An Optimisation-based Framework for Complex Business Process: Healthcare Application

The Irish healthcare system is currently facing major pressures due to rising demand, caused by population growth, ageing and high expectations of service quality. This pressure on the Irish healthcare system creates a need for support from research institutions in dealing with decision areas such as resource allocation and performance measurement. While approaches such as modelling, simulation, multi-criteria decision analysis, performance management, and optimisation can – when applied skilfully – improve healthcare performance, they represent just one part of the solution. Accordingly, to achieve significant and sustainable performance, this research aims to develop a practical, yet effective, optimisation-based framework for managing complex processes in the healthcare domain. Through an extensive review of the literature on the aforementioned solution techniques, limitations of using each technique on its own are identified in order to define a practical integrated approach toward developing the proposed framework. During the framework validation phase, real-time strategies have to be optimised to solve Emergency Department performance issues in a major hospital. Results show a potential of significant reduction in patients average length of stay (i.e. 48% of average patient throughput time) whilst reducing the over-reliance on overstretched nursing resources, that resulted in an increase of staff utilisation between 7% and 10%. Given the high uncertainty in healthcare service demand, using the integrated framework allows decision makers to find optimal staff schedules that improve emergency department performance. The proposed optimum staff schedule reduces the average waiting time of patients by 57% and also contributes to reduce number of patients left without treatment to 8% instead of 17%. The developed framework has been implemented by the hospital partner with a high level of success

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

Towards facilitated optimisation

Optimisation modelling in healthcare has addressed a diverse range of challenges inherent to decision-making and supports decision-makers in determining the best solution under a variety of constraints. In contrast, optimisation models addressing planning and service delivery issues in mental healthcare have received limited attention. Mental healthcare services in England are routinely facing issues relative to scarcity of available resources, inequities in their distribution, and inefficiencies in their use. Optimisation modelling has the potential to support decision making and inform the efficient utilisation of scare resources. Mental healthcare services are a combination of several subsystems and partnerships comprising of numerous stakeholders with a diversity of interests. However, in optimisation literature, the lack of stakeholder involvement in the development process of optimisation models is increasingly identified as a missed opportunity impacting the practical applicability of the models and their results. This thesis argues that simulation modelling literature offers alternative modelling approaches that can be adapted to optimisation modelling to address the shortcoming highlighted. In this study, we adapt PartiSim, a multi-methodology framework to support facilitated simulation modelling in healthcare, towards facilitated optimisation modelling and test it using a real case study in mental healthcare. The case study is concerned with a Primary Care Mental Healthcare (PCMH) service that deploys clinicians with different skills to several General Practice (GP) clinics. The service wanted support to help satisfy increasing demand for appointments and explore the possibility of expanding their workforce. This research puts forward a novel multimethodology framework for participatory optimisation, called PartiOpt. It explores the adaptation and customisation of the and PartiSim framework at each stage of the optimisation modelling lifecycle. The research demonstrates the applicability and relevance of a 'conceptual model' to optimisation modelling, highlighting the potential of facilitated optimisation as a methodology. This thesis argues for the inclusion of conceptual modelling in optimisation when dealing with real world practice-based problems. The thesis proposes an analytics-driven optimisation approach that integrates descriptive, predictive, and prescriptive analytics stages. This approach is utilised to construct a novel multi-skill multi-location optimisation model. By applying the analytics-driven optimisation approach to the case study, previously untapped resource potential is uncovered, leading to the identification of various strategies to improving service efficiency. The successful conceptualisation of an optimisation model and the quantitative decision support requirements that emerged in the initial stages of the study drive the analytics-driven optimisation. Additionally, this research also presents a facilitative approach for stakeholder participation in the validation, experimentation, and implementation of a mathematical optimisation model. Reflecting on the adaptation and subsequent amendments to the modelling stages, the final PartiOpt framework is proposed. It is argued that this framework could reduce the gap between theory and practice for optimisation modelling and offers guidance to optimisation modellers on involving stakeholders in addressing real world problems

A permutation flowshop model with time-lags and waiting time preferences of the patients

The permutation flowshop is a widely applied scheduling model. In many real-world applications of this model, a minimum and maximum time-lag must be considered between consecutive operations. We can apply this model to healthcare systems in which the minimum time-lag could be the transfer times, while the maximum time-lag could refer to the number of hours patients must wait. We have modeled a MILP and a constraint programming model and solved them using CPLEX to find exact solutions. Solution times for both methods are presented. We proposed two metaheuristic algorithms based on genetic algorithm and solved and compared them with each other. A sensitivity of analysis of how a change in minimum and maximum time-lags can impact waiting time and Cmax of the patients is performed. Results suggest that constraint programming is a more efficient method to find exact solutions and changes in the values of minimum and maximum time-lags can impact waiting times of the patients and Cmax significantly

Mind the gap: a review of optimisation in mental healthcare service delivery

Well-planned care arrangements with effective distribution of available resources have the potential to address inefficiencies in mental health services. We begin by exploring the complexities associated with mental health and describe how these influence service delivery. We then conduct a scoping literature review of studies employing optimisation techniques that address service delivery issues in mental healthcare. Studies are classified based on criteria such as the type of planning decision addressed, the purpose of the study and care setting. We analyse the modelling methodologies used, objectives, constraints and model solutions. We find that the application of optimisation to mental healthcare is in its early stages compared to the rest of healthcare. Commonalities between mental healthcare service provision and other services are discussed, and the future research agenda is outlined. We find that the existing application of optimisation in specific healthcare settings can be transferred to mental healthcare. Also highlighted are opportunities for addressing specific issues faced by mental healthcare services

Block-based Outpatient Clinic Appointments Scheduling Under Open-access Policy

Outpatient clinic appointment scheduling is an important topic in OR/IE studies. Open-access policy shows its strength in improving patient access and satisfaction, as well as reducing no-show rate. The traditional far-in-advance scheduling plays an important role in handling chronic and follow-up care. This dissertation discusses a hybrid policy under which a clinic deals with three types of patients. The first type of patients are those who request their appointments before the visit day. The second type of patients schedule their appointment on the visit day. The third type of patients are walk-in patients who go to the clinic without appointments and wait to see the physician in turn. In this dissertation, the online scheduling policy is addressed for the Type 2 and Type 3 patients, and the offline scheduling policy is used for the Type 1 patients. For the online scheduling policy, two stochastic integer programming (SIP) models are built under two different sets of assumptions. The first set of assumptions ignores the endogenous uncertainty in the problem. An aggregate assigning method is proposed with the deterministic equivalent problem (DEP) model. This method is demonstrated to be better than the traditional one-at-a-time assignment through both overestimation and underestimation numerical examples. The DEP formulations are solved using the proposed bound-based sampling method, which provides approximated solutions and reasonable sample size with the least gap between lower and upper bound of the original objective value. On the basis of the first set of assumptions and the SIP model, the second set of assumptions considers patient no-shows, preference, cancellations and lateness, which introduce endogenous uncertainty into the SIP model. A modified L-shaped method and aggregated multicut L-shaped method are designed to handle the model with decision dependent distribution parameter. Distinctive optimality cut generation schemes are proposed for three types of distribution for linked random variables. Computational experiments are conducted to compare performance and outputs of different methods. An alternative formulation of the problem with simple recourse function is provided, based on which, a mixed integer programming model is established as a convenient complementary method to evaluate results with expected value. The offline scheduling aims at assigning a certain number of Type 1 patients with deterministic service time and individual preferences into a limited number of blocks, where the sum of patients’ service time in a block does not exceed the block length. This problem is associated with bin packing problem with restrictions. Heuristic and metaheuristic methods are designed to adapt the added restrictions to the bin packing problem. Zigzag sorting is proposed for the algorithm and is shown to improve the performance significantly. A clique based construction method is designed for the Greedy Randomized Adaptive Search Procedure and Simulated Annealing. The proposed methods show higher efficiency than traditional ones. This dissertation offers a series of new and practical resolutions for the clinic scheduling problem. These methods can facilitate the clinic administrators who are practicing the open-access policy to handle different types of patients with deterministic or nondeterministic arrival pattern and system efficiency. The resolutions range from operations level to management level. From the operations aspect, the block-wise assignment and aggregated assignment with SIP model can be used for the same-day request scheduling. From the management level, better coordination of the assignment of the Type 1 patients and the same-day request patients will benefit the cost-saving control

Physicians Scheduling In Polyclinics

Physician scheduling is an important part of hospital operation management. Fatigue, nervousness, high levels of stress and depression are common negative effects of inappropriate work schedules on physicians. A robust and automated personnel scheduling system, which satisfies physicians' preferences, not only improves the quality of life for physicians but also helps to provide a better care for patients and potentially makes significant savings in time and cost for hospitals. Polyclinics reduce the burden on hospitals and help bridge the gap between primary and secondary care. They provide various hospital services such as X-rays, minor surgeries and out-patient treatment and gather several practices under one roof to cooperate, interact and share available resources. In addition, this structure provides an opportunity for physicians of different disciplines to work together and enables patients with chronic and complex conditions to visit multiple clinics at the same place during the same visit. Our problem of interest is mainly motivated by an extension of physician scheduling problems arising in ambulatory polyclinics, where the interaction of clinics and its consequences in terms of sharing their scarce resources introduce new constraints and add complexity to the problem. In the first part of this thesis, we present an integrated physician and clinic scheduling problem arising in ambulatory cancer treatment polyclinics, where patients may be assessed by multiple physicians from different clinics in a single visit. The problem focuses on assigning clinic sessions and their associated physicians to shifts in a finite planning horizon. The complexity of this problem stems from the fact that several interdisciplinary clinics need to be clustered together, sharing limited resources. The problem is formulated as a multi-objective optimization problem. Given the inherent complexity for optimally solving this problem with a standard optimization software, we develop a hybrid algorithm based on iterated local search and variable neighborhood descent methods to obtain high quality solutions. In the second part we propose a comprehensive bi-level physicians planning framework for polyclinics under uncertainty. The first level focuses on clinic scheduling and capacity planning decisions, whereas the second level deals with physicians scheduling and operational adjustments decisions. In order to protect the generated schedules against demand uncertainty, the first level is modeled as an adjustable robust scheduling problem which is solved using an ad-hoc cutting plane algorithm. To cope with variability in patients' treatment times, we formulate the second level as a two-stage stochastic problem and use a sample average approximation scheme to obtain solutions with small optimality gaps. Moreover, we use a Monte-Carlo simulation algorithm to demonstrate the potential benefits of using our planning framework. In the last part of this thesis we investigate on the impact of physicians work schedules on patient wait-time under uncertain arrival pattern and treatment time of patients. We provide a methodology that combines discrete-event simulation with an optimization search routine to minimize patient wait-time and physician overtime subject to several scheduling/resource restrictions. We indicate the significant impact of adopting the proposed simulation optimization framework for physician scheduling on reducing the aforementioned key performance measures

Multi-objective Operating Room Planning and Scheduling

abstract: Surgery is one of the most important functions in a hospital with respect to operational cost, patient flow, and resource utilization. Planning and scheduling the Operating Room (OR) is important for hospitals to improve efficiency and achieve high quality of service. At the same time, it is a complex task due to the conflicting objectives and the uncertain nature of surgeries. In this dissertation, three different methodologies are developed to address OR planning and scheduling problem. First, a simulation-based framework is constructed to analyze the factors that affect the utilization of a catheterization lab and provide decision support for improving the efficiency of operations in a hospital with different priorities of patients. Both operational costs and patient satisfaction metrics are considered. Detailed parametric analysis is performed to provide generic recommendations. Overall it is found the 75th percentile of process duration is always on the efficient frontier and is a good compromise of both objectives. Next, the general OR planning and scheduling problem is formulated with a mixed integer program. The objectives include reducing staff overtime, OR idle time and patient waiting time, as well as satisfying surgeon preferences and regulating patient flow from OR to the Post Anesthesia Care Unit (PACU). Exact solutions are obtained using real data. Heuristics and a random keys genetic algorithm (RKGA) are used in the scheduling phase and compared with the optimal solutions. Interacting effects between planning and scheduling are also investigated. Lastly, a multi-objective simulation optimization approach is developed, which relaxes the deterministic assumption in the second study by integrating an optimization module of a RKGA implementation of the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to search for Pareto optimal solutions, and a simulation module to evaluate the performance of a given schedule. It is experimentally shown to be an effective technique for finding Pareto optimal solutions.Dissertation/ThesisPh.D. Industrial Engineering 201

Optimisation stochastique de problèmes d’ordonnancement en santé

RÉSUMÉ : Les problèmes d'ordonnancement en santé sont complexes, car ils portent sur la fabrication d'ordonnancements qui absorbent les perturbations survenant dans le futur. Par exemple, les nouveaux patients urgents ont besoin d’être intégrés rapidement dans le planning courant. Cette thèse s'attaque à ces problèmes d'ordonnancement en santé avec de l'optimisation stochastique afin de construire des ordonnancements flexibles. Nous étudions en premier lieu la fabrication d'horaires pour deux types d’équipes d’infirmières: l’équipe régulière qui s'occupe des unités de soins et l’équipe volante qui couvre les pénuries d’infirmières à l’hôpital. Quand les gestionnaires considèrent ce problème, soit ils utilisent une approche manuelle, soit ils investissent dans un logiciel commercial. Nous proposons une approche heuristique simple, flexible et suffisamment facile à utiliser pour être implémentée dans un tableur et qui ne requiert presque aucun investissement. Cette approche permet de simplifier le processus de fabrication et d'obtenir des horaires de grande qualité pour les infirmières. Nous présentons un modèle multi-objectif, des heuristiques, ainsi que des analyses pour comparer les performances de toutes ces méthodes. Nous montrons enfin que notre approche se compare très bien avec un logiciel commercial (CPLEX), peut être implémentée à moindre coût, et comble finalement le manque de choix entre les solutions manuelles et les logiciels commerciaux qui coûtent extrêmement cher. Cette thèse s'attaque aussi à l'ordonnancement des chirurgies dans un bloc opératoire, fonctionnant avec un maximum de deux chirurgiens et de deux salles, en tenant compte de l'incertitude des durées d'opérations. Nous résolvons en premier lieu une version déterministe, qui utilise la programmation par contraintes, puis une version stochastique, qui encapsule le programme précédent dans un schéma de type ``sample average approximation''. Ce schéma produit des plannings plus robustes qui s’adaptent mieux aux variations des durées de chirurgies. Cette thèse présente le problème de prise de rendez-vous en temps réel dans un centre de radiothérapie. La gestion efficace d'un tel centre dépend principalement de l'optimisation de l'utilisation des machines de traitement. En collaboration avec le Centre Intégré de Cancérologie de Laval, nous faisons la planification des rendez-vous patients en tenant compte de leur priorité, du temps d'attente maximale et de la durée de traitement, le tout en intégrant l'incertitude reliée à l'arrivée des patients au centre. Nous développons une méthode hybride alliant optimisation stochastique et optimisation en temps réel pour mieux répondre aux besoins de planification du centre. Nous utilisons donc l'information des arrivées futures de patients pour dresser le portrait le plus fidèle possible de l'utilisation attendue des ressources. Des résultats sur des données réelles montrent que notre méthode dépasse les stratégies typiquement utilisées dans les centres. Par la suite, afin de proposer un algorithme stochastique et en temps réel pour des problèmes d'allocation de ressources, nous généralisons et étendons la méthode hybride précédente. Ces problèmes sont naturellement très complexes, car un opérateur doit prendre dans un temps très limité des décisions irrévocables avec peu d'information sur les futures requêtes. Nous proposons un cadre théorique, basé sur la programmation mathématique, pour tenir compte de toutes les prévisions disponibles sur les futures requêtes et utilisant peu de temps de calcul. Nous combinons la décomposition de Benders, qui permet de mesurer l'impact futur de chaque décision, et celle de Dantzig-Wolfe, qui permet de s'attaquer à des problèmes combinatoires. Nous illustrons le processus de modélisation et démontrons l’efficacité d'un tel cadre théorique sur des données réelles pour deux applications: la prise de rendez-vous et l'ordonnancement d'un centre de radiothérapie, puis l'assignation de tâches à des employés et leur routage à travers l’entrepôt.----------ABSTRACT : Scheduling problems are very challenging in healthcare as they must involve the production of plannings that absorb perturbations which arise in the future. For example, new high-priority patients needs to be quickly added in the computed plannings. This thesis tackles these scheduling problems in healthcare with stochastic optimization such as to build flexible plannings. We first study the scheduling process for two types of nursing teams, regular teams from care units and the float team that covers for shortages in the hospital. When managers address this problem, they either use a manual approach or have to invest in expensive commercial tool. We propose a simple heuristic approach, flexible and easy enough to be implemented on spreadsheets, and requiring almost no investment. The approach leads to streamlined process and higher-quality schedules for nurses. %improves both the process and the quality of the resulting schedule. The multi-objective model and heuristics are presented, and additional analysis is performed to compare the performance of the approach. We show that our approach compares very well with an optimization software (CPLEX solver) and may be implemented at no cost. It addresses the lack of choice between either manual solution method or a commercial package at a high cost. This thesis tackles also the scheduling of surgical procedures in an operating theatre containing up to two operating rooms and two surgeons. We first solve a deterministic version that uses the constraint programming paradigm and then a stochastic version which embeds the former in a sample average approximation scheme. The latter produces more robust schedules that cope better with the surgeries' time variability. This thesis presents an online appointment booking problem for a radiotherapy center. The effective management of such facility depends mainly on optimizing the use of the linear accelerators. We schedule patients on these machines taking into account their priority for treatment, the maximum waiting time before the first treatment, and the treatment duration. We collaborate with the Centre Intégré de Cancérologie de Laval to determine the best scheduling policy. Furthermore, we integrate the uncertainty related to the arrival of patients at the center. We develop a hybrid method combining stochastic optimization and online optimization to better meet the needs of central planning. We use information on the future arrivals of patients to provide an accurate picture of the expected utilization of resources. Results based on real data show that our method outperforms the policies typically used in treatment centers. We generalize and extend the previous hybrid method to propose a general online stochastic algorithm for resource allocation problems. These problems are very difficult in their nature as one operator should take irrevocable decisions with a limited (or inexistent) information on future requests and under a very restricted computational time. We propose a mathematical programming-based framework taking advantage of all available forecasts of future requests and limited computational time. We combine Benders decomposition, which allows to measure the expected future impact of each decision, and Dantzig-Wolfe decomposition, which can tackle a wide range of combinatorial problems. We illustrate the modelling process and demonstrate the efficiency of this framework on real data sets for two applications: the appointment booking and scheduling problem in a radiotherapy center and the task assignment and routing problem in a warehouse

Towards More Nuanced Patient Management: Decomposing Readmission Risk with Survival Models

Unplanned hospital readmissions are costly and associated with poorer patient outcomes. Overall readmission rates have also come to be used as performance metrics in reimbursement in healthcare policy, further motivating hospitals to identify and manage high-risk patients. Many models predicting readmission risk have been developed to facilitate the equitable measurement of readmission rates and to support hospital decision-makers in prioritising patients for interventions. However, these models consider the overall risk of readmission and are often restricted to a single time point. This work aims to develop the use of survival models to better support hospital decision-makers in managing readmission risk. First, semi-parametric statistical and nonparametric machine learning models are applied to adult patients admitted via the emergency department at Gold Coast University Hospital (n = 46,659) and Robina Hospital (n = 23,976) in Queensland, Australia. Overall model performance is assessed based on discrimination and calibration, as measured by time-dependent concordance and D-calibration. Second, a framework based on iterative hypothesis development and model fitting is proposed for decomposing readmission risk into persistent, patient-specific baselines and transient, care-related components using a sum of exponential hazards structure. Third, criteria for patient prioritisation based on the duration and magnitude of care-related risk components are developed. The extensibility of the framework and subsequent prioritisation criteria are considered for alternative populations, such as outpatient admissions and specific diagnosis groups, and different modelling techniques. Time-to-event models have rarely been applied for readmission modelling but can provide a rich description of the evolution of readmission risk post-discharge and support more nuanced patient management decisions than simple classification models