Optimization of Stochastic Models in Health Care: Appointment Scheduling and Disease Testing

We consider two different problems: appointment scheduling and asymptomatic disease testing. For the appointment scheduling problem, the goal is to assign appointment times to minimize a weighted sum of patient wait times, doctor idle time, and clinic overtime. We make the assumption that patients are unpunctual with respect to assigned appointment times and distributional information on unpunctuality is available. We first consider a model with heterogeneous patient distributions in both service time and unpunctuality. This is a complex system that requires heuristic approaches. We are able to show the benefits of capturing patient heterogeneity in addition to the superior performance of our heuristics. Our best methods do not scale well to large patient systems; thus, we consider a second model that allows a large number of patients. For large systems, we assume patient homogeneity; however, patient unpunctuality is permitted to be time-heterogeneous. With this model, we examine the fluid limits of the queue processes to develop a fluid control problem that seeks an asymptotically optimal appointment schedule in the form of an RCLL function. This problem is difficult to solve analytically, so we propose a numerical scheme that converts the control problem into a quadratic program. We examine asymptotically optimal appointment schedules under various unpunctuality distributions, then the superior performance of these schedules in discrete-event simulations. For the asymptomatic disease testing problem, we consider the individual decision-maker problem of choosing when to use disease test kits from a limited supply. We assume an underlying SIR Markov model with split states for asymptomatic and symptomatic states. As only symptoms are directly observable, the decision process is modeled as a partially-observable Markov decision process for deciding when to use tests. The goal is to produce simple instructions for the average consumer to follow. We derive policies that do not require probability computations by the user. Under certain assumptions, we are able to prove that these policies are optimal. Last, we examine a community simulation where infection probabilities are dependent on community infected. Our methods are shown to outperform existing baselines.Doctor of Philosoph

WAITING TIME AND PATIENTS’ SATISFACTION

In line with Vision 2021, the UAE’s National Agenda has six pillars: providing world-class healthcare is one of them. It is hence not surprising that the UAE healthcare industry is allocating substantial weight to the element of quality. Patient-centered care is internationally becoming part of the quality domain. Patient-centered quality may be defined as “providing the care that the patient needs in the manner the patient desires at the time the patient desires”. This requires substantially more attention to learning about patients’ preferences. One of the main dimensions of patient-centered quality is timely access to care, which includes shorter waiting times and efficient use of physicians’ time. Long waiting time is a globally challenging phenomenon that most healthcare systems face; it is the main topic of this thesis. The thesis consists of two main studies. The first empirical study was conducted by interviewing a sample of 552 patients to assess their satisfaction with their waiting experience in UAE hospitals. The collected data allowed us to test several hypotheses that were formulated based on an extensive literature study to better understand the relationship between waiting time and certain variables. In the second study, a simulation model for a typical clinic was built from real data obtained from a public hospital in Abu Dhabi emirate, considering two types of patients’ arrival; by appointment and walk-in, to test the effect of delayed arrivals and number of resources on the waiting time. The objective of the simulation study was to determine effective strategies for reducing the patients’ waiting time. The results of both studies are presented and discussed, with some recommendations, managerial implications, and conclusions

Appointment planning and scheduling in primary care

The Affordable Care Act (ACA) puts greater emphasis on disease prevention and better quality of care; as a result, primary care is becoming a vital component in the health care system. However, long waits for the next available appointments and delays in doctors offices combined with no-shows and late cancellations have resulted in low efficiency and high costs. This dissertation develops an innovative stochastic model for patient planning and scheduling in order to reduce patients’ waiting time and optimize primary care providers’ utility. In order to facilitate access to patients who request a same-day appointment, a new appointment system is presented in which a proportion of capacity is reserved for urgent patients while the rest of the capacity is allocated to routine patients in advance. After the examination of the impact of no-shows on scheduling, a practical double-booking strategy is proposed to mitigate negative impacts of the no-show. Furthermore, proposed model demonstrates the specific circumstances under which each type of scheduling should be adopted by providers to reach higher utilization. Moreover, this dissertation extends the single physician’s model to a joint panel scheduling and investigates the efficiency of such systems on the urgent patients’ accessibility, the physicians’ utilization, and the patients’ waiting time. Incorporating the newsvendor approach and stochastic optimization, these models are robust and practical for planning and scheduling in primary care settings. All the analytical results are supported with numerical examples in order to provide better managerial insights for primary care providers

Essays in Scheduling: Applications in Health Care and Manufacturing

The problem of finding an optimal schedule is ubiquitous in human endeavor. Airlines strive to find the best schedule for their aircrafts and flight-crews, academic scheduling offices at universities schedule classes, and business organizations prioritize their jobs or customers and schedule them accordingly. Even in our day to day lives, whether consciously or not, we decide on our daily schedule and go about our sequence of tasks, prioritizing certain tasks, and procrastinating on others. Not surprisingly, scheduling of people, tasks, and manufacturing jobs constitute a significant proportion of the operations management literature. Despite all the research that has been published on scheduling, we encounter scheduling problems that call for novel approaches, and when treated with appropriate tools and techniques, provide interesting managerial insights. The dissertation consists of three such scheduling problems, two from the health care industry, and one from manufacturing. The first health care paper (Ganguly et al. 2013) employs mixed-integer linear programming to schedule physicians for a medical emergency department (ED). The second paper (Ganguly and Samorani 2013) uses an analytical approach for making real time updates to patient schedules in outpatient clinics that primarily operate on an appointment basis. The paper on manufacturing (Ganguly and Laguna 2013) develops heuristic techniques for a particular type of job-sequencing problem that involves two types of setups

Applying and integer Linear Programming Model to an appointment scheduling problem

Dissertação de Mestrado, Ciências Económicas e Empresariais (Economia e Políticas Públicas), 28 de fevereiro de 2022, Universidade dos Açores.A gestão de consultas ambulatórias pode ser um processo complexo, uma vez que envolve vários stakeholders com diferentes objetivos. Para os utentes poderá ser importante minimizar os tempos de espera. Simultaneamente, para os trabalhadores do setor da saúde, condições de trabalho justas devem ser garantidas. Assim, é cada vez mais necessário ter em conta o equilíbrio de cargas horárias e a otimização dos recursos disponíveis como principais preocupações no agendamento e planeamento de consultas. Nesta dissertação, uma abordagem com dois modelos para a criação de um sistema de agendamento de consultas é proposta. Esta abordagem é feita em programação linear, com dois modelos que têm como objetivo minimizar as diferenças de cargas horárias e melhorar o seu equilíbrio ao longo do planeamento. Os modelos foram estruturados e parametrizados de acordo com dados gerados aleatoriamente. Para isso, o desenvolvimento foi feito em Java, gerando assim os dados referidos. O Modelo I minimiza as diferenças de carga horária entre os quartos disponíveis. O Modelo II, por outro lado, propõe uma nova função objetivo que minimiza a diferença máxima observada, com um processo de decisão minxmax. Os modelos mostram resultados eficientes em tempos de execução razoáveis para instâncias com menos de aproximadamente 10 quartos disponíveis. Os tempos de execução mais altos são observados quando as instâncias ultrapassam este número de quartos disponíveis. Em relação ao equilíbrio da carga horária, observou-se que o número de especialidades disponíveis para atendimento e a procura por dia foram o que mais influenciou a minimização da diferença da carga horária. Os resultados do Modelo II mostram melhor tempo de execução e um maior número de soluções ótimas. Uma vez que as diferenças entre os dois modelos não são consideráveis, o Modelo I poderá representar um melhor conjunto de soluções para os decisores já que minimiza a diferença da carga horária total entre quartos em vez de apenas minimizar o valor máximo da diferença de carga horária entre quaisquer dois quartos.ABSTRACT: Outpatient appointment management can be a complex process since it involves many conflicting stakeholders. As for the patients it might be important to minimize waiting time. Simultaneously, for healthcare workers, fair working conditions must be guaranteed. Thus, it is increasingly necessary to have workload balance and resource optimization as the main concerns in the scheduling and planning of outpatient appointments. In this dissertation, a two-model approach for designing an appointment scheduling is proposed. This approach is formulated as two mathematical Integer Linear Programming models that integrate the objective of minimizing workload difference and improving workload balance. The models were structured and parameterized according to randomly generated data. For this, the work was developed in Java, generating said data. Model I minimizes the workload differences among rooms. Model II, on the other hand, proposes a new objective function that minimizes the maximum workload difference, with a minxmax decision process. The computational models behaves efficiently in reasonable run times for numerical examples with less than approximately 10 rooms available. Higher run times are observed when numerical examples surpass these number of available rooms. Regarding workload balance, it was observed that the number of specialties available for appointments and the demand for each day were the most influential in the minimization of workload difference. Model II results show a shorter model run time and more optimal solutions. As the differences between both Models are not considerable, Model I might propose a better set of solution for decision makers since it minimizes the total workload difference amongst rooms instead of only minimizing the maximum workload difference between any two rooms

Primary Care Appointment Systems: Causes and Implications of Timely Arrivals

The primary goal of this study was to identify potential factors that might contribute to patient punctuality issues, while also assessing the satisfaction of a proposed intervention. In addition, we aimed to learn more about the psychosocial and behavioral implications that patients face with regards to arriving on time for their primary care visits. A mixed-method research study was used to identify and quantify potential factors that might contribute to patient punctuality issues, while also assessing the satisfaction of a proposed intervention. In addition to possible factors that contribute to punctuality, we aimed to learn more about how patients are affected when they arrive late for appointments. Through qualitative assessment, we explored the psychosocial and behavioral implications that patients face with regards to arriving on time for their primary care appointments. A total of 524 individuals out of 1050 patients (50%) responded to the paper-based survey. Of the 524 adult respondents, we excluded 103 (19.7%) participants due to the missing data on either of their historical behavior patterns, future intentions for arrival, or their definition of appointment time. We analyzed the data for the remaining 421 eligible survey participants. In addition, seven of the eight patient interviews were transcribed and analyzed in order to identify themes using the patient’s own words to better understand the psychosocial and behavioral implications patients face on arriving to their appointment on time. Three primary themes emerge in the interviews related to the perception of arriving late to appointments at the FMC. The findings of this study indicate that regardless of patients’ interpretation of appointment time, they typically arrive 10-15 minutes before the appointment time. In addition, there is a significant connection between patients’ perceptions of historically arriving late to appointments and the intent to arrive very early to their future appointments. Combined with the qualitative results, this study suggests that most patients are motivated to be on time, in some cases seeing the idea of lateness as a contradiction of their own self-identity. The behavioral causes and implications of the findings are explained using the concept of Fear Appeals and the Protection Motivation Theory (PMT)

Performance modelling of applications in a smart environment

PhD ThesisIn today’s world, advanced computing technology has been widely used to improve our living conditions and facilitate people’s daily activities. Smart environment technology, including kinds of smart devices and intelligent systems, is now being researched to provide an advanced intelligent life, easy, comfortable environment. This thesis is aimed to investigate several related technologies corresponding to the design of a smart environment. Meanwhile, this thesis also explores different modelling approaches including formal methods and discrete event simulation. The core contents of the thesis include performance evaluation of scheduling policies and capacity planning strategies. The main contribution is in developing a modelling approach for smart hospital environments. This thesis also provides valuable experience in the formal modelling and the simulation of large scale systems. The chief findings are that the dynamic scheduling policy is proved to be the most efficient approach in the scheduling process; and a capacity scheme is also verified as the optimal scheme to obtain the high work efficiency under the condition of limited human resource. The main methods used for the performance modelling are Performance Evaluation Process Algebra (PEPA) and discrete event simulation. A great deal of modelling tasks was completed with these methods. For the analysis, we adopt both numerical analysis based on PEPA models and statistical measurements in the simulation