A discrete event simulation approach for reserving capacity for emergency patients in the radiology department

Medical imaging equipment, such as computed tomography (CT) scanner, constitutes a critical component of a comprehensive health care system and plays a key role in the diagnosis and treatment of disease [1]. The demand for diagnostic imaging services has increased substantially over the past decades [2]. However, high operational costs and their influence in increasing medical costs have resulted in hospitals not extending their capacity at the same rate [3]. The large gap between supply and demand is associated with lengthy wait times, hospital overcrowding, and patient dissatisfaction [4, 5]. Under pressure from rising demand and costs, hospitals must take effective measures to organize their medical services to improve the service delivery process and increase patient satisfaction [6]. Therefore, effective appointment scheduling models [7‐10] are inevitably of great importance.

The motivation behind this study is the practice and problem of the radiology department of West China Hospital (WCH), one of the largest hospitals in China. The normal work hours of the radiology department are 8:00–21:00 (13 h) and the utilization of the equipment is almost 100%. Generally, the medical diagnostic facilities are accessed by three types of patients. Emergency patients arrive randomly with a higher priority. Both inpatients and outpatients are required to make appointments in advance [1, 11]. The daily challenge is to allocate resources among different types of patients. The problem faced by the radiology department is that there is no scientific method to determine how much capacity should be reserved for emergency patients. Through investigation and survey, we find that there is a large imbalance between appointments and service capacity, and the average wait times of outpatients and inpatients are 163.2 min and 144.7 min, respectively. A poor reservation process and poor scheduling lead to operational inefficiency and patient dissatisfaction [12]. In contrast, the overall goal of a well-designed appointment system is to achieve a balance among the competing and conflicting goals of minimizing the patients’ wait times and the doctor’s idle time and overtime [13]. Thus, the above analysis highlights the need for operations research models that provide a scientific emergency reservation policy for hospital managers.

In this study, we use simulation and optimization techniques to solve the described management problems in a complex health care system. The analysis is conducted using primary data from WCH and the following research questions are addressed: (1) How much daily and hourly capacity should be reserved for emergency patients? (2) Do different reservation policies have an influence on non-emergency patients’ wait times? (3) Are there any significant differences between different reservation policies? Through combined optimization with a validated discrete event simulation (DES) model, we evaluate the impact of different emergency reservation policies on a variety of system outcomes. On the basis of this work, practical guidance can be provided on resource allocation and appointment scheduling decisions.

When facing uncertain patient volume, effective schedule management is key to minimizing patient wait times, improving equipment utilization, and reducing the overall system cost. Radiology department scheduling is more challenging than outpatient [7] or operating room scheduling [8, 9, 14, 15], as it involves both appointed and emergency patients [16]. This study focuses on the allocation of medical capacity in the presence of multiple patient classes. Our goal is to design a simple and implementable emergency reservation policy. By combining optimization with DES, we evaluate the impact of different reservation policies on patient and hospital related metrics. Based on our work, practical guidance for appointment scheduling and emergency reservation can be provided.

Results demonstrate that although there is a slight decrease in examination quantity and equipment utilization, reservations for emergency patients greatly shorten the delay for non-emergency patients, with a reduction of over 40% in wait times. Furthermore, the comparison of different reservation policies indicates that they are relatively robust in terms of patients’ wait times. Our results differ from Erdogan et al. [17], who determined that reserving the capacity for urgent patients at the beginning of the session is favorable. Their results were obtained under the condition that the wait costs of urgent patients are high, whereas our study highlights the value of idle time.

The issue of redesigning the appointment scheduling rule and reserving capacity for emergency patients has attracted much attention in recent years. Green et al. [1] investigated a related problem of appointment scheduling and resource allocation for one medical diagnostic facility. They formulated the problem of managing patient demand for diagnostic service as a finite-horizon dynamic program, and identified properties of the optimal policies. Kolisch and Sickinger [18] extended [1] to the multiple facility setting, where they showed that the optimal policy is not simple but exhibits desirable monotonicity properties. Due to the computational complexity, it’s not easy for hospitals to implement the state-dependent optimal policy in practice.

As a result, simulation is an effective tool for allocating scarce resources to improve patient flow, while minimizing health care delivery costs and increasing patient satisfaction. A comprehensive literature review on the use of simulation in health care can be found in [19], where the application of DES modeling to health care and system clinics, such as hospitals, outpatient clinics, emergency departments and pharmacies is summarized. Bhattacharjee and Ray [20] discussed the reasons for selecting DES in the context of health care decision-making processes. Monks et al. [21] developed a DES model for capacity planning in acute and community stroke services. Lebcir et al. [22] adopted a DES model to evaluate the use of community services in the treatment of patients with Parkinson’s disease in the United Kingdom. Vermeulen et al. [23] presented an adaptive approach to automatic optimization of resource calendars, and developed a simulation model to determine optimal resource opening hours in a larger time frame where the allocation of capacity to different patient groups is flexible and adaptive to current and expected future situations. Antognini et al. [24] proposed a Monte Carlo simulation model to guide decisions on how to balance resources for elective and non-elective surgical procedures. This study also provided a simulation approach to radiology patient scheduling, and our results showed that DES is a potent tool for process improvement in health care systems.

The limitations of this study can be summarized as follows. First, we do not consider patients’ behaviors such as no-shows and unpunctuality [25, 26], the inclusion of which would make our simulation model much more practical. Second, our DES model is constructed based on the patient process of one CT scanner, we may extend our model to multiple facilities in the future.

The management of medical imaging resources is challenging because of uncertain demand. To minimize patient wait times in the face of this uncertainty, we proposed a DES approach to radiology patient appointment scheduling. Our results indicated that reserving proper capacity for emergency patients reduces delays and improves operational metrics. DES is an effective tool for studying the effects of proposed scenarios on radiology capacity allocation, and can help to optimize hospital resource utilization.