Demand, capacity, and access of the outpatient clinic: A framework for analysis and improvement

Abstract Rationale While theoretical frameworks for optimization of the outpatient processes are abundant, practical step‐by‐step analyses to give leads for improvement, to forecast capacity, and to support decision making are sparse. Aims and objectives This article demonstrates how to evaluate and optimize the triad of demand, (future) capacity, and access time of the outpatient clinic using a structured six‐step method. Methods All individual logistical patient data of an orthopaedic outpatient clinic of one complete year were analysed using a 6‐step method to evaluate demand, supply, and access time. Trends in the data were retrospectively analysed and evaluated for potential improvements. A model for decision making was tested. Both the analysis of the method and actual results were considered as main outcomes. Results More than 25 000 appointments were analysed. The 6‐step method showed to be sufficient to result in valuable insights and leads for improvement. While the overall match between demand and capacity was considered adequate, the variability in capacity was much higher than in demand, thereby leading to delays in access time. Holidays and subsequent weeks showed to be of great influence for demand, capacity, and access time. Using the six‐step method, several unfavourable characteristics of the outpatient clinic were revealed and a better match between demand, supply, and access time could have been reached with only minor adjustments. Last, a clinic specific prediction and decision model for demand and capacity was made using the 6‐step method. Conclusions The 6‐step analysis can successfully be applied to redesign and improve the outpatient health care process. The results of the analysis showed that national holidays and variability in demand and capacity have a big influence on the outpatient clinic. Using the 6‐step method, practical improvements in outpatient logistics were easily found and leads for future decision making were contrived.


| INTRODUCTION
Accessibility to care providers is one of the main challenges that every specialist outpatient clinic has to deal with. Delays in access time are nowadays such a common phenomenon that it seems to be considered as an inevitable burden by the public. [1][2][3] This acceptation could be a dangerous development; delays in access time are not only unpleasant but also increase the burden to sick or discomforted people and could even become dangerous in the case of (unnoticed) medical urgencies. 4 This makes accessibility a vital aspect of health care in the pursuit of delivering the best clinical care possible. 5 From a logistical point of view, waiting is sometimes considered as unavoidable due to the constraints on capacity. 6 However, seen from other perspectives, the inevitableness of delays in access time is not always shared. A common and frequently used perspective is the regular system perspective of access time. 7,8 In this perspective, delays are explained as a mismatch between supply and demand. 9,10 Supply -or capacity leading to the supply-can be seen as the specialist delivering care, while demand is the number of patients requesting for an appointment. This includes demand that is generated by the specialist scheduling future follow-up appointments. In the most optimal scenario, demand and supply are always synchronized with each other so that no delay in access time nor waste of capacity exists. Unfortunately, demand and supply have always a certain degree of variability and stochasticity. This means that even if they are on average equal but without synchronicity, waiting and utilization will be observed. 9,11 With this perspective in mind, numerous publications have been written that have studied the possibilities to improve matching demand of and supply for outpatient specialist clinics. 7,10,12-18 A significant number of publications focus on reducing the number of noshows. 12,[19][20][21] Others try to reduce access or waiting times by dynamic scheduling techniques or computer simulation to predict the required capacity. 17,18 However, prediction and decision models for outpatient logistics that are usable in daily practice are lacking.
In the logistical struggle of daily outpatient practice, policy makers sometimes try to "solve" delays in access time by manipulating demand and supply, such as discouraging demand for new consultations or stretching up the stake of available capacity by forcing health providers to treat more patients with the same resources. Nonetheless, these measures do not offer a sustainable solution. 22 To be able to overcome long delays in access time, there is a trend in the literature to focus on redesigning outpatient clinics in order to improve the performance in terms of waiting and capacity utilization.
This trend started probably with the model of "advanced access" as first described by general practitioner Mark Murray in 2000. 7,9,10,23,24 In this redesigned system, the outpatient logistics works with "pull" logistics as an alternative for "push" logistics as is common in traditional health care. A push system schedules the availability of appointments in specialist outpatient clinics based on (predicted) demand, while a pull system authorizes the release of appointments based on system status. In other words, instead of planning appointments based on the available-or forecasted-capacity, actual patients demand determine the completion of supply or capacity. In this system, capacity follows demand instead of preplanned capacity leading to potential postponement of demand.
However, studies using the concepts of "push" and "pull" logistics to analyse demand, supply, and access time in the outpatient clinic are very sparse. 7 This is regrettable, as evidence-based studies could give outpatient clinics valuable insights to analyse and optimize their own outpatient logistics. Moreover, studies based on daily outpatient practice could support existing theoretical hypotheses and direct future research of "push" and "pull" logistics.
This study was performed to gain insight in the partly untouched dynamics of real outpatient demand, supply, and access time. This was done by analysing individual patient data of daily practice of an orthopaedic outpatient clinic using a 6-step method. With the goal of a redesigned health care system in mind, the results were used to seek improvements for the match between demand, supply, and access time.
In addition, a model was introduced to forecast demand, to schedule capacity, and to support decisions for future outpatient logistics.
The study was performed using data from a large orthopaedic clinic during one complete year. Three questions were formulated before the data were analysed: • Does the used 6-step method provide valuable insights of the outpatient clinic?
• If so, how can patient demand, outpatient capacity, and access time be characterized during the analysed year?
• Does the 6-step method provide enough tools to improve the outpatient dynamics of this clinic and potentially other clinics as well?
The analysis was done using a structured step-by-step method. Not only the results of the analysis were considered as a goal of this study but the usability of the method itself was seen as an important outcome as well. By this way, a blueprint was given for other clinics to be able to understand their own triad of demand, supply, and access time.

| METHODS AND MODELS
This study was performed taking the regular system perspective in mind. In this study design, demand for first consultations was considered as an independent parameter. Follow-up appointments were (partly) influenced by the specialist, since most follow-up appointments were made on request of the specialist. This influence was analysed and verified in the data. The system of this outpatient clinic was considered mainly as a push system; capacity was largely based on physician availability and scheduling instead of actual demand.
Because of comparable access times in surrounding hospitals, a selection bias based on the access time was not expected. Both patient demand and capacity were considered as statistically normally distributed. This distribution was analysed in the results section.

| Six-step model
The same 6-step analysis was applied to all relevant parameters of demand, capacity, and access times: • Step 1: Defining and gathering of the raw data Data were extracted from a large orthopaedic outpatient clinic, consisting of one main outpatient locations and several smaller close-by locations. No major regional or interregional events took place during the year of analysis. Only appointments with an access time ranging from 1 to 30 days were included. Acute consultations in the outpatient clinic formed only a small part of all consultations with less than 1%. Appointments with an access time longer than 30 days were considered as outliers based on the distribution of the access time as described in the results. All available characteristics per appointment were collected and clustered as given in Table 1.
The data were manually evaluated for outliers, missing data, and ambiguities. Theoretical frameworks have no value without practical consequences. Therefore, in the fifth step, a blueprint of a prediction and decision model was given for outpatient decision makers to forecast future demand and needed capacity. The studied outpatient clinic was used as an example.
The last sixth step, formulate conclusions and potential improvements, gives an overview of the most important findings and improvement found in the previous steps.

| Step 2: analysing the data using basic statistics
Overall, 56.3% of the patients were seen at the main outpatient location, while the other 43.7% were seen at on the 3 smaller outpatient locations. On average, 38 morning and/or afternoon consultation shifts in the outpatient were completed per week, with a standard deviation of 7.5. A total of 610 no-shows were registered, consisting of 482 follow-up appointments and 128 new appointments and making up, respectively, 3.1% and 1.2% of the total number of appointments.  When demand and follow-up consultations were studied in more detail, the data showed that 29% of the registrations of follow-up consultations were registered directly after previous consultations. In other words, part of the future demand was created directly after supply. Because of this bias, only capacity-or the moment of the actual appointment-was used for further analyses.

| Access time
The average access time for all new consultations, measured from the moment of registration until appointment, was 9.8 days, with an SD of 1.6 (CV of 16%). From week 38 onwards, the trend of a rise in average access time is seen (Figure 3). This rise was probably due to queuing because of a mismatch in demand and supply, especially after the summer holiday from week 29 to 34.

|
Step 3: trends and striking characteristics

| New consultations
For both demand and capacity, certain weeks seemed to dip notably ( Figure 1). These-lower than average-weeks turned out to correspond with holiday weeks. For demand of new consultations, a "rebound" effect was seen directly afterwards in which an above average number of patients was registered. From a regular system perspective, this rebound effect can be described as a temporary rise is These numbers can also be translated to percentages to gain a better general sense of the major effect of holidays on the outpatient logistics. When the demand was translated in percentages, a drop of 20% compared with the overall average was seen during holidays and a rise of 9% was noticed for the 2 weeks afterwards. The same is seen for the distribution of weekly averages; a clearly more compact distribution of weekly averages is seen without holiday and rebound weeks (Figure 2A)

| Follow-up consultations
Follow-up appointments were also influenced by the holidays. During

| Access time
When the graph of the weekly average access time is considered, a big variation is seen (Figure 3). On the first sight, the holiday and rebound weeks do not clearly stand out. When the access time is however depicted by its weekly percentage difference, all holiday weeks and following rebound weeks can be noticed again (Figure 4).

| Organization of the outpatient clinic
Another factor for improvement might be the organization of the out-    Figure 5). These results show that capacity seems a bigger logistical challenge than demand. This is contrary to the sometimes heard preconception of demand being the unpredictable bottleneck in outpatient logistics.
As the results show, the second striking outcome is that holidays turned out to be of big influence of demand, supply, and access time.
For demand of new consultations, a postholiday rebound effect was seen, while this was not the case for capacity. This finding suggests that no adjustments in capacity were made in response to the rebound effect seen in demand. With the regular system perspective in mind, it can be expected that a better match between demand and supply favours the access time as well.
In step 3, the influence of holidays for demand was calculated by absolute differences compared with nonholiday weeks. Another way of evaluating the influence of holidays by a time series analysis. In other time series analysis, seasons or months are frequently evaluated.
In this analysis, the year is divided by 3 "seasons" or series, which are holiday weeks, rebound weeks, and other weeks.
In Figure 6, the results of a time series analysis are depicted.
The graph shows the absolute demand per week, centered moving means of 8 consequent weeks, and a linear trend line. Since this analysis is only depicting 1 year, the results are of limited (prospective) quality. When the average of the holidays was compared with the moving means, an average difference of −9.0% is seen, for rebound weeks was this difference +9.6%, and for the other weeks +1.3%. The difference for the 3 series compared with the trend line was comparable with, respectively, −8.4%, 11.1%, and 3.6%.
As described in Section 1, the literature frequently focusses on a perfect match between demand and supply. 7,9 In this clinic, the Pearson correlation coefficient between demand and supply in this clinic was 0.43, indicating a moderate linear correlation. However, when the holidays and rebound weeks were excluded, the Pearson correlation coefficient dropped to only P = .23. The same trend was seen for follow-up consultations, with a correlation coefficient of P = .62 with holidays and a decrease to P = .42 without. This suggests that the correlation between demand and capacity was mainly due to the influence of the holidays and not because of a direct "match" between demand and supply ( Figure 7).
Nevertheless, a fairly stable and highly comparable demand and supply were seen when all holidays and their rebound weeks were excluded. When these weeks were excluded, both demand and supply turned out to have an average of 223 and coefficient variation of 8.6%. This shows that weekly variability (due external factors such as holidays) seems to form a bigger problem that is an absolute mismatch of average demand and supply. This corresponds to the

| Step 5: a model for predicting future demand and capacity
In the last research question, the need for "tools" is expressed to support decision making in daily practice. When a blueprint is available to assess and predict outpatient logistics, delays in access time and wastes of capacity can be minimized. A model for forecasting demand, scheduling capacity, and supporting decision forms the last step in the 6-step model. This model can be applied on the studied outpatient clinic with the data and results of the previous steps as an example.
In this example and for this clinic, "only" a single year was analysed.
A longer (time series) analysis probably leads to more reliable and therefore usable results. Nevertheless, the steps in this model would be the same.  By setting up shifts that consist of fixed forecasted and flexible parts for either short-term follow-up appointments or weeks with a relatively high demand for new consultations, overcapacity might be reduced.
By this way, usage of the 6-step method might lead to a more efficient triad of demand, capacity, and access time.

| Step 6: conclusions and potential improvements
The formulated 6-step model showed to be comprehensive enough to discoverer different trends of the outpatient logistics. The model showed that that not only the specific results of the analysis but also the method itself can be of great value for other clinics.
While the above conclusion answers the first research question, the second research question was focused on finding improvements for demand, capacity, and access time of this and other outpatient clinics. As the first 4 steps of the 6-step model show, different relevant findings and leads for improvement were found. First, it was showed that a linear correlation or match between demand and supply turned out to be quite low in real practice. This differs from the linear correlation that is sometimes assumed in the literature. 8,12,[14][15][16] Secondly, the analysis showed that capacity was more variable than demand, although the overall average of both was comparable. Big variations in access time were observed as well. These conclusions lead to one of the main points of observation and improvement; not only is capacity more easy adaptable than demand, it is also highly likable that ensuring a less variable capacity leads to a better match between demand and supply and favours the access time as well.
Another important finding was that holidays showed to have a big influence on demand. Strikingly, capacity does not seem to react adequately on this. In the light of a redesigned outpatient system, adjustment of capacity to withstand this rebound effect will probably lead to a better match of demand and supply.
When the capacity was seen in context of weekly shifts and ratio's between new and follow-up consultations, big variations throughout the year were again seen. Simple plotting of these data gave valuable insights and points for improvement, such as a more aware distribution and ratio between new and follow-up consultations of adjustments of the ratio for certain periods such as during rebound weeks.
Last, the results of steps 1 to 4 could be used in step 6 to create a model to forecast demand, schedule capacity, and support decision making. While the reliability and usability of the results of this model are correlated with the amount and quality of the data, the model can serve as a guideline for capacity planning in outpatient logistics.
This study and the 6-step model can therefore not only be a reference for future research but also be of value for daily practice of the outpatient clinic.