Robust Appointment Scheduling in Healthcare

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1		Bhagwat Ram	--	1564	2022-11-28 11:08:14	\|
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This entry is adapted from the peer-reviewed paper 10.3390/math10224317

The quality and experience of healthcare systems affect the economy and prosperity of cities all over the world. Governments of several countries are struggling to improve the efficiency of their healthcare systems and decrease healthcare spending costs.

scheduling healthcare management hospital management optimization

1. Introduction

Most countries are experiencing the problems of aging and expanding populations. With more than seven million citizens, Hong Kong is considered one of the Asian Tigers and has seen an increasing and aging population. According to the statistics of the Hong Kong Government, the median age of Hong Kong’s people has risen from 37.2 to 51.8. However, the ongoing COVID-19 pandemic has affected a large proportion of elderly people. Therefore, it impresses a need for elderly care services and personnel requirements, such as doctors and nurses, which results in the deterioration of hospitals’ service quality and government expenditure. The Health Department of the Hong Kong Special Administrative Region (HKSAR) indicated in 2014 that over HKD 93 billion in healthcare spending was slashed in 2013, which comprised 5.1% of the total GDP (gross domestic product). Nearly 13 thousand Hong Kong dollars per capita was contributed to health treatment, which exceeded the median salary of the Hong Kong workforce. The government predicts that the number of people aged 55 and up will double in the next 15 years, while the workforce will shrink. As a result, the elderly dependency ratio, which measures the pressure on the production population, will rapidly increase. However, due to the unpredictable explosion of COVID-19, there has been an exponentially increased number of confirmed cases of the virus in Hong Kong that affected the aging population. To address the problem of the aging population and inadequate provision of healthcare services, the government can either allot more money to boost the capacities of healthcare facilities or enhance the efficiency of the existing healthcare system. The former requires a longer timeframe and a substantial amount of capital from the planning stage to the implementation stage. Another issue is the inadequacy of the workforce in the healthcare sector. Many doctors refuse to join public hospitals due to the long working hours and relatively low remunerations compared to private clinics or hospitals. The government has resorted to increasing the salaries of doctors and nurses and transferring the cost to the patients. Therefore, governments are now pursuing the latter method, which is more practical and favorable to long-term development. To accommodate more patients with the existing facilities, higher efficiency in resource allocation is required.

2. Background

In many service operations, the appointment-scheduling problem emerges as a challenging problem in which patients are serviced sequentially, the service time is unpredictable, and the practitioner must allocate time slots for serving patients in advance. Modern healthcare utilizes many types of expensive equipment and facilities, such as MRI installations, operation theaters, and CT scanners, in addition to highly skilled and well-paid workers. For instance, the appointment-scheduling problem for scheduling surgeries for outpatients was considered. The information on which surgery is to be done on a particular day is known in advance; however, the time to carry out the scheduled surgery can vary. Typically, on the preceding day, the hospital manager makes decisions on the number of operation theaters to be opened, the allocation of surgeries to operation theaters, and the sequencing of surgeries.

3. Related Literature Review of Robust Appointment Scheduling in Healthcare

Cayirli and Veral ^[1] provided a comprehensive review of research on appointment scheduling in outpatient services, formulated the general problem, and modeled considerations and a taxonomy of methodologies. Gupta and Denton ^[2] demonstrated the design of an appointment scheduling system and identified the potential for the novel application of IE/OR models. Cayirli et al. ^[3] examined the connections between appointment system components and patient panel characteristics to evaluate the performance of ambulatory care. Kim and Giachetti ^[4] developed a stochastic mathematical overbooking model to predict the optimal number of appointments that patients accept to maximize the expected total earnings. A universal “Dome” appointment rule was introduced by Cayirli et al. ^[5] and can be parameterized for different clinics by a planning constant based on environmental factors, such as walk-ins, no-shows, the number of appointments made per session, the variability of service times, and the cost of doctors’ idle time and patients’ waiting time. Meskens et al. ^[6] optimized the usage of the operating room by reducing makespan and overtime and maximizing affinities between surgical team members by taking advantage of the “expressive power” of the constraint programming paradigm. For scheduling arrivals at a medical facility with no-show behavior, Zacharias and Pinedo ^[7] suggested an overbooking model intending to minimize the predicted weighted sum of patient waiting time, doctor idle time, and overtime. Kemper et al. ^[8] proposed a method for establishing appointment times in the D/G/1 queuing system by systematically minimizing the predicted loss per customer.

Since the main concern herein is to investigate the appointment-scheduling problem with uncertain service time, the robust optimization technique for addressing the uncertainty problem was also reviewed. Robust optimization is an approach that ensures the solutions remain feasible and near-optimal when data is changed. Soyster ^[9] investigated the work on robust optimization by attaining all uncertain parameters to reach their worst-case value, which was deemed over-conservative in a practical setting. Mulvey et al. ^[10] integrated the concept of scenario-based analysis, and goal programming and presented stochastic programming formulations to derive robust solutions. By using an ellipsoidal uncertainty set to modify the level of conservatism, Ben-Tal and Nemirovski ^[11] achieved some progress and provided comprehensible mathematical reformulations. By creating a polyhedron for each parameter, Bertsimas Bertsimas and Thile ^[12] addressed uncertainty to develop the idea of a “budget of uncertainty” to rein in conservatism. When employing numerous ranges to characterize unknown parameters, Düzgün and Thile ^[13] noted that a single range for each parameter still produced excessively conservative findings.

A substantial number of papers in the literature relevant to robust appointment scheduling dealing with uncertain service time was found. Denton et al. ^[14] proposed a stochastic optimization model and derived some practical heuristics to compute operation theatres schedules that hedged against the uncertainty in surgery duration. Utilizing statistical data on surgery duration, Hans et al. ^[15] considered the robust surgery-loading problem for the operation theatres department in a hospital and proposed various constructive heuristics and local search techniques to maximize capacity utilization and minimize the risk of overtime; Denton et al. ^[16] mentioned two types of models for assigning surgery blocks to operating rooms under uncertainty. When each work has a random processing length determined by a joint discrete probability distribution, Begen and Queyanne ^[17] examined the best appointment-scheduling strategy by minimizing the projected total underage and overage costs. Mittal et al. ^[18] used a strong optimization framework to investigate the appointment-scheduling problem, prove the existence of a closed-form optimal solution, and create the first constant-factor approximation algorithm. In a multistage operating room department with stochastic service time and numerous patient types, Saremi et al. ^[19] addressed the appointment scheduling of outpatient surgeries. To reduce the patients’ waiting time, surgical completion time, and cancellation rate, three simulation-based optimization strategies were proposed. Rachuba and Werners ^[20] integrated data on stochastic parameters into a scenario-based mixed integer optimization model with a focus on different stakeholders’ objectives that are simultaneously taken into account within a multi-criteria optimization model to avoid rescheduling when taking into account uncertainties of treatment duration and emergency arrivals. Mak et al. ^[21] created distribution-free models that precisely describe tractable conic programs to solve the appointment-scheduling problem by assuming only moment-by-moment information about job durations. To determine the best arrival order for patients with different features, Kong et al. ^[22] investigated a stochastic appointment-sequencing problem. They investigated the best sequencing rules using the idea of stochastic ordering, and they discovered why the smallest variance first rule was not as effective as they had hoped. Zhang et al. ^[23] investigated a distributional resilient formulation based on an ambiguity set that exploited the first two moments and derived an approximated semi-definite programming model for appointment scheduling under random service duration with uncertain distributions. They assigned their scheduled arrival times to reduce the anticipated total waiting time and used a chance constraint to limit the likelihood of the server over time given a sequence of appointments arriving at a particular server. A systematic literature review for no-shows in appointment scheduling and the application of robust optimization in heath appointment other domains can be seen in ^[24]^[25]^[26]^[27]^[28]^[29]^[30]^[31]^[32]^[33]. Wang et al. ^[34] presented a multi-station network model that carefully established a compromise between assumptions that permitted tractability and assumptions that prevented real-world adoption. Sequential appointment scheduling in a network of stations with exponential service delays was examined, no-show potential, and overbooking to allow for real-world applicability and claimed that a heuristic myopic scheduling method was nearly ideal. Cox III and Boyed ^[35] offered a universal strawman method for creating a reliable system for robust scheduling of provider appointments in most situations. To verify the existence of both entities and causalities, an examination of the theory of limited thinking processes was conducted by utilizing a primary care practice. Recently, based on information about patient appointments, Issabakhsh et al. ^[36] created a mathematical model for mixed integer programming infusion appointment scheduling. Through the planning horizon, this model reduced the weighted sum of patient wait times overall and the number of beds utilized. To determine the best patient appointment times, a mathematical model using mixed integer programming and resilient slack allocation was used, taking into account the possibility that patient infusion times may be longer than anticipated ^[37]^[38]^[39].

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Subjects: Mathematics, Applied

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Yuan Gao

Qian Zhang

Chun Kit Lau

Bhagwat Ram

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Update Date: 29 Nov 2022

Table of Contents

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1. Introduction

2. Background

3. Related Literature Review of Robust Appointment Scheduling in Healthcare

References