming model – the LTCroutes – for supporting the daily planning of routes to visit LTC patients’ homes in National Health Service-based countries. The model allows exploring the impact of considering different objectives relevant in this sector, including the minimization of costs and the maximization of service level. Patients’ preferences, traffic conditions and budget constraints are also considered in the proposed model. To illustrate the applicability of the model, a case study based on the National Network of LTC in Portugal (RNCCI) is analysed.O planeamento adequado de cuidados continuados ao domicílio é essencial na conjuntura atual Europeia em que a procura de cuidados continuados está a aumentar rapidamente, e em que os cuidados ao domicílio representam uma alternativa com potencial de poupança de custos relativamente ao tradicional internamento hospitalar. Particularmente, é necessário haver um planeamento adequado das rotas dos profissionais de saúde às casas dos pacientes. No entanto, a literatura na área específica de planeamento de cuidados continuados ao domicílio ainda é escassa. Nesse sentido, este artigo propõe uma ferramenta baseada num modelo de programação matemática - o LTCroutes - para apoiar o planeamento diário das rotas para visitar as casas dos pacientes com necessidade de cuidados continuados em países com Serviço Nacional de Saúde. O modelo desenvolvido permite explorar o impacto de considerar diferentes objetivos relevantes neste setor, incluindo a minimização de custos e a maximização do nível de serviço. As preferências dos pacientes, condições de trânsito e restrições de orçamento também são consideradas no modelo proposto. Para ilustrar a aplicabilidade do modelo, é analisado um caso de estudo baseado na Rede Nacional de Cuidados Continuados Integrados (RNCCI) em Portugal

Planning Strategies for Home Health Care Delivery

In home health care, continuity of care, wherein a patient is always visited by the same nurse, can be just as important as cost, as it is closely correlated to quality of care. While a patient typically receives care for two to three months, such that assigning a nurse to a patient impacts operations for lengthy periods of time, previous research focusing on continuity of care uses planning horizons that are often a week or shorter. This paper computationally demonstrates that considering a long planning horizon in this setting has significant potential for savings. Initially, a deterministic setting is considered, with all patient requests during the planning horizon known a priori, and the routing cost of planning for two to three months is compared with the cost when planning is done on a weekly basis. With inherent uncertainty in planning for such a long time horizon, a methodology is presented that anticipates future patient requests that are unknown at the time of planning. Computational evidence shows that its use is superior to planning on a weekly basis under uncertainty

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

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

IMPROVING HEALTHCARE DELIVERY: LIVER HEALTH UPDATING AND SURGICAL PATIENT ROUTING

Growing healthcare expenditures in the United States require improved healthcare delivery practices. Organ allocation has been one of the most controversial subjects in healthcare due to the scarcity of donated human organs and various ethical concerns. The design of efficient surgical suites management systems and rural healthcare delivery are long-standing efforts to improve the quality of care. In this dissertation, we consider practical models in both domains with the goal of improving the quality of their services. In the United States, the liver allocation system prioritizes among patients on the waiting list based on the patients' geographical locations and their medical urgency. The prioritization policy within a given geographic area is based on the most recently reported health status of the patients, although blood type compatibility and waiting time on the list are used to break ties. Accordingly, the system imposes a health-status updating scheme, which requires patients to update their health status within a timeframe that depends on their last reported health. However, the patients' ability to update their health status at any time point within this timeframe induces information asymmetry in the system. We study the problem of mitigating this information asymmetry in the liver allocation system. Specifically, we consider a joint patient and societal perspective to determine a set of Pareto-optimal updating schemes that minimize information asymmetry and data-processing burden. This approach combines three methodologies: multi-objective optimization, stochastic programming and Markov decision processes (MDPs). Using the structural properties of our proposed modeling approach, an efficient decomposition algorithm is presented to identify the exact efficient frontier of the Pareto-optimal updating schemes within any given degree of accuracy. Many medical centers offer transportation to eligible patients. However, patients' transportation considerations are often ignored in the scheduling of medical appointments. In this dissertation, we propose an integrated approach that simultaneously considers routing and scheduling decisions of a set of elective outpatient surgery requests in the available operating rooms (ORs) of a hospital. The objective is to minimize the total service cost that incorporates transportation and hospital waiting times for all patients. Focusing on the need of specialty or low-volume hospitals, we propose a computationally tractable model formulated as a set partitioning based problem. We present a branch-and-price algorithm to solve this problem, and discuss several algorithmic strategies to enhance the efficiency of the solution method. An extensive computational test using clinical data demonstrates the efficiency of our proposed solution method. This also shows the value of integrating routing and scheduling decisions, indicating that the healthcare providers can substantially improve the quality of their services under this unified framework

Planning the delivery of home social services: a mathematical programming-based approach to support routing and scheduling assignments

The increased average lifespan, together with low birth rates, are transforming the European Union's age pyramid. Currently, we are experiencing a transition towards a much older population structure. Given that the institutions that provide care to these population groups are limited by budgetary constraints, it is imperative to optimize several processes, among which route planning and staff scheduling stand out. This dissertation aims to develop a mathematical programming model to support the planning of routes and human resources for providers of Home Social Services. Beyond general Vehicle Routing Problems assumptions, the proposed model also considers the following features: i) working time regulations, ii) mandatory breaks, iii) users' autonomy, and iii) meals' distribution. The present model, implemented using GAMS software, focuses simultaneously on two objective functions: minimization of operating costs, and maximization of equity through the minimization of differences in teams' working times. Chebyshev's method was chosen to solve the developed multiobjective model. The model was built based on a Portuguese Private Institution of Social Solidarity. Through the application of the model, significant improvements are obtained when compared to the current planning of the partner institution, such as it is the case of an improved workload distribution between caregivers and routes that will result in lower costs for the institution. This model is fully enforceable to other institutions that provide services similar or equal to the institution used as a reference.O aumento da esperança média de vida, juntamente com baixas taxas de natalidade, estão a transformar a pirâmide etária da União Europeia. Atualmente, estamos a vivenciar uma transição direcionada para uma estrutura populacional muito mais envelhecida. Dado que as instituições que prestam cuidados a esta fração se encontram limitadas por restrições orçamentais, torna-se imperativo otimizar vários processos, dos quais se destacam planeamento de rotas e escalonamento de funcionárias. Esta dissertação visa introduzir um modelo de programação matemática com a finalidade de apoiar o planeamento de rotas e recursos humanos para prestadores de Serviços de Apoio Domiciliário. O modelo assenta, além dos pressupostos de um "Vehicle Routing Problem", nos seguintes: i) regulações de tempo de trabalho, ii) pausas obrigatórias, iii) autonomia dos utentes, e iv) distribuição de refeições. O modelo, desenvolvido através de software GAMS, foca-se em duas funções objetivo, simultaneamente: minimização dos custos operacionais, e maximização da equidade, através da minimização das diferenças nos tempos de trabalho das equipas. O método de Chebyshev foi o escolhido para desenvolver o modelo multiobjetivo. O modelo foi construído tendo por base uma Instituição Particular de Solidariedade Social em Portugal. Através da aplicação do modelo, obtêm-se melhorias significativas, quando comparado com o atual planeamento da instituição parceira, como é o caso de uma melhor distribuição da carga de trabalho entre as funcionárias e das rotas que resultam da redução dos custos operacionais da instituição. Este modelo é totalmente extensível a outras instituições que prestem serviços semelhantes ou iguais à instituição utilizada como referência

Strategies for dynamic appointment making by container terminals

We consider a container terminal that has to make appointments with barges dynamically, in real-time, and partly automatic. The challenge for the terminal is to make appointments with only limited knowledge about future arriving barges, and in the view of uncertainty and disturbances, such as uncertain arrival and handling times, as well as cancellations and no-shows. We illustrate this problem using an innovative implementation project which is currently running in the Port of Rotterdam. This project aims to align barge rotations and terminal quay schedules by means of a multi-agent system. In this\ud paper, we take the perspective of a single terminal that will participate in this planning system, and focus on the decision making capabilities of its intelligent agent. We focus on the question how the terminal operator can optimize, on an operational level, the utilization of its quay resources, while making reliable appointments with barges, i.e., with a guaranteed departure time. We explore two approaches: (i) an analytical approach based on the value of having certain intervals within the schedule and (ii) an approach based on sources of exibility that are naturally available to the terminal. We use simulation to get insight in the benefits of these approaches. We conclude that a major increase in utilization degree could be achieved only by deploying the sources of exibility, without harming the waiting time of barges too much

Hospital-wide therapist scheduling and routing: exact and heuristic methods

In this paper, we address the problem of scheduling and routing physical therapists hospital-wide. At the beginning of a day, therapy jobs are known to a hospital's physical therapy scheduler who decides for each therapy job when, where and by which therapist a job is performed. If a therapist is assigned to a sequence which contains two consecutive jobs that must take place in different treatment rooms, then transfer times must be considered. We propose three approaches to solve the problem. First, an Integer Program (IP) simultaneously schedules therapies and routes therapists. Second, a cutting plane algorithm iteratively solves the therapy scheduling problem without routing constraints and adds cuts to exclude schedules which have no feasible routes. Since hospitals are interested in obtaining quick solutions, we also propose a heuristic algorithm, which schedules therapies sequentially by simultaneously checking routing and resource constraints. Using real-world data from a hospital, we compare the performance of the three approaches. Our computational analysis reveals that our IP formulation fails to solve test, which have more than~30 jobs, to optimality in an acceptable solution time. In contrast, the cutting plane algorithm can solve instances with more than 100 jobs optimally. The heuristic approach obtains good solutions for large real-world instances within fractions of a second