A Study of Block Scheduling

Transcription

1 21-1 Spring 21 PEDIATRIC DENTAL SIMULATION: Pediatric Dental Office Simulation: A study of Block Scheduling Erin Hopper, Abby Sly, Meagan Simmons A Study of Block Scheduling 4A Fpro'r- Erin Hopper Abby Sly Meagan Simmons

2 PEDIATRIC DENTAL OFFICE SIMULATION: A Study of Block Scheduling Erin Hopper Abby Sly Meagan Simmons

3 TABLE OF CONTENTS I. Executive Summary...1 TI. Background and Problem Description...3 III. Analysis of the Situation...7 IV. Technical Description of the Model...9 V. Analysis and Managerial Interpretation...15 Table 1: Average Chair Idle Time Table 2: Average Server Idle Time Table 3: Average Partial Occupation of Waiting Room...18 Table 4: Average Patient Waiting Time for Hygienists Figure 1: Comparison: Dentist Chair Idle Time Among Various Scenarios... 2 Figure 2: Comparison: Hygienist Chair Idle Time Among Various Scenarios.22 Figure 3: Comparison: Dentist Idle Time Among Various Scenarios...23 Figure 4: Comparison: Hygienist Idle Time Among Various Scenarios...25 Figure 5: Comparison: Percent Waiting Room Occupancy Among Various Scenarios...26 VI. Conclusions and Critiques...28 VII. Appendix...31

4 I. EXECUTIVE SUMMARY The following report discusses a simulation study conducted on the block scheduling techniques used in Dr. Roy Green's pediatric dental practice in Fort Myers, Florida. The purpose of this study was to analyze the current block scheduling procedure in order to determine the efficiency of Dr. Green's scheduling system in terms of chair idle time, patient waiting time, and server idle time. The study began by researching various papers on scheduling techniques for the purpose of applying appropriate methodology to our own study. This included, among other things, the justification of the use of simulation as the most accurate and efficient way to study scheduling problems and the approbation of the use of block scheduling in pediatric dental offices. After the research was complete, a collection of historical data was necessary to create the experimental environment and the parameters under which the simulation would be run. By gaining a thorough understanding of the current block scheduling system, along with a detailed description of dental procedures and staff allocation, this knowledge allowed for the creation of several assumptions useful in both clarifying and simplifying the model. This insight also permitted the application of variability and appropriate statistical distributions to the simulation that mimicked the existing dental office environment. With the use of the ProModel simulation software package, the simulation was developed to model Dr. Green's real world scheduling practices. In this basic queue system, patients arrive, are greeted by the receptionist, and escorted to dental chairs where they have the appropriate and predetermined procedures performed by either a dentist or hygienist. ProModel then gathers statistics and reports on the model's distinguishing characteristics, including chair idle time, patient wait time, and server idle time. Dr. Green's block schedule is different for each day of the week, thus five versions of the simulation were necessary to portray the model accurately. In addition, the simulation for each day of the week was run five times in order to obtain results representing a full month's worth of scheduling. The greatest strength of simulation modeling is the ability to accurately represent changes to the system without having to actually endure the time and expense demanded by such a change.

5 Therefore, by slightly altering the basic models' parameters during the initial run, the simulation was able to accurately reflect different changes applied to the system. Using this technique for three additional and different scenarios, the model was modified to include an extra dentist, an extra chair, and both an extra dentist and chair. The results of those runs were then compared to the original scenario run to detect and analyze changes in chair idle time, server idle time, and patient waiting time. - Our simulation study of Dr. Green's pediatric dental practice indicated substantial chair idle time for dentists and hygienists, as well as considerable dentist idle time and waiting room occupancy. it IV6f.J'd L1ItLy l( t'c4. 'r k.- In comparison, the results suggested that hygienist idle time afid patient waiting time were the more efficient characteristics of Dr. Green's current scheduling procedure. However, as with any health care system, including a pediatric dental practice, continual evaluation and modification is required. Our team felt that with greater time and resourc/a more intense study could be conducted to include various patient volumes, increased duties for the additional pediatric dentist, and an appointment call-in procedure. The interpretation of the results obtained from the altered scenarios and their comparison to the original simulation led us to our final recommendation of inviting an additional pediatric dentist to join Dr. Green's practice. Involving another pediatric dentist in the scheduling system decreases dentist and hygienist chair idle time and dentist idle time by a factor of 2 while reducing the waiting room occupancy and patient waiting time by at least a factor of 5. Overall, the addition of an extra dentist to the practice results in a more efficient dental office, with better patient quality and increased profitability. FA

6 II. BACKGROUND AND PROBLEM DESCRIPTION "Pediatric dentistry is an age-defined specially that provides primary and comprehensive preventive and therapeutic oral health care for infants and children through adolescence, including those with special health care needs." (American Dental Association) Pediatric dentists are able to provide care to a specific age group of patients with no limitation to the types of treatments they may administer. In addition, they have the training and experience to evaluate and treat patients that are medically compromised. This includes patients with severe diseases such as hemophilia, leukemia and congenital syndromes. In fact, many pediatric dentistry (pedo) practices treat more patients in one day than general and specialty dental practices treat in a week (PMM). Thus, with such a high volume of patients needing a broader variety of treatments and procedures, patient scheduling in a pediatric dental practice involves greater difficulty and complexity as compared to scheduling for other dental practices. The pediatric dental practice of Dr. Roy Green of Fort Myers, Florida faces similar scheduling challenges on a daily basis. Presently, the practice attempts to overcome these difficulties by implementing a block scheduling system. By definition, block scheduling (blocking) consists of scheduling like treatments together as closely as possible. The scheduling coordinator must visualize each day of the workweek in horizontal blocks (or bands) of time units. This system allows the dentists to remain busy, while preventing them from alternating between simple and complex procedures (PMM). Dr. Green and his colleagues believe that block scheduling is the most effective method for patient scheduling because it is a dynamic system that can accommodate varying patient volume. In fact, block scheduling allows them to "provide dental treatment in as relaxing an environment as possible and in a timely manner (Green)." Overall, blocking that adjusts to patient flow, preferred work pace, production goals and availability of resources and locations becomes most beneficial for pediatric dental practices in terms of production and profitability. 3

7 Various factors influence the existing appointment scheduling system in Dr. Green's office. They include the following: Dr. Green's practice treats 6-8 patients per day. Approximately 12 new patient examinations, 6 regular check-ups and 34 restorative dentistry doctor hours are performed each month. Procedures performed by the resources of the office are organized in the following four categories: 1) Regular Check-Up (RC): Includes polishing, x-rays and sealants 2) Light Operative, Regular Restorative (PM): Includes fillings, crowns, extractions, nerve treatments and space maintainers 3) Heavy Operative, Oral Sedation (OP): Includes extraction of infected teeth or extractions for orthodontic treatment 4) Intra-Muscular (IM): Includes extractions due to severe infection or emergency-related procedures Six chairs, three chairs for operative dentistry, two chairs for regular check-ups and one chair for new patient examinations, are able to be scheduled daily The office employs two pediatric dentists, one general dentist and an orthodontist (who only works in the office 5 times per month and is not considered in the model design). Two types of sedation are used in the practice: oral and intra-muscular. All of the dentists can perform the same procedures and treat patients with oral sedation. However, only the pediatric dentists are able to treat patients using intra-muscular sedation. 4

8 . All of the dental assistants (hygienists) have expanded duty certification. Their training allows them to take x-rays and impressions, polish children's teeth and administer sealants, fluoride treatments and cementation of space maintainers. The office is structured with a 5-hour morning shift and a 3-hour afternoon shift. The present doctor shift schedule is as follows: SHIFT Monday Tuesday Wednesday Thursday Friday AM 2 Dentists 2 Dentists 3 Dentists 2 Dentists 2 Dentists PM 2 Dentists 1 Dentist 2 Dentists 2 Dentists 1 Dentist With these factors taken into consideration, we evaluated the efficiency of the block scheduling system used in Dr. Green's pedo practice. This evaluation involved comparing Dr. Green's current scheduling system to three simulated office scenarios in (1) an additional pediatric dentist, (2) an additional dental chair and (3) an additional pediatric dentist and dental chair. The comparison and analysis among these four scenarios was centered on chair idle time, server idle time and patient waiting time. From a businessman's and health care provider's perspective, the reasoning for the comparison is twofold. First, resource (server) and chair idle time are approximate measures of the practice's production and profitability and thus indicative of generated revenue. The financial prosperity and success of Dr. Green's practice are dependent on how many patients are treated on a daily basis. If there is considerable resource and chair idle time, potential patients are not receiving treatment, resulting in potential revenue not being captured. Furthermore, when idle time persists, those patients requiring dental treatment are not being seen in the most efficient manner, thereby compromising patient care, which can lead to patient dissatisfaction and the consequential loss of such patients. Second, the evaluation of patient waiting time provides information concerning overall efficiency of the doctor-patient flow throughout the office. In fact, in a worse case scenario, excessive patient waiting time can prevent patients from continuing their treatment and influence potential patients to either choose against treatment or 5

9 look elsewhere for dental services. Overall, high levels of chair and server idle time and patient waiting time indicate a possible misallocation of resources and locations in Dr. Green's pediatric dentistry practice. 6

10 III. ANALYSIS OF THE SITUATION Our team began the study of the scheduling problem in Dr. Green's pedo practice by investigating previous research done on scheduling issues. This included locating and analyzing several articles involving various kinds of scheduling models and deciphering what key elements had been utilized in previous research that could be applied to our study and the building of the pediatric dental scheduling model. We discovered that though several studies had been conducted on different scheduling techniques and applied to various industries, very few focused on medical or dental offices. From our limited selection, one article (Kiassen and Rohleder 1995) seemed particularly applicable to our study because it involved determining an optimal scheduling technique for a typical family outpatient medical clinic. After analyzing this article, we discovered some striking differences between the scheduling techniques tested by Klassen and Rohieder and the methods currently used by Dr. Green's pediatric dental practice. The most notable difference was the lack of a block scheduling technique in the different methods analyzed. The pedo practice in question currently uses a form of block scheduling suggested by the Pediatric Management and Marketing News (PMM) as the optimal technique for pediatric dental offices. In block scheduling, horizontal segments of time are scheduled with an emphasis on maintaining similar treatments across blocks scheduled at the same time. Of the various techniques studied in the article, all were vertically based and independent of appointment or procedure type. Although the article's model and ours are distinctly different, we found several similarities that we determined to be useful. In both models, patients were scheduled without knowledge of what types of procedures would be booked for future patients. Moreover, both the model proposed by the Kiassen and Rohieder article and our own had a one-patient, one-server methodology and dealt strongly with the question of service time variation. In addition, Kiassen and Rohieder's model sought to minimize patient waiting time and server idle time, two criteria also applied to our model. 7

11 Because such similarities existed between our model and the model outlined in the article, we paid special attention to the way in which Kiassen and Rohieder chose to study the, various modeling techniques. Klassen and Rohieder used a simulation analysis procedure to study their appointment-scheduling problem. Simulation modeling involves using numerical methods to study problems that have complex systems and uncertainty. Simulations normally consist of variables representing particular features of the actual system, and instructions that give rules as to how the variables change over time given certain circumstances. Variables are usually either deterministic, that is they can be calculated from other set values, or stochastic, meaning that there is a set of possible outcomes and a set of probabilities associated with each outcome. By assuming some initial situation in the simulation, the rules can be applied to the system, consequently adjusting the values of the variables and allowing statistics to be taken that describe the system over a period of time. After conducting more research, we found that Bailey's study conducted in the 195s provided further evidence to support the effectiveness of simulation models in studying appointmentscheduling problems (Bailey). Bailey discovered that because most servers only see approximately 2-3 clients (in our case, patients) in a session, say a morning or afternoon, steady state in the simulation is never reached. This discovery indicates that the stochastic variables never fall into a predictable repeating pattern and simulation is the only way to study the model effectively over time. Another advantage to using simulation in this case is that it allows virtual changes and key sensitivity analysis to be done to the model for testing purposes, without having to actually perform the changes in the office under real-life conditions. This saves not only money, but also time. Additionally, simulation is the most comprehensive method to test for the effects of certain changes, such as adding a new dentist or chair to the practice. Therefore, we concluded that performing simulation analysis on our own model would be the most efficient way to analyze the situation efficiently. Details of our model and the manner in which it was applied is discussed in the subsequent Technical Description. 8

12 IV. TECHNICAL DESCRIPTION OF THE MODEL After organizing data from Dr. Green's pedo practice and analyzing the current scheduling system, we formulated our model and the experimental environment in which it would be run. Because a block scheduling system was firmly established amongst the office staff in Dr. Green's practice, we did not attempt to modify his appointment-scheduling system, as this would have resulted in additional training and cost for the practice. Instead, we sought to maintain this same scheduling structure while analyzing three influential components, chair idle time, server idle time and patient waiting time. We also analyzed how the current simulation model would be affected by the addition of another dentist and/or chair to the practice. Our team began by establishing assumptions upon which our model would be based. The following assumptions were based on the data organized from the pediatric dental office as well as previous research: Each block contains one patient, one server, and one chair. Each day is independent of the next. Each day of the week's block schedule is predetermined 6-8 weeks in advance. The probability that a scheduled patient arrives for his/her appointment is.9 (or 9%). The additional dentist added for the purpose of the study, takes on a block schedule for each day consisting of OP and PM procedures in alternating half hour and one-hour intervals. Every staff member arrives on time and works for their entire scheduled shift. All break times are negligible, excluding a one hour scheduled lunch break. Patients calling in with life-threatening illnesses are referred to local emergency rooms and are not seen or scheduled. The first assumption, one client, one server, one chair, might be contradictory to the average dentist office experience in which an assistant performs some initial duties, such as greeting patients and collecting paperwork. However, in our model we allotted an initial 5-minute time 9

13 segment for these responsibilities to be taken care of by the receptionist. It is also important to note the one chair per server assumption. This is a characteristic of Dr. Green's practice in which every dentist is given an assigned chair for every day. This type of assignment does not occur for hygienists; however, in either case at no time is any one server responsible for more than one chair or servicing more than one patient. Therefore, once the patient leaves the waiting room and is seen to a chair, this assumption takes hold for the remainder of the patient's time at the office. The second assumption is the result of some logical thinking as well as research concerning simulation modeling. Dr. Green's office closes at approximately 5 p.m. every afternoon, and does not reopen until 8 a.m. the following morning (assuming it is a weekday). Therefore, it is only logical to assume that every day is independent of the next. For example, if the office were forced to stay open one evening until 6 p.m., this would not affect the patients arriving the next morning for their respective appointments. In other words, a delay in one day does not affect the start time for the following day. In this way, every day is independent of the next. Another assumption used to define our model concerns the way in which Dr. Green establishes the block schedule for each day of the week. Depending on the number of dentist in the office, the hours the staff is available, and the expected volume of patients, the block scheduling system is predetermined up to 6-8 weeks in advance, and differs for each day of the week. This means that even though every Monday in the month has the same block schedule, the schedule for Monday and Tuesday is not the same. Therefore, 6-8 weeks in advance, as patients call to schedule appointments, the schedule is established and patients are put into appropriate blocks. Though our model does not encompass this patient scheduling process, it is important to note that it exhibits a Poisson distribution. The next assumption concerning whether or not a scheduled patient arrives for his/her appointment comes from historical data and is also supported by research. According to Dr. Green, the number of patients who do not show up for their scheduled appointments is approximately 6-8 per day, or about 1% of the total number of patients seen in a day. From this data we concluded that the probability of a patient arriving for his/her appointment is set at.9 II,J

14 (9%), with a probability of.1 (1%) that the patient will fail to arrive or cancel an appointment. This is consistent with the research conducted by Kiassen and Rohieder (1996) that found that patient no-shows was often no more than twenty percent (2%) of the total number of patients scheduled per day The fifth assumption concerning the schedule used for the additional dentist was added to clarify the model. At Dr. Green's request, we modeled the additional dentist after Dentist 2's Monday schedule consisting of alternating half hour and one hour sessions of OP and PM procedures. This schedule is consistent with the procedures that a regular dentist is capable of and therefore seems like a reasonable model for testing the effects of adding the dentist to the practice. The last two assumptions were used to simplify the model. Assuming every staff member arrives promptly for work was reasonable considering the professional way in which Dr. Green conducts his practice and the expectations he has for his staff. This assumption does not mean that every staff member works five days a week from 8 a.m. and to 5 p.m. without exception. Rather, it simply means that the staff is expected to schedule work shifts so that they can arrive on time and work without interruptions throughout the shift. In addition, any small breaks that occur during work shifts, such as using the restroom, are negligible and are accounted for during server idle time. The final assumption concerning emergency patients was necessary because Dr. Green does not have a consistent policy regarding how he handles these patients. Though the practice will see some patients without an appointment, Dr. Green felt that it happened so infrequently that it was unnecessary to include this aspect of scheduling in our simulation, as its effects would be negligible on our results. The variability within procedure time and among different servers must also be discussed in order to understand the model to the fullest extent. As explained in the background section of this paper, four main categories, RC, OP. PM, and IM, are used to distinguish the various procedures performed in the office. However, these categories are very broad and each one actually encompasses several different but related procedures. Therefore, one cannot assume that every procedure in the same category takes an equal amount of time to accomplish. For example, most procedures that involve having a cavity filled are in the OP category. However, it 11

15 is only logical to assume that filling two cavities would take longer than filling just one. To account for this procedure variability with in categories, we have utilized Dr. Green's historical data and applied the following to our model: For procedures in the RC category, 8% take the allotted thirty minutes or less and 2% take approximately five additional minutes. For procedures in the OP and PM categories, approximately 75% take one hour and 25% take 3 minutes. For procedures in the IM category, almost all take the allotted 3 hours to complete. Just as variability exists among procedures, there is also variability between servers. One factor influencing this idle time is server experience. A dentist who has been practicing for several years might perform a procedure faster than a new dentist. In addition, the fatigue and endurance of servers may also result in variability. A third factor influencing variability among servers has to do with the patient being served. For example, a server might take longer to perform a procedure on a small child than on a young adult. Moreover, this same procedure might take even longer if performed on a mentally handicapped child. Therefore, to account for the variability that exist among servers we adjusted our model by adding a standard deviation to all procedures performed by both dentists and hygienists. For hygienists, this deviation was +I 5 minutes, as the procedures performed by hygienists are fairly routine. However, for dentists, the deviation jumps to +1 1 minutes because the procedures are far more complicated and experience plays a much larger part. Once all the components of our model were determined, we selected a simulation software package that would meet the needs of our simulation flow. It was determined that the ProModel package would be the appropriate choice, as it seemed to be user-friendly and was a very efficient package to analyze our inputs. ProModel is a simulation-based software package that uses the familiar Windows environment to aid in the building of a simulation model. The application has certain requirements that must be included in the model, such as locations, entities, resources and path networks. In addition, high-level programming may be added to 12

16 increase ProModel's ability to simulate real-world environments. With the Autobuild feature, building our dental office model was easily done once parameters were defined. A final feature of ProModel is its ability to gather data after a simulation run, reporting on statistics including resource/server (dentist/hygienist) utilization, server idle time, entity (patient) waiting time and location (chair) utilization. The automatic collection of such statistics would help us in analyzing the data more efficiently and in avoiding human error in calculating such information. The dental office environment is a basic queue, where patients arrive, check in with the receptionist and move onto their respective "processing locations," or chairs, where value is added to each patient (i.e. patient receive dental services). Once services are rendered, the patient simply exits the queue, without checking out with the receptionist. The following flowchart gives a visual representation of the flow for the dental office: Essentially, patients enter the dental office queue at the waiting room. Patients are retrieved by a tech or hygienist in the waiting room and placed in a pre-determined chair for dental processing. Once value is added to patients, they simply exit the dental office. Resources, including dentists and hygienists, are put in a virtual "holding area" until they are called on to perform dental services or to pick up patients from the waiting room. Therefore, the flow from the holding area 13

17 can go either directly to the dental chairs, as in the dentists' case, or resources can go to the waiting room and then onto the chairs, which is the case for hygienists and the tech. Resources will return to the holding area if they are idle. With the chief simulation model established, we then developed a technique to alter the initial model to distinguish the block scheduling routine for each day of the working week. This involved changing such things as the number of dentists and hygienists available and the number and type of procedures planned for a particular day's schedule. It also involved performing sensitivity analysis by altering the model to include the additional dentist and chair for the purpose of studying how these changes might alter our simulation results. Once all the models were complete, we then ran the simulation software five times for each model and each day. This allowed us to collect a month's worth of useful data for the purpose of analysis. An analysis and discussion of the results are included in the proceeding section of the report, Analysis and Managerial Interpretation. 14

18 V. ANALYSIS AND MANAGERIAL INTERPRETATION After simulating and comparing five weeks of the original scheduling system in Dr. Green's pedo practice and three other office scenarios, we analyzed and interpreted the averaged data in order to make meaningful conclusions to the owners and management of the dental office and their patients. Original Scheduling System Chair Idle Time With regards to the existing scheduling scenario in Dr. Green's pedo practice, ProModel gathered the following percent (%) idle times of dentist and hygienist chairs in Table 1. Di D2 D3 Hi H2 H3 H4 Monday n/a Tuesday n/a Wednesday n/a Thursday n/a Friday n/a Table I: Average Chair Idle Time, % Overall, the dental office presently experiences considerable chair idle time each week. However, in a day-to-day comparison, we observe that the lowest percent chair idle time for dentists and hygienists occurs on Wednesdays. This observation seems reasonable and thus was expected on this day because the office experiences its highest patient volume requiring the more complex procedures, OP, PM and JIM on Wednesdays. In. addition, on the average Wednesday, hygienists performed more complex procedures, such as x-rays and sealants, which require one-hour treatment blocks. With more patients in the system requiring more complex procedures, the dental chairs are occupied in a more consistent manner as demonstrated by the low percentage chair idle time. One would expect the highest percent chair idle time for dentists and hygienists to exhibit similar trends, with the highest results falling on the days with the fewest patients and the simplest treatments. However, our analysis indicates otherwise. For dentists, the highest percent chair idle time occurs on Tuesdays. This is because only one dentist is scheduled 15

19 in the afternoon, while two are scheduled for the longer, morning shift. Therefore, during the afternoon shift, the second dentist's chair remains idle, seeing no patients in this chair. When this idle time is averaged in for the entire day, total chair idle time is increased significantly. 5c1%., lj r;1: i-i- 4 _' fioj- f-oti C6A5çAOY\ 4fl For hygienists, the highest chair idle time occurs on Fridays. This is best explained by the decreased demand on Fridays for the RC procedures performed by hygienists. With less demand for these procedures, the hygienist chairs experience higher idle time. Dr. Green has observed this in his current practice, as the office frequently closes on Fridays when the demand drops and opportunity costs become greater than potential profitability. \Q * w\ tcit' 5' By the dentist-hygienist comparison, we observe an uneven distribution of chair't'dle time among the dentists, but not with hygienists. The explanation for this disproportional ---'----- distribution becomes two- First, each of the hygienists is assigned similar daily schedules while each dentist's schedule varies considerably. The dentists' schedules involve a variety of predetermined, procedure blocks while hygienists' schedules are randomly assigned patients needing regular check-ups. OP, IM and PM treatments are executed at each dentist chair while only regular check-up (RC) procedures are executed at every hygienist chair. In other words, more of a variety of dental procedures are executed at the dentist chairs. Second, this uneven distribution of labor is also a result of patient cancellations. Each day 6-8 patients cancel or do not show up for their dental appointments. These cancellations may be distributed among all the resources of the office or concentrated within one resource, and thus, the cancellations randomly affected the resource schedules. Resource Idle Time The ProModel calculations of percent idle time for the office resources are shown in Table 2 on the next page.

20 Hi H2 H3 H4 H5 H6 Monday Tuesday Wednesday Thursday Friday Table 2: Average Server Idle Time, % The percentage dentist idle time is not observed in Table 2 due to the assumptions we 4 applied to our ProModel simulation. In our model, the dentists are assigned daily to a specific dental chair. This deliberate assignment indicates that Dentist 1 only performs procedures at dental chair 1 and so on for the other dentists and dental chairs. This assignment also means dental procedures are not simultaneously performed at multiple dental chairs. Thus, the operations executed by dentists and the operations taking place at dental chairs become equated. Subsequently, analysis of percent dentist idle time is incorporated in the chair idle time analysis discussed previously. This assumption does not apply to hygienists, and therefore, their percentage idle time must be discussed separately from the chair idle time. Overall, Table 2 indicates the hygienist idle time is relatively low in the current block scheduling system. However, Wednesdays appear to average 25% hygienist idle time in comparison to the other days of the week with 1.5% idle time. This difference is caused by the fact that more dentists are scheduled during the Wednesday morning shift than any other day of the week. This results in fewer chairs allotted for hygienist procedures; however, the total number of hygienists scheduled remains the same. Therefore, as the ratio of hygienists to hygienist chairs increases, the hygienist idle time also increases. Patient Waiting Time Table 3 on the next page illustrates the daily percent occupation of the waiting room involved in Dr. Green's present scheduling policy. This characteristic of the block scheduling system helps define patient wait time by indicating what percentage of the workday has at least one patient occupying the waiting room. For example, on the average Monday, there is at least one person occupying the waiting room 91.24% of the workday. 17

21 % Occupied Waiting Room Monday Tuesday Wednesday Thursday Friday 93.1 Table 3: Average Partial Occupation of Waiting Room, % In general, Table 3 indicates a relatively uniform daily occupancy of Dr. Green's waiting room. This observation was expected because not all appointments for dentists and' hygienists begin and end at the same time, leaving patients waiting for their scheduled appointments. Each day of the workweek averages approximately 92% partial occupancy of the waiting room except for Wednesday that averages 99%. Wednesday becomes the exception to the 92% because more complex procedures are scheduled and performed by dentists on Wednesday than any other day and this complexity lends to more variability. More involved, complex procedures often consist of intricate, detail-oriented steps that regularly result in longer processing times. Subsequently, the occupancy of the waiting room increases. Table 4, below, demonstrates the average percent of the patients' time in the system spent waiting for a hygienist (server). This table does not indicate the wait time for dentists ev (.- because the block scheduling technique left this resulting data negligible. % Wait for Hygienist Monday 13.8 Tuesday 13.5 Wednesday Thursday Friday Table 4: Average Patient Waiting Time for Hygienist, % Even though the data organized in Table 4 lacks the desired level of accuracy and precision, we felt that it does provide important information concerning patient waiting time in Dr. Green's dental office. The first trend that is noteworthy is that every day of 18

22 the workweek, with the exception of Wednesday, has approximately a 13% patient wait time. This indicates that patients experience about a 13% wait time regardless of the procedure or day of the week scheduled, with the exception of Wednesday. For example, a patient scheduled for a one-hour RC appointment with hygienists on Tuesday would expect to be waiting approximately 8 minutes. As discussed in the previous paragraph, Wednesdays are not consistent with the other days of the week. This is because Wednesdays have the highest number of dentists scheduled and the fewest number of operating hygienists. As discussed at the beginning of the Patient Waiting Time section, dentists' procedures are blocked, resulting in almost no patient wait time. This data supports the PMM article that suggests that block scheduling is the more efficient scheduling technique for pedo practices in terms of patient wait time. Comparison among Altered Scenarios Seeking improvements, three additional varied office scenarios including (1) an additional pediatric dentist (2) an additional hygienist chair and (3) an additional pediatric dentist and hygienist chair were compared to the original scenario. The comparison of these four scenarios was measured in terms of chair idle time, server idle time and patient waiting time. Chair Idle Time With regards to percent idle time of dentist and hygienist chairs, the current scheduling system was compared with the three simulated scenarios. The average data concerning dentists and hygienists is organized in Figure 1 and 2, respectively, which are found on the following pages. 19

23 Qj I 6 Dentist Comparison Among Simulated Scenarios. < 5 4Q -- -I- El Monday lltuesday II I - OWednesday Thursday Friday C3 1 Original Add Dentist (1) Add Chair (2) Add Dentist and Chair (3) Simulated Scenarios Figure 1: Comparison: Dentist Chair Idle Time among Various Scenarios, % The scenario involving an additional chair decreased the percent dentist chair idle time on Tuesday and Friday, which previously were the days with the largest chair idle time. However, Monday and Thursday remained similar to the current scenario while Wednesday increased by a factor of two. Involving another chair in Dr. Green's office did not have as significant effect on the percent dentist chair idle time. The additional chair simulation did not affect dentists as much as hygienists because only those procedures performed by hygienists were scheduled at the additional chair. i. The scenarios of an additional pediatric dentist and an additional pediatric dentist and hygienist chair demonstrated the most profound improvement on Dr. Green's office. Concerning percent dentist chair idle time, these two situations provided the exact same data. These similarities resulted due to the fact that dentists were daily assigned to a specific chair to treat all of their patients for the day, and thus, ProModel equated dentists and dentist chairs. Nonetheless, when another dentist was involved in the scheduling system, whether a chair was or was not, the percent dentist chair idle time drastically 2

24 Od( t ) + ks se ev'() decreased because more procedures were executed at the dentist chairs. Obviously more Plf <- S(L dentists scheduled indicated more dental procedures, and the increased dental procedures 4't - resulted in less chair idle time for dentists. 'L JP 14t ILVO k vi56 'ii-ec e.. ;& G- ire L'to Lc Moreover, these two simulations redistributed the patients among the dentists in a more 4, proportional manner. This feature of the dental office is extremely important because it improves overall patient care, patient satisfaction and office morale. When one dentist treats considerably more patients than the others, the patient waiting time becomes unevenly distributed. The patients of the dentist with a heavier patient load wait longer for their treatments than the patients of the dentist performing fewer procedures. Disproportional patient waiting time lowers the quality and efficiency of patient care. In general, the success of dental practices', including Dr. Green's practice, is based on the patient care they provide. Thus, when patient care is compromised, the prosperity of the practice is jeopardized. Furthermore, the unbalanced division of labor among the dentists also affects office morale. The excess labor can cause a dentist to become over stressed, over worked and resentful towards his/her colleagues. Such resentment may infiltrate through the office, possibly affecting quality of care. Consequently, the simulations of adding a dentist and adding a dentist and chair not only decrease chair idle time, but also the efficiency, quality and prosperity of the overall practice. OA E! meck (WS IW7 21

25 Hygienist Comparison Among Simulated Scenarios 6 5 M Monday 2 Tuesday j3. Original 2 2 j [fj Add Dentist (1) Add Chair (2) Add Dentist and Chair (3) Simulated Scenarios Figure 2: Comparison: Hygienist Chair Idle Time among Various Scenarios, % In comparison to the current scenario, the simulations involving another hygienist chair and an additional dentist with another hygienist chair negatively impact the pedo practice environment, creating a higher percent hygienist chair idle time whereas an additional dentist decreases the chair idle time. Involving an additional chair, whether an additional pediatric dentist is involved or not, automatically heightens hygienist chair idle time. The extra chair in the system becomes an additional hygienist chair because the number of hygienist in the system outnumbers the number or working dentists. Nonetheless, the demand for procedures executed by hygienists remains constant, thereby increasing chair idle time. In addition, these two simulations maintained the balanced distribution of labor among hygienists. The significance of this dental office feature was discussed previously with regards to dentist chair idle time. An extra pediatric dentist lowers the percent hygienist chair idle time on Mondays, Tuesdays, Thursdays and Fridays while maintaining the current chair idle time on Wednesday. These improvements to the current scenario 22

26 stemmed from the fact that the new dentist is assigned a chair previously known as a hygienist chair. For example, on the average Thursday of the current simulation, two chairs are associated with dentists and four with hygienists. When another dentist is involved in the office scheduling system, three chairs are assigned to dentists and three for hygienists. Thus, the patient demand for hygienists that was previously arranged : among 4 chairs becomes be arranged among 3 chairs, thereby lowering their chair idle time. Server Idle Time With regards to percent idle time of dentists and hygienists, the current scheduling system was compared with the three simulated scenarios. A visual representation of the average data concerning the dentists and hygienists was organized in Figure 3 and 4 respectively. Dentist Idle Time Among Simulated Scenarios 6 51 E Monday 4 Tuesday DWednesday 3 DThursday Friday I Original Add Dentist (1) Add Chair (2) Add Dentist and Chair (3) Simulated Scenarios Figure 3: Comparison: Dentist Idle Time among Various I I Scenarios, % Even though ProModel equates the results of scenarios involving an additional dentist and dentist chair, dentist idle time and dentist chair idle time vary slightly. The minute 23 I

27 variations result because dentists must wait for the tech's move logic, the time during which the tech picks up patients from the waiting and proceeds to drop them off at a dentist's chair. ProModel does not incorporate this move logic consideration in the idle time calculations, and therefore, differences can be seen. Involving an additional hygienist chair into the system causes a negative effect of increasing dentist idle time on Wednesdays while decreasing dentist idle time on Thursdays and Tuesdays. On Mondays and Fridays, the results remain consistent compared to the original scenario. With the exception of Wednesdays, all differences are minute due to the move logic discussed in the previous paragraph. This exception results from the fact that the RC procedures previously executed by dentists are now performed at the additional hygienist chair. Fewer procedures being performed by a dentist indicates heightened dentist idle time. Scenarios (1) and (3) demonstrate similar results, as explained in the discussion concerning percent dentist chair idle time. Once again, if a dentist is added, regardless of the involvement of a chair, dental procedures increase and idle time decreases. As before, Wednesdays are the exception. In this case it is a result of the fact that Wednesdays have the most scheduled dentists. Because of this, there is no supplementary need, or demand, for an additional dentist and this is clearly evident in the resulting data. 24

28 Hygienist Idle Time Among Simulated Scenarios 6 5 C, E 4 I- C, D 3 U, a> 2 E3 Monday Tuesday o Wednesday o Thursday Friday 1 Original Add Dentist (1) Add Chair (2) Add Dentist and Chair (3) Simulated Scenarios Figure 4: Comparison: Hygienist Idle Time among Various Scenarios, % The hygienist idle time resulting from scenario (2) involving an additional hygienist chair remains relatively consistent with the current scenario. More specifically, on Tuesdays and Wednesdays, hygienist idle time decreases slightly while on Mondays and Thursdays, the idle time increases slightly. Data remains the same on Fridays. The additional chair does not have a significant effect because it simply rearranges the hygienists' duties. For example, a hygienist that was assisting a dentist in the current scenario will perform RC procedures at a hygienist chair in scenario (2). When an additional pediatric dentist becomes involved in the scheduling system, whether another hygienist chair is included, the hygienist idle time drastically increases. The additional dentist is assigned a previously allocated hygienist chair. Thus, just as the extra dentist lowers percent hygienist chair idle time, it follows that the dentist also heightens hygienist idle time. The hygienist previously performing RC procedures at a chair begins to assist the dentists and other hygienists when needed. 25

29 Patient Waiting Time In order to evaluate the patient waiting time of Dr. Green's pedo practice, we compared the calculated percent waiting room occupancy and percent patient waiting time for a resource of the current scenario to that of the three simulated scenarios. 1 Percent Occupancy Among Simulated Scenarios 8 > Monday C Q- 2 6 Tuesday o Wednesday 4 O Thursday Friday Original Add Dentist (1) Add Chair (2) Add Dentist and Chair (3) Simulated Scenarios Figure 5: Comparison: Percent Waiting Room Occupancy among Various Scenarios, % The comparison between the original scheduling-system to scenario (2) indicates that percent occupancy of the waiting room remains consistent for every day of the workweek except Wednesdays. On Wednesdays, the waiting room occupancy decreases by a factor of 5. Once again, the involvement of another hygienist chair alleviates the dentists' patient load with regards to RC procedures. Subsequently, the patients scheduled to see dentists do not become as backed up. Furthermore, scenario (2) also alleviates the patient load of the individual hygienists. The overall effect is a significantly lowered waiting room occupancy. Scenarios (1) and (3) demonstrate that the waiting room occupancy decreases by a factor of approximately 4.5 for all days of the week. This improvement is due to the fact that these scenarios distribute the patient volume more evenly among the working dentists and 26

30 hygienists. As mentioned before, balanced division of labor results in the improved quality of patient care. For all three simulated scenarios, the percent patient waiting time for a resource decreases drastically in comparison to the current scenario. In fact, the patient waiting time becomes negligible. Although the detailed data lacks accuracy and precision, we still feel a profound improvement resulted. 27

31 VI. CONCLUSIONS AND CRITIQUES While functioning within time and resource constraints, our team has diligently researched, designed, and simulated an accurate representation of Dr. Green's pediatric dental practice scheduling system. The original simulation reveals considerable chair idle time, dentist idle time, and waiting room occupancy. In addition, the results suggest that hygienist idle time and patient waiting time are the most efficient characteristics of the current scheduling system. After this evaluation of the original appointment scheduling system, we simulated three altered scenarios in order to improve the current system with regards to chair idle time, server idle time, and patient waiting time. Our insightful analysis and interpretation of the results obtained have led us to our final recommendation of inviting an additional pediatric dentist to join Dr. Green's practice. Involving another pediatric dentist in the scheduling system decreases the dentist and hygienist chair idle time and dentist idle time by at least a factor of 2. It also reduces the waiting room occupancy and patient waiting time by at least a factor of 5. Overall, these significant improvements take great strides toward a more efficient dental office, with better patient quality and increased profitability. However, we do feel it is notable that the hygienist idle time drastically increases in our recommended office scenario. Due to their more significant contribution to the practice's profitability, we presume the dentists' time is weighed more heavily than that of the hygienists. This exception to the server idle time does not lessen the overall effectiveness of the simulation. We concede that often a give and take approach must be realized in the greater improvement of a system, in this case, the scheduling procedures of a dental practice. For example, Dr. Green may want to consider scheduling another pediatric dentist on every day of the week except Wednesdays. All of the altered scenarios, including Scenario (1), result in increased dentist idle and patient wait times. The scheduling system currently applied to Wednesdays is rather efficient, and thus, does not require the same modifications. Nonetheless, we are confident that the addition of a new pediatric dentist will reduce the general idle time of the system, thereby enriching the quality of patient care and furthering the practice's profitability. 28

32 Our team feels our final recommendations provide crucial and valuable information to Dr. Green to improve the overall efficiency of his practice in terms of the allocation of resources and locations. Nevertheless, we believe further simulation and analysis would provide supplementary information and additional value to optimize the pediatric dental practice. In fact, we feel the issues of patient volume, procedures executed by the additional pediatric dentist and appointment call-in procedures are most worthy of further analysis. Fort Myers, Florida, the location of Dr. Green's practice, has experienced vast growth over the last ten years and this growth is projected to continue. The expansion of the local community college and entry of new companies into the market indicates an increase of patient volume for all health care provides in the area. Subsequently, the efficiency of Dr. Green's pediatric dental practice has become increasingly burdened by patient volume increases. Further 'simulations involving an annual 5% increase in patient load would enable Dr. Green, with each patient volume modification, to determine the maximum patient load his practice would be able to handle with various suggested resource and location combinations. In addition, we assumed that the additional pediatric dentist in the scheduling system would only perform OP and PM procedures. We feel this assumption was more than valid because over 9% of the procedures performed by the pediatric dentists involve OP and PM. Nevertheless, our simulation equated the duties of a pediatric dentist and general dentist. Since the costs of these two resources vary, and thus, the affect the practice's total income, we recommend further simulation. With a daily block schedule pre-designed for the additional pediatric dentist including RC, OP, PM and IM procedures, the simulation of this extra resource would provide more detailed information concerning the economic and patient care efficiency of the office. The duties of the pediatric dentists and general dentist would become differentiated, thereby providing a more realistic interpretation of chair and resource idle times and patient waiting times. Finally, our team believes that the inclusion of the appointment call-in procedure within the simulation model would provide a more sophisticated analysis with more accurate results. 29

33 Medical systems involve a human factor that is not as pronounced in industrial systems. In a dental practice, the human resources, dentists and hygienists, perform procedures on human patients, and thus, human variability plays an influential role in the overall dentist-patient flow of the office. The modified simulation would incorporate the office scheduler receiving the appointment calls in a Poisson distribution. Thus, patient demand would be more accurately represented as compared to our sole reliance on historical data for this study. In addition, the simulation of the reception area would also involve the office's procedures concerning the scheduling of emergencies and rescheduling of cancellations. Furthermore, future study could involve the handling of emergencies and cancellations that greatly affect the efficiency of the dental practice. In general, these modifications would include more variability in the simulation model, thereby heightening the applicability of the resulting data and analysis.

34 APPENDIX A: Summary of Practice Management and Marketing News Article APPENDIX B: Summary of Journal of Operations Management Article APPENDIX C: Table C.1: Chair Idle Time for Dentists and Hygienists for Simulated Scenarios Table C.2: Average Chair Idle Time for Dentists and Hygienists for Simulated Scenarios Figure C.!: Daily Comparison: Average Dentist Chair Idle Time for Simulated Scenarios Figure C.2: Daily Comparison: Average Hygienist Chair Idle Time for Simulated Scenarios APPENDIX D: Table D.1: Dentist and Hygienist Idle Time for Simulated Scenarios Table D.2: Average Dentist and Hygienist Idle Time for Simulated Scenarios Figure D.1: Daily Comparison: Average Dentist Idle Time for Simulated Scenarios Figure D.2: Daily Comparison: Average Hygienist Idle Time for Simulated Scenarios APPENDIX E: Table E.1: Waiting Room Expectancy for Simulated Scenarios Figure E.2: Daily Comparison: Average Waiting Room Expectancy for Simulated Scenarios APPENDIX F: ProModel Output: Original Simulation ProModel Output: Simulation with Additional Dentist ProModel Output: Simulation with Additional Chair ProModel Output: Simulation with Additional Dentist and Chair

35 APPENDIX A: Summary of Article in Practice Management and Marketing News in Pediatric Dentistry (Vol. 9, No. 4, Aug. 2 PMM) Scheduling the Pediatric Dental Practice With the exception of orthodontic practices, the most pronounced difference between pedo and other dental practices is patient volume. Depending on number of staff, available chairs and dentist's preferred work pace, some profitable dental offices treat 3-35 patents daily while others see 9-1. Regardless of these factors, block scheduling can be effective. By definition, block scheduling is scheduling like treatments together as much as possible. It is a dynamic process accommodating the flow of patient demand. While the placement appointment types (or blocks) remain fairly constant, the amount of time dedicated to each type may vary occasionally. Concepts of Block Scheduling Block scheduling means the scheduler must visualize the day in blocks of horizontal time units. Blocking allows the dentist to remain busy, while not jumping from a simple to complex procedure. Other details of block scheduling include: Children under five years should be scheduled in the morning while older children should be scheduled in the afternoon. Pre-determine alternate days of the week for different blocks in order to offer a choice to the patient. With regards to procedure times, use 1-minute units. Only scheduling coordinator(s) should make appointments. Only offer a parent or patient the choice of two appointment times.

36 Conclusions The mindset and commitment of the dentists, hygienists and office staff are most important. If you believe block scheduling will work in your office, it will. In addition, the staff must develop the verbal skills necessary to convince the parents or patients that it is to their advantage to come at certain times on certain days. Overall, any pediatric dental practice can benefit from block scheduling adjusted to meet their particular patient flow, work pace, production goal and available staff and chairs.

37 APPENDIX B: Summary of Journal of Operations Management Article Klassen, Kenneth J. and Rohleder, Thomas R., "Scheduling outpatient appointments in adynamic environment." 14(1996) The primary issue that Klassen and Rohleder address in this paper is how to schedule medical clients as they call for appointments, without knowing what other clients might call in the future. In researching this topic, the authors main goals were to compare various kinds of scheduling rules as determined by previous studies for the purpose of determining which rule minimizes both patient wait time and server idle time. Using a simulation model, Klassen and Rohleder determined the specific decision variable: the scheduling rule in affect. Two environmental factors were also important: expected mean of the clients' service time and the expected percentage of clients with low service time standard deviation to those with high. Klassen and Rohleder used a simulation model to reveal which scheduling rules are best for a clinics' specific needs in order to minimize patient wait time and decrease server idle time. The authors begin by discussing previous research on this topic for the purpose of presenting the various scheduling rules and other principles utilized in their simulation. First, Klassen and Rohleder justify the use of simulation models in the study of scheduling by sighting Bailey's research (1952, 19554) that found that because a steady state is never reached for a given server in a single appointment session. The various scheduling rules that the authors use in their simulation are from Ho's and Lau's research done for the case where all clients are homogeneous in regards to service time. The authors also use Braham and Worthington's (1991) conclusion that most clients arrive on or before their scheduled appointment time. The authors then go on to discuss the research methodology and experimental environment used to simulate the, "typical family outpatient clinic." The authors found that by analyzing a patient's medical history, the service requested, and the experience of the server, receptionists were very competent at determining the approximate time to allow for each client. In addition, each server typically had their own clientele and no-shows usually only amount to 5% of all appointments. Kiassen and Rohieder established their own experimental environment with the following assumptions One client, one server per visit

38 Steady state not reached Each session is independent Serious patients, those with life threatening conditions, are not served The authors also used their research to simplify the model by allowing some values to be fixed. This includes the following:. Each appointment session last 3.5 hours Every appointment slot is made for 1 mm (21 slots/session) The number of no-shows fixed at 5% The number of urgent calls per session is distributed Poisson with a mean equal to 2 and a uniform distribution over the 21 minute sessions Kiassen and Rohleder sought to minimize the following equation: WIT = p*e(cwt) + w*e(sit) where WIT represents the expected total cost of client and server idle time. CWT is the client waiting time and is found by the summation of each client's waiting time. It is then multiplied by the unit idle costs of the server (p). Likewise, SIT is the server idle time, the summation of the individual idle times, and is multiplied by the unit idle time of the client (w). A second equation is also useful to make sure that the appointment session does not run significantly over the scheduled time. This is done by the equation: ET = A(l) + CWT(l) + 5T(l) where ET is the session ending time with I representing the last patient per session. A is the start time(arrival), CWT the client wait time, and ST the service time. These equations together serve to almost "check and balance" each other in order to satisfy both client and server. Using a lognormal distribution to model service times, the authors then explored the different scheduling rules. Eight scheduling rules were used: FCFS-first come, first serve 2AtBeg- placing 2 patients in the first appointment slot, then one per slot remaining 4AtBeg-same idea with 4 clients in the first slot OFFSET- adjusts slots so that earlier patients arrive earlier than scheduled appointment time and later clients arrive later Alt] -schedule begins with a low variance patient in slot one and then alternates between high and low variance patients A1t5- begins with five low variance clients, then five high, five low... l-ivbeg-high variance clients scheduling in appointment slots l,21,2,2... (in that order) and low variance clients in 12,1,13,9...

39 LvBeg-opposite of the above with low,v clients in 1,21,2,2... and high v clients in 12,1,13,9... In regards to which scheduling rule to utilize, the following results were found: OFFSET- was the best ten out of 15 times; however, ET=272, over an hour longer than the scheduled appointment session, therefore OFFSET was eliminated If all clients are homogenous in regards to standard deviation of service time, FCFS should be utilized due to its simplicity When CWT=SIT, LvBeg is the best LvBeg also best with OFFSET eliminated The authors conclude by mentioning the fact that in today's world, most outpatient service centers are biased towards decreasing SET by compromising CWT. In addition, by using LvBeg, a 6.7% decrease in WIT over FCFS is achieved and if the standard deviation of the client service time is known, this jumps to a 1.8% decrease. These decreases are attributed to a lower client wait time, something worth noting for our own endeavors. Kiassen and Rohleder finish their paper by suggesting some possible further research ideas.

40 APPENDIX C: Table C.! Chair Idle Time for the Dentists and Hygienists for the Simulated Scenarios (%) Di D2 D3 D4 Hi H2 H3 H4 H5 Original Monday n/a n/a n/a Tuesday n/a n/a n/a Wednesday n/a n/a n/a Thursday n/a n/a n/a Friday n/a n/a n/a Add Dentist Monday n/a n/a n/a Tuesday n/a n/a n/a Wednesday n/a n/a n/a Thursday n/a n/a n/a Friday n/a n/a n/a Add Chair Monday n/a n/a Tuesday n/a n/a Wednesday n/a n/a Thursday n/a n/a Friday n/a n/a Add Dentist Monday n/a n/a and Chair Tuesday n/a n/a Wednesday n/a n/a Thursday n/a n/a Friday n/a n/a Table C.2 Average Chair Idle Time for Dentists and Hygienists for the Simulated Scenarios (%) Monday Tuesday wednesday. hursday Friday Original Dentist Hygienist Add Dentist Dentist Hygienist Add Chair Dentist Hygienist Add Dentist Dentist and Chair Hygienist '

41 Figure C.1 Daily Comparison: Average Dentist Chair Idle Time for Simulated Scenarios (%) 6 Daily Comparison of Dentist Chair Idle Time 5 a) E : 4 a) E3 Original UAdd Dentist DAdd Chair DAdd Dentist and Chair cs Weekday Figure C.2 Daily Comparison: Average Hygienist Chair Idle Time for Simulated Scenarios '%) 6 Daily Comparison of Hygienist Chair Idle Time ;5 E C a) ) 1 I c? 6bA O Original UAdd Dentist DAM Chair DAdd Dentist and Chair Weekday

42 APPENDIX D: Table D.1 Server Idle time for the Simulated Scenarios (%) Dl D2 D3 HI H2 H3 H4 H5 H6 Original Mon n/a Tues n/a Wed Thurs n/al Fri n/a Add Dentist Mon Tues Wed Thurs Fri Add Chair Mon n/a Tues n/a Wed Thurs n/al Fri n/a Add Dentist and Chair Mon Tues Wed Thurs Fri Table D.2 Average Server Idle time for Simulated Scenarios (%)l Monday Tuesday Wednesday Thursday Friday Original Dentist Hygienist Add Dentist Dentist Hygienist Add Chair Dentist Hygienist Add Dentist IDentist and Chair jhygienist

43 S S Figure D.1 Daily Comparison: Average Dentist Idle Time for the Simulated Scenarios (%) Daily Comparison of Dentist Idle Time 6 S a U) a 2 a, 1 o Original Add Dentist DAdd Chair DAdd Chair and Dentist Weekday Figure D.2 Daily Comparison. Average Hygienist Idle Time for the Simulated Scenarios (%) Daily Comparison of Hygienist Idle Time 6 i5 a) E 4 a) -a U) a) IM 3 2 1oJ] o Original Add Dentist DAdd Chair DAdd Chair and Dentist G S S Weekday

44 APPENDIX E: Table E.1 Average Waiting Room Occupancy for the Simulated Scenarios (%) Monday Tuesday Wednesday Thursday Friday Current ' E 93.1 Add Dentist Add Chair ' ' 93.1 Add Dentist E and Chair _ Figure E.l Daily Comparison: Average Waiting Room Occupancy for Simulated Scenarios (%) Daily Comparison of Waiting Room Occupancy 1-8 > U C. (3 (3 o 4 -S C C) '.3 i- 2 C) a- D Original UAdd Dentist [3 Add Chair 13 Add Dentist and Chair..,.<, Weekday