The influence of appointment scheduling on admission times of
multiple patient groups
A simulation study in healthcare operations
University of Groningen
Faculty of Economics and Business
MSc Technology and Operations Management
25-8-2017
Rob Nieuwenhuis
Student number: S2812916
r.b.nieuwenhuis@student.rug.nl
Supervisor RUG: dr. J.A.C. Bokhorst
Co-assessor: dr. ir. D.J. van der Zee
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Abstract
In recent years, demand in hospitals has grown extensively. While patients expect short admission times, the resources of hospitals become scarcer. Hospitals experience difficulties with the coordination of this increasing demand and the available capacity. As a result, the admission times of patients increases; this has an impact on patient groups with life threatening diseases such as cancer. A method for controlling the capacity and decrease admission times is to make use of appointment scheduling. The coordination of capacity becomes more difficult when different patients make use of the same resources. From the perspective of hospitals, patient groups that use the same resources are more efficient in terms of costs and utilization. However, from the patient’s perspective, it results in longer waiting times. Currently, studies focus on the reduction of waiting times with the use of appointment scheduling; however, they do not consider multiple patient groups. This study examines the effects of appointment scheduling, by using policy slots, on the admission times of multiple patient groups that make use of the same resource. The study is conducted on the basis of a simulation study in a Dutch hospital. The results indicate that appointment scheduling contribute to admission-time reduction. However, the challenge is to find a trade-off between the different patient groups. A reduction of admission time for one patient group, could have negative consequences for other patient groups.
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Preface
This thesis represents the final part in finishing my master Technology and Operations Management at the University of Groningen. I would like to take this opportunity to express my gratitude to some people.
First of all, I would like to thank my supervisor dr. J.A.C. Bokhorst for his feedback, input and time dedicated to support me with this research. Also, I would like to thank my secondary supervisor dr. ir. D.J. van der Zee for his feedback on the research proposal.
Furthermore, my thanks go out to the employees of Medisch Centrum Leeuwarden for their input and time for answer my questions. In particular, I would thank Jantina Marra and Kelvin van der Heide for their support and contribution with my study and simulation model the past period.
Finally, I would express my gratitude to my girlfriend, family, and friends for providing me with support, trust and encouragement during my years of study. Thank you.
Groningen, June 2017
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Content
Abstract ... 2 Preface ... 3 1. Introduction ... 6 2. Theoretical Background ... 10 2.1 Hospital Setting ... 10 2.2 Appointment Scheduling ... 11 2.3 Slot Policies ... 122.4 Multiple Patient Groups ... 15
2.5 Patient Scheduling in Combination with Multiple Patient Groups ... 16
2.6 Theoretical Framework ... 18
3. Case Description ... 19
3.1 Patient Groups ... 19
3.2 The Process of Patients ... 22
4. Methodology ... 25
4.1 Research Design ... 25
4.2 Data Collection ... 26
4.3 Data Analysis ... 27
5. Simulation Model ... 28
5.1 Overview of the Simulation Model... 28
5.2 Model Verification and Validation ... 30
5.3 Experimental Design ... 30
5.4 Experimental Setting ... 31
5.5 Output Analysis ... 32
6. Results ... 33
6.1 Base Case Results ... 33
6.2 Effects of Slot Policies ... 33
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6.4 Different Capacity Levels ... 36
6.5 Three-way ANOVA ... 39
7. Discussion ... 40
7.1 Implications ... 41
7.2 Limitations and future research ... 42
8. Conclusion ... 43
References ... 44
Appendix I – Conceptual Model ... 47
Appendix II – Patient Flow Diagram ... 50
Appendix III – Warm-up Period and Number of Replications... 51
Appendix IV – Output Data of ANOVA Test ... 53
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1. Introduction
Currently, improving overall performance in hospital systems and maintaining better patient focus are the main challenges that hospital management faces. As patient expectations of medical services increase, competition between hospitals intensifies (Klassen and Rohleder, 1996). At the same time, demand for hospital services has increased greatly, while hospital resources have become scarcer (Vissers, 1995; Burdett and Kozan, 2016). This represents an operational challenge that requires coordination between capacity and demand. This problem can be seen from two perspectives: from the perspective of patients and that of hospital centers (Woodall et al., 2013). Increased demand, from a patient’s perspective, can result in longer waiting times. From the perspective of hospitals, it increases the utilization of resources. Furthermore, resources are often used to serve a single patient group, even though serving multiple patient groups can sometimes be more efficient in terms of a higher utilization of these resources (Ma et al., 2016). However, most studies in hospital settings focus on either patient demand or hospital capacity without discovering how the combination of these two aspects affects patient flow (White, Froehle and Klassen, 2011). One way to combine the capacity and demand components is by making use of appointment scheduling techniques (Cayirli and Veral, 2003). Well-designed appointment schedules can reduce waiting times for patients.
In the hospital industry, appointment scheduling has been widely studied in the last decades by researchers such as Cayirli and Veral (2003), Gupta and Denton (2008), White et al. (2011), and Liang et al. (2014), always with a trade-off between demand and capacity (Gupta and Denton, 2008). The main goal of using appointment scheduling is to reduce patients’ waiting times and to use resources as efficiently as possible. Shorter waiting times are generally considered to be an important influence on patient satisfaction, especially when hospitals are dealing with life threatening diseases because shorter waiting times reduce the period of uncertainty for a patient (Romero et al., 2013). By contrast, increasing demand leads to higher resource utilization, which also has an effect on patients’ waiting times.
7 patients’ waiting times and move patients through the system faster (White, Froehle and Klassen, 2011).
In general, most studies on appointment systems do not address the fact that patients can be classified into different groups, such as new or returning patients or based on the type of treatment. They assume patients to be a homogeneous group for scheduling purposes (Cayirli, Veral and Rosen, 2006). In this case, patients are often assigned to available slots based on a first come, first served sequencing rule, which is not always the most effective solution for waiting-time improvements.
This study is motivated by the fact that oncology centers in hospitals face difficulties in reducing the waiting times of patients. These are not internal waiting times, for example, the time between the moment a patient enters the hospital and receives treatment, but rather external waiting times, also called admission times. Admission times can be defined as the time between the moment patients make a call for an appointment and the day of the appointment (Gupta and Denton, 2008). Reasons for these long waiting times are insufficient coordination between demand and supply, variability in patient arrivals, and limited capacity of some resources that were used by multiple patient groups.
Patients visit oncology centers for many reasons: referrals from a general practitioner (GP) or for control appointments (second opinions), treatments, and follow-ups after completing treatments (Woodall et al., 2013). In general, an oncology center is designed to have several departments, including the clinic, radiology department, laboratory, treatment center, and pharmacy department. In a generic process, a patient first visits an oncologist at the clinic, which is organized by type of cancer (for example, lung, breast, or bowel). After the intake, the radiology department makes a scan of the abnormality, based on the type of cancer. After the radiology research, the patient goes back to the clinic where the results are discussed. Based on these results, the diagnosis and subsequent steps are determined.
8 Different studies found that appropriate appointment schedules have the potential to reduce the waiting times of patients (Cayirli and Veral, 2003; Gupta and Denton, 2008; Joustra et al., 2012). However, most of these studies were focused on the reduction of internal waiting times; literature focusing on reducing admission times is rare. In addition, studies on appointment scheduling that deal with multiple patient groups, each with its own needs, is limited. Examples of studies that use appointment scheduling techniques dealing with multiple patient groups are Cayirli, Veral and Rosen (2006) and Klassen and Rohleder (2004). Cayirli, Veral, and Rosen (2006) investigated the influence on the waiting times of patients in a hospital by scheduling two patient groups (new and returning patients) based on different sequencing and appointment rules. The study of Klassen and Rohleder investigated the effect of allocating multiple patient groups (acute and regular patients) by using a slot policy, which means that each patient group was allocated to specific slots. In both studies, the use of scheduling rules contributes to lower patients’ waiting times.
Due to the fact that multiple patient groups are involved, a trade-off should always be made between the patient groups, for example, in terms of priorities. A reduction of admission time for one patient group can have a negative effect on another group(s). Therefore, it is interesting to study the effect of applying different scheduling rules on the admission times of patients, when multiple patient groups are involved that all make use of the same resource. Addressing the problem of this case by applying scheduling rules can have an improvement both on the quality of care for patients and the efficient use of resources (Han et al., 2005). Therefore, the research question in this study is as follows:
What is the effect of applying appointment scheduling on the admission times of multiple patient groups that make use of the same resource?
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2. Theoretical Background
The relevant literature is reviewed in this chapter. Section 2.1 provides a short description of a general hospital setting. Section 2.2 discusses the different characteristics of appointment scheduling in hospitals, and section 2.3 explains the use of slot policies in hospitals. Section 2.4 describes the use of multiple patient groups, and section 2.5 discusses the combination of patient scheduling and multiple patient groups. Based on the literature, a theoretical framework is established in section 2.6.
2.1
Hospital Setting
A hospital provides different forms of treatment and surgery based on an urgent or elective basis. In addition to the fact that patients can be classified into different types of patients, hospitals or their departments can also be classified based on the treatments they provide. They can provide treatments either on an outpatient or inpatient basis (Gupta, 2007). In outpatient settings, patients arrive at the hospital on the day of the treatment, and they only stay in the hospital until the treatment is complete. In inpatient settings, patients are admitted to the hospital, and they are assigned to a bed, for example, because they are waiting for a surgery (Gupta, 2007). According to Matta and Patterson (2007), hospital outpatient settings can be described as complex systems that comprise an integrated network of multiple facilities.
Outpatient clinics serve multiple patient groups, each with its own specific needs; therefore, it is important for an outpatient clinic to schedule these patients efficiently. For example, urgent patients or patients who need special care often need to be treated as soon as possible. Therefore, it is essential for a hospital to be able to deliver timely and convenient access to healthcare services, which means it should have sufficient capacity to handle demand. According to White, Froehle, and Klassen (2011), capacity management in an outpatient clinic can be a complex issue because of the variability of both patient demand and the availability of resources. This means that, in terms of operations management, outpatient clinics can be defined as a queueing system, characterized by the different conditions that must be considered when an appointment system is designed (Cayirli and Veral, 2003). Furthermore, the allocation of capacity determines the number of patients that can be admitted to a resource and how the available capacity should be divided among different patient groups (Schütz and Kolisch, 2012).
11 scheduled patients are using the same resources, which is often the case, and a distinction must be made about which patient should be treated first (Aronsson, Abrahamsson and Spens, 2011). Such issues can be addressed with well-designed appointment schedules (Gupta and Denton, 2008). In the next section, the different elements of appointment scheduling are described.
2.2 Appointment Scheduling
Appointment scheduling at clinics has been widely studied for many years. One of the first studies about patient scheduling was conducted by Bailey (1952), who studied the relationship between patients’ waiting times and physicians’ idle times, based on a queueing system. Since then, there have been many more studies on appointment scheduling in healthcare environments, including those by Magerlein and Martin (1978), Cayirli and Veral (2003), Gupta and Denton (2008), White et al. (2011), and Liang et al. (2014). They explore different schedule optimization methods that address variations in arrival rates and service times, the effects of patient no-shows, and the use of individual and multiple appointment types.
The goal of patient scheduling is to improve access to hospital services and minimize the cost (Geng and Xie, 2016). However, the daily challenge that schedulers face is allocating the available capacity among patients with different needs with the aim of minimizing their waiting times (Patrick, Puterman and Queyranne, 2008). In other words, the way in which the match between demand and supply is made must be determined. Therefore, it is important to strike a balance between different priorities when committing the available capacity. For example, a lower-priority patient may want to be seen today; however, the capacity needs to be reserved for a potential higher-priority patient that may arrive tomorrow (Erdelyi and Topaloglu, 2009).
12 The use of multiple patient groups is the second element that Cayirli and Veral define. This describes which patient groups are used within the planning system. In the majority of the studies, patients are assumed to be a homogenous group. However, especially in outpatient settings, demand is often heterogeneous when multiple patient groups are used.
The third element of appointment scheduling includes the adjustments that must be made to reduce the disruptive effects of walk-ins, no-shows, and emergency patients (Cayirli and Veral, 2003). In the literature, many researchers studied the effects of walk-ins and no-shows, and how they can be minimized (Cayirli, Veral and Rosen, 2006; Gupta and Denton, 2008; White, Froehle and Klassen, 2011). The problem with no-shows is that the limited capacity is wasted because it is often impossible to fill a last-minute cancellation with another patient (Thompson, Day and Garfinkel, 2013).
The description of Cayirli and Veral (2003) provides a sufficient overview of the elements in appointment scheduling. Based on the scope of this study, slot policies and multiple patient groups are the most important elements. Therefore, the next sections discuss these two elements in more detail. Furthermore, in most studies, appointment scheduling (rules) are used to minimize the waiting times in minutes. This means that the scheduling rules are used to optimize daily operations. However, scheduling rules are not only useful for optimizing daily operations, but also for longer time periods (for example, days or weeks).
2.3 Slot Policies
13 The difficulty in allocating capacity to each patient group is deciding on the amount of available capacity that each patient group should receive. Several studies, such as Klassen and Rohleder (1996), indicate that there is always a trade-off between the different patient groups, for example, when there must be a trade-off of capacity allocation between urgent patient groups and other patient groups. Logically, the more capacity that is allocated to urgent patients, the higher the chance is that these patients can be treated quickly. However, the possibility that not all these allocated urgent slots are used also becomes higher. Otherwise, these unused slots could be allocated to other patient groups. Furthermore, allocating more capacity to one patient group had an influence on the admission time of other patient groups.
Another important aspect of capacity allocation is the position of the slots within a certain period. In some cases, it would be better to have the same number of slots per day, whereas an uneven distribution of slots might offer better results when the demand fluctuates during a period (Klassen and Rohleder, 2004). In the study of Klassen and Rohleder (1996), it was found that the placement of slots could have an influence when demand is variable. In some cases, it was better to leave open slots in the middle of the session, while in other scenarios, open slots at the end of the day demonstrated better results in terms of shorter waiting times.
2.3.1 Dedicated and Reserved Slots
The type of slots should also be considered. Slots could be dedicated or reserved to one specific patient group, or they could be shared by multiple patient groups. Dedicated time slots are used to handle multiple requests from different specialties for the available capacity of (shared) resources. Dedicated time slots are defined as the specific amount of resource capacities dedicated to a specific group of patients (Drupsteen, 2013). In defining dedicated time slots, hospitals allocate capacity to each patient group; this allocation can be based on criteria such as duration, type of disease or treatment, or urgency (Vissers, Bertrand and De Vries, 2001). A result of this allocation is that each patient group will have its own waiting queue for the same resource, instead of one main queue (Drupsteen, 2013).
14 positive effect on the admission times. However, the reduction of admission time for acute patients results in an increase in admission time for control patients.
Reserved time slots are slots that can be used by multiple patient groups. These reserved slots imply that patients from a specific group can be planned in these slots; however, if necessary, the slots can also be used by other patient groups (Gupta and Denton, 2008; Romero et al., 2013). In comparison to dedicated time slots, where only one specific patient group is allocated to a certain number of slots, reserved slots are more flexible because they can be allocated to multiple patient groups. Another advantage of reserved slots is the fact that they offer the possibility of improving the utilization of resources because of this flexibility.
2.3.2 Scheduling Rules
To schedule patients, rules are used to determine the order in which patients are treated or receive an appointment slot (Gupta and Denton, 2008). In the literature, different types of scheduling rules are studied related to waiting times. In almost all studies, it is assumed that patients are homogeneous, and they are often served on a first come, first served basis (Magerlein and Martin, 1978; Cayirli and Veral, 2003; Sauré et al., 2012; Geng and Xie, 2016; Ma et al., 2016). However, recent studies have demonstrated that rules with variations in the length of the slots during a period, such as a dome-shaped scheduling rule (where short slots are planned at the beginning and end of a session, while longer slots are planned in the middle part), perform better than the first come, first served rule (Cayirli, Veral and Rosen, 2006).
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2.4 Multiple Patient Groups
Often, when hospitals departments operate as outpatient centers, these centers consist of many patient classes rather than one homogeneous patient type (Matta and Patterson, 2007). According to Matta and Patterson (2007), patient classes can be differentiated by the type of patient (for example, new, return, or control patients) or by the type of disease. Other classes that can be differentiated are type of treatment, level of difficulty, or physical mobility (Cayirli, Veral and Rosen, 2006; Matta and Patterson, 2007). In the literature, patient classes are often also noted as patient groups. For example, Romero et al. (2013) divided patients into two groups (new and returning patients), while Cayirli, Veral, and Rosen (2006), who also use new and returning patients in their study, noted them as patient classes or classification. To prevent confusion between these words, “patient groups” will be used in this study.
An analysis of the literature by Cayirli, Veral, and Rosen (2006) finds that most studies that consider appointment scheduling assume that patient groups are homogeneous. However, different (heterogeneous) patient groups should often be scheduled as well, especially when they make use of the same resource(s). For example, a radiology department will serve multiple patient groups, each with its own specific needs. In this scenario, the radiology department is shared by multiple patient groups. A consequence of multiple patient groups sharing resources is an increase in the complexity of scheduling patients (Hoekstra and Romme, 1992; Cayirli and Veral, 2003). From a patient perspective, this can negatively influence patient satisfaction. One reason for this complexity is that shared resources are not committed to homogeneous groups of patients but to heterogeneous groups. This means that the planning decisions concerning one patient group have consequences for other patient groups (Drupsteen, 2013). A way to address the complexity of scheduling (shared) resources for heterogeneous patient groups is to establish scheduling rules (Vissers, 1995).
16 One of the first studies that examined the problem of serving multiple patient groups with different needs within one appointment system was that of Klassen and Rohleder (1996). Klassen and Rohleder made a trade-off between patients’ waiting times and the idle times of doctors. Based on these results, more studies were conducted about this topic by, for example, Cayirli, Veral, and Rosen (2006) and Ma et al. (2016). However, these studies focused on internal waiting times, not on admission times.
Due to the fact that appointment scheduling can be a useful method when multiple patient groups are involved, it also becomes more difficult (Cayirli and Veral, 2003). An increase in the number of patients, each with his or her distinctive needs, means that the total number of available slots for a certain period should be divided among these patient groups. Therefore, the allocation of the number of slots per patient group should be distributed based on the priority levels of each patient group.
2.5 Patient Scheduling in Combination with Multiple Patient Groups
Since the investigation of one of the first studies on appointment scheduling by Bailey (1952), and later by Magerlein and Martin (1978) and Chase and Tansik (1983), many researchers have tried to contribute to this subject. Where most studies were focused on homogeneous patient groups in the beginning, the distinction between different patient groups was made later on. As mentioned in the previous sections, apart from the fact that dealing with multiple patient groups leads to more difficulties in planning patients, it can also increase the performance of appointment scheduling systems (Cayirli and Veral, 2003). However, the use of multiple patient groups also creates new difficulties.18
2.6 Theoretical Framework
To provide a better understanding of the focus of this research in the context of the different theoretical concepts, a theoretical framework is developed (figure 2.1). Most of the studies that investigated appointment scheduling focused on homogenous patient groups and/or internal waiting times. However, the scope of this study concerns the appointment scheduling of multiple patient groups that make use of a shared resource, and the investigation of the effect of these factors on admission times.
This study investigates the effect of using appointment scheduling techniques on the relationship between demand, resources, and patients’ admission times. As mentioned, the number of patients (demand) has a positive influence on patients’ waiting times. This includes the fact that an increase in demand leads to an increase in waiting times. The capacity of resources has a negative influence on waiting times because an increase in capacity results in shorter waiting times. The influence of appointment scheduling techniques is studied. The theoretical framework suggests a direct effect of the demand size on the admission time of patients and of the capacity of the shared resources on the admission time of patients. The application of appointment scheduling techniques has a moderating effect on this relationship. As indicated in figure 2.2, the main focus of this study is the moderating effect of appointment scheduling techniques on the admission times of patients in combination with multiple patient groups that use the same resource.
Figure 2.1 - Theoretical framework
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3. Case Description
This chapter provides a description of the case that is used for this study. In this chapter, the main elements and information are described.
The case company used in this study, MCL, is a hospital located in the north of the Netherlands. The MCL has more than 40 different specialties; one of these is the oncology center (OCL), an important part of the healthcare that the MCL provides. The areas of the OCL consist of an outpatient-care department, a day-care department, and a clinical-care department. The OCL treats different types of cancer, such as lung, bowel, and breast cancer; however, this research focuses only on breast-cancer patients. At this moment, the demand for breast-cancer treatment at the OCL is increasing at a minimum of 11% per year, based on the demand of the last four years. In the future, demand will possibly increase even more as a result of a centralization of all breast-cancer treatments at one hospital in the province of Friesland. The MCL is one the qualified hospitals for this centralization project. The OCL was confronted with this news, and it wonders about the measures it should take to meet future demand on the one hand, but also lower the admission times for patients on the other hand.
The demand of breast-cancer patients can separated into four patient groups that make use of the same resources, yet each group has its own needs. Each patient group has its own needs; therefore, the type of demand can be defined as a heterogeneous demand. The four patient groups are identified as new patients (NPs), returning patients (RPs), control patients (CPs), and other (cancer) patients (OPs). First, the characteristics of each patient group are discussed.
3.1
Patient Groups
In this sub section the characteristics of the different patient groups will be discussed. For each patient group a short description of their characteristics is written.
New patients
20 Patients who obtain a referral experience much uncertainty about what is happening with their bodies and the possibility that there is something wrong. Therefore, short admission times positively influence the satisfaction of NPs. The problem that currently occurs in the OCL is that the average admission time of NPs is six days or more (figure 3.1). This means that governmental regulations have been exceeded. One of the regulations is that (new) patients who receive a referral from a GP should be able to make an appointment with an OCL specialist within five working days at most. These five days include the day a patient calls to make an appointment and the day of the appointment. Based on figure 3.1, fewer than 50% of the NPs had an appointment within five days.
Figure 3.1 – Frequency of average admission time for NPs
Returning patients
In 80% of the cases, there are no abnormalities found around or on the breast. In the case of a negative result, meaning that an abnormality is found, NPs must make a new appointment for further examination. These patients are defined as RPs.
The average admission time for RPs is 18 days. Figure 3.2 presents a histogram of admission times for RPs. As can be seen, the pattern of admission times is not smoothly distributed, compared to the average admission time for NPs. One reason for this variation is the patients themselves. Sometimes, patients need time alone to process the situation when they hear that something might be wrong. Furthermore, there are no governmental regulations for RPs. This
0% 20% 40% 60% 80% 100% 0 10 20 30 40 50 1 2 3 4 5 6 7 8 9 10 11 12 13 >13 F requenc y
Admission time (days)
Frequency of new patients' average admission
times
21 means that they are free to schedule appointments on their own terms, which results in a larger variation in admission times.
Figure 3.2 – Frequency of average admission times for RPs
Control patients
In the past, when patients were treated, they had to return for control visits. They should visit the hospital once every 3, 6, or 12 months, depending on the results of previous control visit. These control visits are important for patients to stay informed about the state of their health until they are free of the cancer. In contrast to NPs, admission times are less important for CPs. For these patients, the exact dates of the control visits are less important. The next appointment should not be planned precisely three months later; in these cases, it is acceptable to schedule a visit several weeks (for example, two weeks) earlier or later.
Other patients
This group of patients is defined as patients who have another type of cancer, but use the same resources as the breast-cancer patients. Normally, each type of cancer group could also be divided into different (sub)groups, for example, NPs, RPs, and/or CPs. Due to the fact that the focus of this study is on breast-cancer patients, all other types of cancer patients are merged into one group. In addition, they are only patients that make use of the same resource as the breast-cancer patients. 0% 20% 40% 60% 80% 100% 0 5 10 15 20 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 Fr eq u en cy
Admission time (days)
Frequency of returning patients' average
admission times
22 However, even though there is less focus on this patient group, short admission times are also important for them. In general, these patients also include a combination of NPs, RPs, and CPs.
Arrival process
The oncology department deals with different patient groups and therefore different arrival patterns, including the prediction of each patient group entering the clinic—each group with its own needs. Furthermore, the arrival of some patient groups is predictable, while others are more difficult to predict. The needs of all four patient groups are summarized in table 3.1.
As mentioned in the literature, walk-ins, no-shows, and emergency patients are also elements of an arrival process that could have an impact on waiting times. However, the influence of these elements is often defined in minutes, whereas this study is focused on admission times, which are defined in days. This means that those elements are not included in this study. Moreover, a visit to the hospital can only be achieved by making an appointment.
Patient group Enters clinic based on: Predictable? Goal visit Importance
New patients Referral GP No Diagnosis Short admission times
Returning patients
Making an appointment
Yes Diagnosis/Treatment Often short admission times (depends on the
patient itself) Control
patients
Making an appointment
Yes Control visit Regular control visits
Other patients Referral GP/make an appointment
No Diagnosis/Treatment/Control visit
All of the three above
Table 3.1 – Needs Different Patient Groups
3.2 The Process of Patients
In this sub section the process of the different patient groups will be discussed. First NPs will be discussed in detail. The process of the RPs, CPs and OPs will be discussed more in general.
New patients
23 admission times of patients instead of internal waiting times. A detailed overview of the internal process steps is presented in Appendix II.
The first step is an appointment with a specialist. This meeting contains an intake with the patient and a preparation of what is going to take place during the next steps. In the second step, a radiology examination is performed, which includes a scan of or around the breast. The resources used during this step are a radiologist, a laboratory, and a mammograph. After the radiology exam, the patient returns to the specialist, who discusses the results with him or her. These three steps are performed on the same day. If one of these resources is not available, the entire first-phase process cannot be performed.
Visiting Specialist and/or Radiology
Admission time NP Process Admission time RP
First Phase
Further Examination Phase
No abnormalities
Figure 3.3 - Flow diagram for new and returning patients at the MCL
As mentioned, the second step in an NP’s process is a visit to the radiology department. Currently, the radiology department reserves an amount of its daily capacity for new breast-cancer patients; this capacity is limited to three NPs per day. A consequence of that limitation is that the OCL is limited to providing first-phase treatments to, at most, three NPs per day. The reason for this limitation has to do with the fact that the radiology research equipment is shared among other cancer-patient groups, such as patients with skin, lung, or bowel cancer and breast-cancer patients who make returning or check-up appointments.
24 new appointment for a check-up or further examination. In general, 20% of NPs who visit the hospital have to make an appointment for additional examinations.
Currently, when an NP calls to make an appointment, the OCL schedules them at the beginning of the day (also called the morning slot), often between eight and 11 o’clock. Returning patients are scheduled in the remaining slots of the day. These slots are from 11 to two o’clock and from two to five o’clock in the afternoon. This also applies to patients who are scheduled for a control appointment or other patient groups using the same resources. In the current situation, the OCL does not differentiate between the priorities for treatment for NPs versus RPs; all patients have the same priority. These morning and remaining slots are defined as reserved slots. In the case of the morning slots, available slots are reserved between eight and 11 o’clock; however, they can also be used by the other three patient groups if enough capacity is available. The remaining slots are only reserved for RPs, CPs, and OPs.
Returning, Control and Other patients
In the case of further examination, a puncture is performed. The resources used for performing punctures are the same (mammograph, radiologist, and laboratory) as those used in the first phase. Unfortunately, the mammograph is not able to perform the scan and puncture procedures at the same time. In this case, the OCL does not take into account the variability between NPs and RPs. If, for example, the average demand for NPs is five per day, after a certain period, the waiting list is long, while the mammograph may be idle in the second half of the day.
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4. Methodology
This study aims to demonstrate the effect of appointment scheduling techniques on the relationship between, on the one hand, capacity and demand and, on the other hand, the waiting times of patients in a situation with shared resources and multiple patient classifications. A simulation is used to gain insights into this problem because it is a suitable method for addressing complexity and variability, for example, in arrivals. The different variables are presented in the theoretical framework (figure 2.1). The unit of analysis in this simulation study is the oncology department at the MCL. A detailed description of the conceptual model for the simulation study is provided in Appendix I.
4.1
Research Design
To investigate the effects of scheduling rules on the admission times of multiple patient groups at the oncology department of a hospital, a simulation was used to provide the results. Therefore, this research uses a quantitative approach to answer the main research question. Before the simulation model was developed, the most relevant information about the properties of patient scheduling, the characteristics of multiple patient groups, and the relationship between these two concepts were studied. Then, a description of the system was formulated to obtain a clear understanding of the processes a patient goes through. Data from the MCL were analyzed, and face-to-face meetings were conducted. Next, after obtaining a clear understanding of the patient processes, a simulation model was developed to simulate different scenarios to determine the effect on patients’ admission times if different patient classifications are using the same resources. Section 4.1.1 explains why a simulation approach was chosen.
4.1.1 Discrete-Event Simulation
26 The simulation model was developed in FlexSim 5.1. This simulation program focuses entirely on the healthcare environment, and the MCL uses it for modeling logistics problems. During the process of building and testing the model, it was important to validate the model. The outcomes of the simulation model were compared to reality by discussing them with specialists in the field. They were able to provide useful feedback and assess the model using their knowledge about simulation and the real situation.
4.2 Data Collection
According to Robinson (2004), three different types of data are required for simulation. The first is contextual data, which are necessary to create a solid understanding of the problem situation. In this study, the sources of such data are literature, articles, books, and data from the hospital. The second type of data that Robinson (2004) requires is data needed for realizing the model. In this study, data from the MCL are used (for example, arrival patterns of demand and activity times). The third type of data is the data used to validate the model.
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4.3 Data Analysis
The dataset used here consisted of the registration of all activities performed in the MCL oncology department from April 2016 to April 2017. Only data from last year were used because the MCL began using a new database system (EPIC) in April 2016, which means that only data from last year were available. The activities ranged from patient appointments to treatment procedures. The patient groups also varied, and they included NPs, RPs, CPs, and OPs.
The first step was to analyze the different patient patterns. This included an analysis of the average admission time of NPs. The next step was to determine the average number of NPs per day and how many of them had to come back as RPs. This was also done for CPs and OPs. The third step was to determine the inter-arrival times between the arrivals of NPs, RPs, CPs, and OPs. For the inter-arrival times, statistical distributions were used. The determination of the statistical distributions was done by testing some distribution methods and assessing the one that best fit the data.
Furthermore, a detailed description of the simulation model, the assumptions that had been made, the validation and verification process of the data, the experimental settings, and the output analysis is presented in chapter 5.
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5. Simulation Model
The simulation model is based on a real situation in the case company, the MCL. To obtain reliable output data, it was important that the simulation model was a prime reflection of the MCL’s situation. However, some assumptions were made because of the complexity of the case company. An overview of the simulation model and its assumptions is discussed in section 5.1. The verification and validation of the model are elaborated in section 5.2. Based on the complexity of this hospital, assumptions had to be made to simplify the model and complete this study in the available time. In section 5.3, the experimental design of this study is described. The experimental setting is described in section 5.4 and section 5.5 describes the output analysis.
5.1
Overview of the Simulation Model
The developed simulation model is complex and can be difficult to understand. Therefore, each step or decision that is made in the system will be described. The run length of the model is one year, and it generated the admission times for each patient group. The flowchart of the simulation model is presented in figure 5.1, and it provides an overview of the steps that the simulation model made. In Appendix I, a detailed description of the conceptual model of the simulation is presented.
29 After the process step, RPs, CPs, and OPs leave the system. For NPs, there are two options. The first is that no abnormalities are found, which means the patient is healthy, does not have to return, and leaves the system. In the second option, something could be wrong, and the patient has to come back for an additional examination. If this is the case, these patients have to make new appointments. This is done immediately after receiving the results, and then the patient leaves the system. Patients who require additional exams enter the system later as an RP.
In general, hospitals are complex systems with many variable factors that can have an influence on internal processes, patients, and resources. To address this complexity, several assumptions had to be made to simplify the simulation model due to time constraints. These assumptions facilitate the complexity of the real system without affecting the most important aspects of the problem. The assumptions are presented in Appendix I
30
5.2 Model Verification and Validation
Before the simulation model was developed, the validity of the proposed model was checked by discussing it with several employees from the oncology department. The validation of the data was done according to the verification and validation framework described by Robinson (2014). To compare the simulation model with the real system, box validation was used. In black-box validation, the overall behavior of the model represents the real-world situation with sufficient accuracy for the purpose at hand (Robinson, 2014, p. 254) . This was done by checking whether the simulation model provides an accurate representation of the real system. With black-box validation, the outcomes for average admission times of NPs and RPs were compared with the historical data.
The validation of the experiments involves determining whether the experimental procedures adopted are providing sufficiently accurate results (Robinson, 2014). The main issues to assure the accuracy of the validation is to determine the warm-up length, the run length, and the number of replications (Robinson, 2014).
A hospital is a difficult and complex system with many influencing factors; therefore, it was important to verify the sequence of the steps. FlexSim offers an integrated debugger that notifies the user when an incorrect code is applied to the model, thereby avoiding significant mistakes while building the simulation model. Furthermore, to ensure that the simulation model is a representation of the real situation, the output of the simulation model was verified with the real data.
5.3 Experimental Design
To answer the question regarding the effects of appointment rules on admission times for multiple patient groups, different experiments were conducted. The results of these experiments were compared to the current situation according to the model. The different experiments are elaborated on in the following sections.
31 model performs under different circumstances. Therefore, the following three experimental factors were added to the simulation model:
- Four slot policies
- Two different positions of the slots
- Three capacity levels of the resource for NPs
The main focus of these experimental factors is based on the different slot policies. These slots are divided into dedicated time slots and a combination of dedicated and reserved time slots. For both factors, these are only dedicated or reserved for NPs and/or RPs. According to the literature, dedicated and reserved time slots are useful for reducing the admission times of a patient group (Klassen and Rohleder, 2004). Due to the fact that, in this study, there was also a distinction between two patient groups with similar levels of urgency (acute and regular patients), which were compared to this study, these two types of slots are used. The positions of the slots are tested with two positions. The first position, based on the current situation, is that slots are equally distributed during the week. This means that every day of the week had the same slot positions for each patient group. The second type is an uneven distribution during a week. This includes more slots being positioned for NPs and RPs at the beginning and the end of a week. Finally, the limited capacity level for NPs will be increased. This limitation is one of the main reasons that admission times are too long; therefore, it is interesting to observe the size of influence when this limited capacity level is raised to four or five NPs per day.
As shown in table 3.1 short admission times are not important for CPs. Therefore the outputs of the CPs will not be used and included in the results and following sections.
5.4 Experimental Setting
32 done by making 10 replications with the average admission time of NPs as the output variable. The warm-up period for this model was determined to be 30 days (1 month). Appendix III provides an overview of the warm-up period.
The run length of the simulation was 365 days, excluding weekends. The rule of thumb states that the run length should be at least 10 times the warm-up period. In this case, this means that the run length of the model should be 300 days. With a rung length of 365 days, this simulation satisfies the minimal run-length criterion. In total, with the 30-day warm-up period, the total run length was set at 395 days.
To determine the number of replications, a confidence interval method, as described by Robinson (2014: 184–186), was used with the average admission time of NPs. Table III.A in Appendix III demonstrates that a confidence interval of more than 95% was obtained by 25 replications. However, to obtain an effect power of 80% when using an analysis of variance (ANOVA) test for measuring the differences between or among groups, Wilson, VanVoorhis, and Morgan (2007) recommend a rule of thumb of using at least 30 replications. Therefore, for each experiment, 30 replications were conducted to ensure that the output data were useful for performing the ANOVA test.
5.5 Output Analysis
33
6. Results
In this section the results of the simulation study will be presented. Each experimental factor will be discussed. First only the results based on the limited capacity of three new patients per day will be discussed. This capacity level is chosen because of the fact that these results show the biggest effects and aremost related to the real situation.
6.1
Base Case Results
To analyze what the effects of the slot policies are on the admission times, the results of the base case were used as reference points. To give a first indication of the output measures of the base case situation generated by the simulation model, table 6.1 shows the admission times and the number of patients served in one year. The number of patients is presented as validation for the real situation but also to determine whether around 20% of new patients came back as returning patients. The outcomes in table 6.1 show that the number of new patients that become returning patients (21%) is in line with the average standard percentage of 20%.
Base case NP RP CP OP
Admission time (in days) 6.0 18 90 - 365 1
Number of patients 747 159 266 4716
Table 6.1 – Outputs of base case scenario
As shown in table 6.1, the admission time of control patients is three months till one year. This is because of the fact that these patients make immediately a new appointment during their current visit. The downside of the way of scheduling results in two constraints. First it will lead (in the system) too long admission times and these CPs also fill the open slots in the future. A consequence is less flexibility of planners to schedule other patient groups.
6.2 Effects of Slot Policies
34
Admission times (in days)
Scenario Type of slots NP RP OP
1 No slots (Base case) 6 18 1
2 Dedicated NP 4,8 17 8,3
3 Dedicated NP and RP 4,8 14,8 16
4 Reserved NP 6,1 15,1 10,1
5 Reserved NP and RP 5 14,9 9,2
Table 6.2 – Admission Times Slot Policies
Table 6.2 shows dedicating slots for NPs and RPs will lower their admission times, but lead to an increase in the admission time for other patients. Furthermore, three of the four scenarios shows a reduction of admission time for NPs. In addition, two of the scenarios (2 and 3, table 6.2) show an admission time below the governmental rule of five days.
The dedicated slot policy for NPs and RPs (scenario 3, table 6.2) shows the highest reduction of admission times (NP -20% and RP -18%). As shown in table 6.2, due to the fact NPs and RPs are allocated to dedicated slots, less slots are available for the other patient groups. This results in higher admission times. It is interesting to see the admission times of OPs in the dedicated slots for NPs (scenario 2, table 6.2) are almost doubled compared to the admission times in the dedicated slots for NPs and RPs (scenario 3, table 6.2).
Figure 6.1 – Visualization of the Admission Times performed by the Slot Policies
0 2 4 6 8 10 12 14 16 18 20 No slots (Base
case) Dedicated NP Dedicated NPand RP Reserved NP Resevered NPand RP
A dmi ss io n ti mes (i n days ) Slot Policies
Admission Times Slot Policies
35 The reserved slots for NPs shows a small increase (2% compared to the base case) in their admission times. Furthermore, in the reservation of slots for both NPs and RPs (scenario 5), the admission times of NPs are lower (-16.6%) than the admission times of NPs in the base case. The admission times of RPs in scenario 5 show a reduction as well (-17,2%).
These results show a good example of the trade-off in allocating capacity to one patient group over another group. However, it is interesting to see that using dedicated or reserved slots for NPs and RPs results in a small reduction of the admission times, but have a big negative impact on the admission times of OPs. A reason for this could be the fact that the capacity of NPs is limited to three patients per day. Besides the fact slots are dedicated or reserved, as long the demand is higher than the capacity, admission times will be occur.
6.3 Effects Position of Slots
Table 6.3 shows the scenarios which were used for testing the effects on the admission times when changing the position of slots into an uneven distribution. Currently, the position of slots is equally distributed during the week. By changing the position of slots into an uneven distribution, new and returning patients have more slots in the beginning and the end of a week. This uneven distribution is combined with the different types of slots.
Position of slot: Uneven distributed Admission times (in days)
Scenario Type of slots NP RP OP
6 No slots (Base case) 6 18 1
7 Dedicated NP 3,6 15,3 10
8 Dedicated NP and RP 3,6 12,6 18
9 Reserved NP 4,8 13,3 12
10 Reserved NP and RP 4,0 13,6 11
Table 6.3 – Admission Times based on Position of Slots
36
Figure 6.2 – Effects of Slot Position on Admission Times NPs
Figure 6.3 - Effects of Slot Position on Admission Times OPs
6.4 Different Capacity Levels
In section 6.2 and 6.3 the different experimental factors are used to find out if they had any effect on the admission times for each different patient group. Despite the fact the positions and the type of slots will influence, positively or negatively, the admission times of each patient group, it is also interesting to see what the effects are if the limited capacity for NPs increase. The capacity levels for NPs are increased to four and five patients per day. The results are presented in table 6.4 and 6.5
0 1 2 3 4 5 6 7 No slots (Base
case) Dedicated NP Dedicated NPand RP Reserved NP Resevered NPand RP
A dmi ss io n ti mes (i n days ) Slot Policies
Effects of Slot Position Admission Times NP
Equally distributed Uneven distributed 0 5 10 15 20 No slots (Base
case) Dedicated NP Dedicated NPand RP Reserved NP Resevered NPand RP
A dmi ss io n ti mes (i n days ) Slot Policies
Effects of Slot Position Admission Times OP
37
Capacity 4 Admission times (in days)
Scenario Type of slots NP RP OP
11 No slots (Base case) 6 18 1
12 Dedicated NP 2,1 17 9,6
13 Dedicated NP and RP 2,1 14,8 16,4
14 Reserved NP 3,5 15,1 11
15 Reserved NP and RP 4,1 14,9 10,4
Table 6.4 – Effects Capacity Level 4 on the Admission Times
Table 6.4 shows an increase in capacity from three to four new patients per day results in an average admission time reduction (average admission time of all four slot types divided by the base case) for NPs of more than 50%. Separately from each other, dedicated slots NPs show the highest reduction (-56%) of admission time compared to reserved slots (reserved NP -42%, reserved NP and RP -18%).
Furthermore, there is studied what the effect is when the capacity is limited to five new patients per day. These results are presented in table 6.5.
Capacity 5 Admission times (in days)
Scenario Type of slots NP RP OP
16 No slots (Base case) 6 18 1
17 Dedicated NP 1 17,3 14,9
18 Dedicated NP and RP 1 14,9 20,1
19 Reserved NP 1 15,5 1
20 Reserved NP and RP 1 15,1 1
Table 6.5 - Effects Capacity Level 4 on the Admission Times
The first points that stand out are the high reduction of admission times for as well NPs as OPs. On the first place this seems strange, but it is explainable. The number of NPs that call for an appointment is on average at least four patients (4,2 patients) per day. Now the capacity is limited to five new patients per day, every NP that makes a call has the ability to make an appointment within one day. Furthermore, the dedicated slots results in higher admission times for the OPs compared to the reserved slots. Caused by the fact when a slot is dedicated to NPs and/or RPs, other patient groups can’t be allocated to these slots. When slots are reserved for NPs and/or RPs, other patients groups can also be allocated to these slots, under the condition these slots will not be used by NPs or RPs.
38
Figure 6.4 – Effect Capacity levels on Admission Time NPs
However, it will have an effect on the admission times for OPs as well. This seems logical, because more slots can be allocated to NPs. This means less slots will be available for the other three patients groups. Figure 6.4 and 6.5 show the effects of the different capacity levels for NPs and OPs. However, focusing on the admission times of the OP groups, the results show that an increase in capacity for new patients has small effects on the admission times for the OP group. This applies only for slots which are dedicated. Reserved slots perform the opposite and lead to an admission time reduction for OP groups.
Figure 6.5 - Effects Capacity Level 4 on the Admission Times
0 1 2 3 4 5 6 7 3 4 5 A dmiss ion ti mes ( in da ys ) Capacity Level
Effect Capacity Levels on Admission Time
NP
Dedicated NP Dedicated NP&RP Reserved NP Reserved NP&RP 0 5 10 15 20 25 3 4 5 A dmi ss io n ti mes (i n days ) Capacity LevelEffect Capacity Levels on Admission Time
OP
39
6.5 Three-way ANOVA
A three-way ANOVA was conducted to test whether the experimental factors had a significant and interaction effect on the admission times of the different patient groups (NPs, RPs and OPs). The different capacity levels, the slot policies and the slot position were used as the independent variables. The admission time was used as the dependent variable. The results of the ANOVA test are presented in table 6.6.
Source F Sig. Slot_Policy 443,48 0,000 Capacity 103,10 0,000 Patient_Group 6895,98 0,000 Slot_Policy * Capacity 104,98 0,000 Slot_Policy * Slot_Position 225,46 0,000 Capacity * Slot_Position 104,83 0,000
Slot_Policy * Capacity * Slot_Position 158,97 0,000
Table 6.6 – Overview Results ANOVA Test
The results present that all the independent variables show significant main effects. Figure 6.6 and 6.7 show the main effect of capacity and slot policies on the admission times. Furthermore, a post hoc test is performed to compare the means of all the independent variables. The results show a significant difference between each independent variable. The total output is presented in Appendix IV.
Figure 6.6 – Main Effect Slot Policy Figure 6.7 – Main Effect Slot Policy
40
7. Discussion
In this study, different slot policies were compared in order to identify the effect on patients’ admission times when multiple patient groups make use of the same resources. The results show dedicated or reserved slots are useful for the reduction of admission times of one or two patient groups. On the other hand it can have a negative impact on other patient groups as well. In addition, all the patient groups have to use the same resource. These results confirms the findings and suggestions of Klassen and Rohleder (2004).
The main context of this study was the allocation to limited amount of capacity of the resources per day of one patient group (NPs). Therefore, it was interesting to study any influences of slot policies are useful to lower the admission times of this patient group. Based on the results, when new patient groups are allocated to dedicated slots, it will perform the lowest admission times. Also when slots are dedicated for returning patients it will result in the lowest admission times. On the other hand, these reductions will have a big (negative) impact on the admission times of the OP group. Because slots are now dedicated or reserved for specific patient groups (NPs and RPs), less slots are available for this OP group.
Furthermore, as expected, the increase of capacity for NPs results in lower admission times for this patient group. With a capacity level of four NPs per day, the results show that the admission times of NPs in every slot policy scenario is below the governmental rule that says patients must be seen within five days. Also an interesting pattern can be observed in the admission times of RPs. Despite the fact allocation of slots results in lower admission times, the differences between the admission times of the scenarios and the base case are relatively small. With the allocation of slot polices the hospital is able to schedule the patients more efficiently, but there is always the decision of the patient itself. As mentioned in the case description section (Chapter 3), there are no rules which describe that RPs need an appointment within a certain number of days.
41 Assuming the dedicated slots for NPs supposed as the most suitable slot policy for the MCL, it is interesting to compare the admission times of the dedicated slot policy with the admission times of the base case. Chapter 3 figure 3.1, illustrates the frequency of the average admission times for NPs. In this figure the cumulative line shows that less than 50% of all the patients are served in a maximum of five days. This means more than 50% of the patients had to wait longer than five days, what is inhumane with this type of disease. In figure 7.1, the frequency graph of the average admission time for NPs in combination with the dedicated slot policy for NPs is shown. In addition, the results are based on a capacity level of four NPs per day. The cumulative line shows that more than 95% of the patients were able to make an appointment within a maximum of five days. Compared to the current situation this is a large improvement in the reduction of the admission times.
Figure 7.1 – Frequency average admission time NP
7.1 Implications
Examination about appointment scheduling in healthcare environments has been widely studied for many years. To the author’s knowledge this study is one of the first studies that investigate the effects of appointment scheduling (slot policies) on admission times with multiple patient groups that make use of the same resource. This study has shown that, despite the fact multiple patient groups make use of a shared resource, admission times can be reduced by using different slot policies. However, this does not mean that the used slot policies, performed in this study, provide also a reduction in admission times in other hospital settings. For instance, Cayirli and Veral (2003) state that every appointment system will perform totally different based on the
0% 20% 40% 60% 80% 100% 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 1 2 3 4 5 Freq uency
Frequency Average Admission Times NP
42 particular circumstances. Furthermore, most studies about appointment scheduling analyzed the situation of a specific hospital setting, what means that the findings of these studies are not applicable in a general setting. Therefore, each hospital that decides to implement an appointment scheduling must take different circumstances in consideration before an appointment system can be suggested (Cayirli and Veral, 2003).
7.2 Limitations and future research
In this study there are several limitations. First, in the model the resource had a maximum amount of available capacity for three NPs per day. To simulate the situation as the best as possible, this restriction is include into the simulation model. However, in the current situations this restriction occurs as the bottleneck in the process of NPs. Therefore, it was not possible to treat more than three NPs per day. However, with the use of slot policies it is possible to perform small reductions on the admission times of NPs. But, in order to achieve a properly solution, this restriction will always obstruct the path to perform lower admission times. Despite of the fact the results of the different slot policies shows improvements in admission times, in real case the admission times will be higher compared to the simulation outputs. This because of the assumptions made in the simulation model. For instance, in real life situations no-shows of patients will definitely occur, what means that the utilization rate of resources will decrease. Also the allocated slot cannot be used anymore, because patients enter the hospital by making an appointment.
43
8. Conclusion
The aim of this study was to identify the effects of appointment scheduling on the admission times of multiple patient groups that used the same resource. This study is conducted on the basis of a simulation study in a Dutch hospital. The research question of this study was:
What is the effect of applying appointment scheduling on the admission times of multiple patient groups that make use of the same resource?
Based on the results there can be concluded that the application of appointment scheduling has a positive effect on the reduction of admission times for NPs and RPs. However, reduction for one or two patient groups will lead to an increase in admission times for other patient groups which are involved in the same scheduling system. A main criterion, related to the NPs and set up by the government, was the maximum admission time of five days. The results show that the use of dedicated slots for NPs contribute to lower admission times. Furthermore, a combination of this slot policy with an increase of the capacity level will show a admission time reduction of at least 50%. In addition, the results demonstrate that these variables show a significant effect compared to the base case.
44
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