Fast evaluation of appointment schedules for outpatients in health care

We consider the problem of evaluating an appointment schedule for outpatients in a hospital. Given a fixed-length session during which a physician sees K patients, each patient has to be given an appointment time during this session in advance. When a patient arrives on its appointment, the consultations of the previous patients are either already finished or are still going on, which respectively means that the physician has been standing idle or that the patient has to wait, both of which are undesirable. Optimising a schedule according to performance criteria such as patient waiting times, physician idle times, session overtime, etc. usually requires a heuristic search method involving a huge number of repeated schedule evaluations. Hence, the aim of our evaluation approach is to obtain accurate predictions as fast as possible, i.e. at a very low computational cost. This is achieved by (1) using Lindley's recursion to allow for explicit expressions and (2) choosing a discrete-time (slotted) setting to make those expression easy to compute. We assume general, possibly distinct, distributions for the patient's consultation times, which allows us to account for multiple treatment types, as well as patient no-shows. The moments of waiting and idle times are obtained. For each slot, we also calculate the moments of waiting and idle time of an additional patient, should it be appointed to that slot. As we demonstrate, a graphical representation of these quantities can be used to assist a sequential scheduling strategy, as often used in practice

Index Polices for Patient Scheduling and ATM Replenishment

Markov Decision Processes (MDP) are one of the most commonly used stochastic models to solve sequential decision making problems. The optimal solution to many real-world problems cannot be achieved due to the curse of dimensionality. It is common to use a heuristic policy called the index policy, which is obtained by applying one-step policy improvement to a simple initial policy. The index policy performs close to the optimal policy and is easily implementable, which makes it attractive to use in practice. In this dissertation, we first introduce the background information on MDP and index policies in Chapter 1. We then study their applications in two problems: the appointment scheduling problem with patient preferences, and the automated teller machine (ATM) replenishment problem. In Chapter 2, we build an MDP model to design appointment scheduling policies in the presence of patient preferences. We model the patient preferences by assuming that each patient has a set of appointment days that are equally acceptable to the patient. We consider a service provider which receives the appointment-booking requests and makes an appointment decision one at a time. The objective is to minimize the long-run average cost while responding to the patients' booking requests based on their preferences. We propose the index policy and show it performs close to the optimal policy in the two-day horizon and outperforms other benchmarks in the multi-day horizon. In Chapter 3, we build an MDP model to design ATM replenishment schedules, while balancing the cost of replenishments and the cost of stock-outs. We propose a method to establish a relationship between the service level and the cost of a stock-out. We also assume that the replenishment cost is a sub-modular function of the set of ATMs that are replenished together. We derive the index policy, prove it has the same structural properties as the optimal policy, and show it performs close to the optimal policy when there are two or three ATMs. When there are a large number of ATMs, we show the index policy outperforms a benchmark policy through a simulation study and a real-world data-set.Doctor of Philosoph

Capacity Planning for Heterogeneous Patient Populations in Primary Care and Specialty Networks

Access to primary care has a direct impact on morbidity and mortality, and is strongly influenced by indirect waiting time: the delay between the requested and allotted appointment day. Our models describe the heterogeneous appointment seeking patterns of a primary care patient panel using stochastic processes parameterized to reflect the diversity of primary care visit rates in the US. For capacity planning, we estimate the distribution of daily appointments, and show that the distribution variability can be reduced by heuristics that use patient flexibility regarding the day of the appointment. For delays, we demonstrate that in a first-come, first-served system, patients who need the most frequent appointments suffer the greatest delays, motivating the need to reserve slots for high-visit patient classes. To further understand the inequity in delay, we model the primary care appointment system as a Discrete-Time Markov Chain. We derive an analytical expression for delay in terms of the patient’s probability of daily visit. We show that conditions for monotone mapping of the probability of visit to delay are intractable and give numerical results that support monotonicity. In our last chapter, we expand our scope to include specialty care networks. Using patient-level longitudinal data from the Medical Expenditure Panel Survey, we model the sequence of appointments with multiple specialty types and the time intervals between such appointments as a Markov Renewal Process (MRP). We use comorbidity count to model patient heterogeneity and extract the MRP parameters for each patient subgroup. Next, we adapt the steady state results to provide an analytical expression of the expected appointment fill-rate by specialty and patient subgroups. Our analytical results demonstrate that patients with higher comorbidity count typically have a lower fill-rate because of shorter lead time between appointments thereby necessitating either overtime or reserved slots to ensure timely access. We further simulate appointment seeking patterns of a nationally representative panel of patients in the specialty network and estimate the distribution of daily appointment requests for each specialty. Similar to the primary care case, we show that heuristics that leverage patient flexibility regarding the day of the appointment can reduce variability in appointment requests for each specialty

Online Algorithms for Dynamic Resource Allocation Problems

Dynamic resource allocation problems are everywhere. Airlines reserve flight seats for those who purchase flight tickets. Healthcare facilities reserve appointment slots for patients who request them. Freight carriers such as motor carriers, railroad companies, and shipping companies pack containers with loads from specific origins to destinations. We focus on optimizing such allocation problems where resources need to be assigned to customers in real time. These problems are particularly difficult to solve because they depend on random external information that unfolds gradually over time, and the number of potential solutions is overwhelming to search through by conventional methods. In this dissertation, we propose viable allocation algorithms for industrial use, by fully leveraging data and technology to produce gains in efficiency, productivity, and usability of new systems. The first chapter presents a summary of major methodologies used in modeling and algorithm design, and how the methodologies are driven by the size of accessible data. Chapters 2 to 5 present genuine research results of resource allocation problems that are based on Wang and Truong (2017); Wang et al. (2015); Stein et al. (2017); Wang et al. (2016). The algorithms and models cover problems in multiple industries, from a small clinic that aims to better utilize its expensive medical devices, to a technology giant that needs a cost-effective, distributed resource-allocation algorithm in order to maintain the relevance of its advertisements to hundreds of millions of consumers

Online Clinic Appointment Scheduling

Health care is a fast growing industry in the United States. Appointment scheduling is one of the key processes in this industry. This thesis focused on on-line appointment system for clinics. The objective of this thesis is to maximize patients\u27 preferences and the number of patients seen during normal business hours. This is a multi-objective problem to balance the trade-off between overtime and patients\u27 preferences.To achieve the objective, a simulation model was built to compare four policies proposed. Based on simulation results, it was found that most of non-dominated solutions were close both minimum objective values, so policies proposed were helpful for the clinics to balance overtime and patients\u27 preferences

STOCHASTIC MODELS FOR RESOURCE ALLOCATION, SERIES PATIENTS SCHEDULING, AND INVESTMENT DECISIONS

We develop stochastic models to devise optimal or near-optimal policies in three different areas: resource allocation in virtual compute labs (VCL), appointment scheduling in healthcare facilities with series patients, and capacity management for competitive investment. A VCL consists of a large number of computers (servers), users arrive and are given access to severs with user-specified applications loaded onto them. The main challenge is to decide how many servers to keep “on”, how many of them to preload with specific applications (so users needing these applications get immediate access), and how many to be left flexible so that they can be loaded with any application on demand, thus providing delayed access. We propose dynamic policies that minimize costs subject to service performance constraints and validate them using simulations with real data from the VCL at NC State. In the second application, we focus on healthcare facilities such as physical therapy (PT) clinics, where patients are scheduled for a series of appointments. We use Markov Decision Processes to develop the optimal policies that minimize staffing, overtime, overbooking and delay costs, and develop heuristic secluding policies using the policy improvement algorithm. We use the data from a local PT center to test the effectiveness of our proposed policies and compare their performance with other benchmark policies. In the third application, we study a strategic capacity investment problem in a duopoly model with an unknown market size. A leader chooses its capacity to enter a new market. In a continuous-time Bayesian setting, a competitive follower dynamically learns about the favorableness of the new market by observing the performance of the leader, and chooses its capacity and timing of investment. We show that an increase in the probability of a favorable market can strictly decrease the leaders expected discounted profit due to non-trivial interplay between leaders investment capacity and timing of the dynamically-learning follower.Doctor of Philosoph

Appointment Scheduling in Health Care

We propose two complementary approaches to the scheduling of outpatient appointments. The first approach is to dynamically assign appointment times depending on the continuously updated patient schedule. The second approach is to statically design the system by either limiting the appointment backlog or regulating the demand rate through controlling the panel size, i.e. the population receiving the medical service. For the first approach - dynamic scheduling, we start with the assumption that patients come from a single class with homogeneous no-show and cancellation behaviors. We develop a Markov decision process model and propose easily implementable heuristic dynamic policies. In a simulation study that considers a model clinic, which is created using data from practice, we find that the proposed heuristics outperform all the other benchmark policies, particularly when the patient load is high compared with the regular capacity. We then extend our model to consider the scheduling of patients from multiple classes. In this model, different classes of patients are assumed to have different probability distributions for their no-show and cancellation behaviors. As in the single-class case, we develop heuristic dynamic policies. Simulation results suggest that our proposed heuristics perform well when the regular capacity is small. For the second approach - static design, we model the appointment backlog as a single-server queue where new appointments join the backlog from the back of the queue. Motivated by empirical findings, we assume that patients do not show up for their appointments with probabilities that increase with their waiting times before receiving service. We first study the model under the assumption of exponential service times. We characterize the optimal appointment backlog size and the optimal demand rate that maximize the system throughput and investigate how they change with other system parameters. Then we consider a special case where patients' no-show probabilities follow a specific parametric form. Under this special case, we obtain a simple closed-form expression for the optimal demand rate if we do not put a limit on the appointment backlog. Finally we conduct extensive numerical studies to investigate the situation where the service times are deterministic. The numerical results suggest that the insights generated in our analytical study by assuming exponential service times also hold for the situation with deterministic service times

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

Data-Driven Analytics to Support Scheduling of Multi-Priority Multi-Class Patients with Wait Targets

The aim of dynamic scheduling is to efficiently assign available resources to the most suitable patients. The dynamic assignment of multi-class, multi-priority patients over time has long been a challenge, especially for scheduling in advance and under non-deterministic capacity. In this paper, we first conduct descriptive analytics on MRI data of over 3.7 million patient records from 74 hospitals. The dataset captures patients of four different priority levels, with different wait time targets, seeking treatment for one of ten classes of procedures, which have been scheduled over a period of 3 years. The goal is to serve 90% of patients within their wait time targets; however, under current practice, 67% of patients exceed their target wait times. We characterize the main factors affecting the waiting times and conduct predictive analytics to forecast the distribution of the daily patient arrivals, as well as the service capacity or number of procedures performed daily at each hospital. We then prescribe two simple and practical dynamic scheduling policies based on a balance between the First-In First-Out (FIFO) and strict priority policies; namely, weight accumulation and priority promotion. Under the weight accumulation policy, patients from different priority levels start with varying initial weights, which then accumulates as a linear function of their waiting time. Patients of higher weights are prioritized for treatment in each period. Under the priority promotion policy, a strict priority policy is applied to priority levels where patients are promoted to a higher priority level after waiting for a predetermined threshold of time. To evaluate the proposed policies, we design a simulation model that applies the proposed scheduling policies and evaluates them against two performance measures: 1) total exceeding time: the total number of days by which patients exceed their wait time target, and 2) overflow proportion: the percentage of patients within each priority group that exceed the wait time target. Using historical data, we show that, compared to the current practice, the proposed policies achieve a significant improvement in both performance measures. To investigate the value of information about the future demand, we schedule patients at different points of time from their day of arrival. The results show that hospitals can considerably enhance their wait time management by delaying patient scheduling

Bloody fast blood collection

This thesis consists of four parts: The first part contains an introduction, the second presents approaches for the evaluation of waiting times at blood collection sites, the third uses these to present approaches that improve waiting times at blood collection sites. The final part shows the application of two of the approaches to data from real blood collection sites, followed by the conclusions that can be drawn from this thesis. Part I: Introduction, contains two chapters. Chapter 1 introduces the context for this thesis: blood banks in general, the Dutch blood bank Sanquin and blood collection sites. The chapter sketches some of the challenges faced with respect to blood collection sites. As blood donors are voluntary and non-remunerated, delays and waiting times within blood collection sites should be kept at acceptable levels. However, waiting times are currently not incorporated in staff planning or in other decisions with respect to blood collection sites. These blood collection sites will be the primary focus of this thesis. This thesis provides methods that do take waiting times into account, aiming to decrease waiting times at blood collection sites and leveling work pressure for staff members, without the need for additional staff. Chapter 2 then presents a technical methods that will be used most of the chapters in this thesis: uniformization. Uniformization can be used to transform Continuous Time Markov Chains (CTMCs) — that are very hard to analyze — into Discrete Time Markov Chains (DTMCs) — that are much easier to analyze. The chapter shows how the method works, provides an extensive overview of the literature related to the method, the (technical) intuition behind the method as well as several extensions and applications. Although not all of the extensions and applications are necessary for this thesis, it does provide an overview of one of the most valuable methods for this thesis. Part II: Evaluation, contains two chapters that propose and adapt several methods to compute waiting times and queues at blood collection sites. A blood collection site is best modeled as a time-dependent queueing network, requiring non-standard approaches. Chapter 3 considers a stationary, i.e. not time-dependent model of blood collection sites as a first step. A blood collection site consists of three main stations: Registration, Interview and Donation. All three of the stations can have their own queue. This means that even the stationary model is non-trivial for some computations. However, for the stationary model, an analytic so-called product form expression is derived. Based on this product form, two more results are shown. The first result is that the standard waiting time distributions from M|M|s queues are applicable, as if the queue is in isolation. It is then concluded that no closed form expression exist for the total waiting or delay time distribution, as the distributions of the three stations in tandem are not independent. Therefore a numerical approach is presented to compute the total delay time distribution of a collection site. All of the results are supported by numerical examples based on a Dutch blood collection site. The approach for the computation of the total delay time distribution can also be combined with the approach from Chapter 4 for an extension to a time-dependent setting. Chapter 4 shows an approach to deal with these time-dependent aspects in queueing systems, as often experienced by blood collection sites and other service systems, typically due to time-dependent arrivals and capacities. Easy and quick to use queueing expressions generally do not apply to time-dependent situations. A large number of computational papers has been written about queue length distributions for time-dependent queues, but these are mostly theoretical and based on single queues. This chapter aims to combine computational methods with more realistic time-dependent queueing networks, with an approach based on uniformization. Although uniformization is generally perceived to be too computationally prohibitive, we show that our method is very effective for practical instances, as shown with an example of a Dutch blood collection site. The objective of the results is twofold: to show that a time-dependent queueing network approach can be beneficial and to evaluate possible improvements for Dutch blood collection sites that can only be properly assessed with a time-dependent queueing method. Part III: Optimization, contains four chapters that aim to improve service levels at Sanquin. The first three chapters focus on three different methods to decrease queues at blood collection sites. Chapters 5 and 6 focus on improving the service by optimizing staff allocation to shifts and stations. Chapter 7 focuses on improving the arrival process with the same goal. Chapter 8 is focused at improving inventory management of red blood cells. Donors do not arrive to blood collection sites uniformly throughout the day, but show clear preferences for certain times of the day. However, the arrival patterns that are shown by historical data, are not used for scheduling staff members at blood collection sites. As a first significant step to shorten waiting times we can align staff capacity and shifts with walk-in arrivals. Chapter 5 aims to optimize shift scheduling for blood collection sites. The chapter proposes a two-step procedure. First, the arrival patterns and methods from queueing theory are used to determine the required number of staff members for every half hour. Second, an integer linear program is used to compute optimal shift lengths and starting times, based on the required number of staff members. The chapter is concluded with numerical experiments that show, depending on the scenario, a reduction of waiting times, a reduction of staff members or a combination of both. At a blood collection site three stations (Registration, Interview and Donation) can roughly be distinguished. Staff members at Dutch blood collection sites are often trained to work at any of these stations, but are usually allocated to one of the stations for large fractions of a shift. If staff members change their allocation this is based on an ad hoc decision. Chapter 6 aims to take advantage of this mostly unused allocation flexibility to reduce queues at blood collection sites. As a collection site is a highly stochastic process, both in arrivals and services, an optimal allocation of staff members to the three stations is unknown, constantly changing and a challenge to determine. Chapter 6 provides and applies a so-called Markov Decision Process (MDP) to compute optimal staff assignments. Extensive numerical and simulation experiments show the potential reductions of queues when the reallocation algorithm would be implemented. Based on Dutch blood collection sites, reductions of 40 to 80% on the number of waiting donors seem attainable, depending on the scenario. Chapter 7 also aims to align the arrival of donors with scheduled staff, similarly to Chapter 5. Chapter 7 tries to achieve this by changing the arrivals of donors. By introducing appointments for an additional part of donors, arrivals can be redirected from the busiest times of the day to quiet times. An extended numerical queueing model with priorities is introduced for blood collection sites, as Sanquin wants to incentive donors to make appointments by prioritizing donors with appointments over donors without appointments. Appointment slots are added if the average queue drops below certain limits. The correct values for these limits, i.e. the values that plan the correct number of appointments, are then determined by binary search. Numerical results show that the method succeeds in decreasing excessive queues. However, the proposed priorities might result in unacceptably high waiting times for donors without appointments, and caution is therefore required before implementation. Although this thesis mainly focuses on blood collection sites, many more logistical challenges are present at a blood bank. One of these challenges arises from the expectation that Sanquin can supply hospitals with extensively typed red blood cell units directly from stock. Chapter 8 deals with this challenge. Currently, all units are issued according to the first-in-first-out principle, irrespective of their specific typing. These kind of issuing policies lead to shortages for rare blood units. Shortages for rare units could be avoided by keeping them in stock for longer, but this could also lead to unnecessary wastage. Therefore, to avoid both wastage and shortages, a trade-off between the age and rarity of a specific unit in stock should be made. For this purpose, we modeled the allocation of the inventory as a circulation flow problem, in which decisions about which units to issue are based on both the age and rarity of the units in stock. We evaluated the model for several settings of the input parameters. It turns out that, especially if only a few donors are typed for some combinations of antigens, shortages can be avoided by saving rare blood products. Moreover, the average issuing age remains unchanged. Part IV: Practice and Outlook concludes this thesis. The first of two chapters in this part shows the combined application of two approaches from this thesis to data from three collection sites in the Netherlands. The final chapter of this thesis presents the conclusions that can be drawn from this thesis and discusses an outlook for further research. Chapter 9 shows the combined application of the methods in Chapters 5 and 6 to three real collection sites in Dutch cities: Nijmegen, Leiden and Almelo. The collection sites in Nijmegen and Leiden are both large fixed collection sites. The collection site in Almelo is a mobile collection site. The application of each one of the methods individually reduce waiting times significantly, and the combined application of the methods reduces waiting times even further. Simultaneously, small reductions in the number of staff hours are attainable. The results from Chapter 9 summarize the main message of this thesis: waiting time for blood donors at blood collection sites can be reduced without the need for more staff members when the working times of staff members are used more effectively and efficiently, and controlling the arrival process of donors. The approaches presented in this thesis can be used for this purpose. This is not only beneficial for blood donors, but will also result in more balanced workload for staff members, as fluctuations in this workload are reduced significantly