Synagogue Capacity Planning

Transcription

1 Synagogue Capacity Planning Ellie Schachter Professor Lefkovitz JWSS Module 22 March 2017

2 Introduction 3 Current State 3 Data Analysis 4 Predictive Model 7 Future State 15 Works Cited 16 2

3 Introduction While the concept of a Jewish community evolving around a synagogue with vast event spaces and a full social calendar was normative for Baby Boomers and Generation X, Millennials and Generation Z have shied away from synagogue centric activity in favor of social practice that aligns more closely with their secular community. Once a staple of the Jewish community, JCCs are now closing their doors, combining congregations, and planning for the next fad in religious community construct. Attendance at synagogue events is fluctuating with the seasons, following trends year over year. One challenge for synagogues is to predict capacity needs with respect to these trends for events such as weekly services, group meetings, and major religious events. Synagogues generally have little to no data on attendance or participation, making forecasting trends definitively speculative and unreliable. Implementing methods for gathering data on attendance and capacity of a synagogue will help synagogues plan for events throughout the year, ultimately providing a more personal experience to the congregation. Current State To measure the current state capacity of a synagogue there must be a way to collect the amount of people that enter and exit the space daily. This is vital to understand trends in attendance over the course of a day, week, year, and multiple years. This data may be aggregated over time to make computations for predictive modeling faster. Daily data needed to model the current state includes the number of people that enter and exit per hour collected every hour throughout the day. This data can be collected through a counter located over each door to the space. This data collection uses a camera to detect the head of each person along with the direction of their movement. (J. García, 2012) A sample of data is shown in Table 1 below, depicting the first twelve hours of traffic in a synagogue on New Year s Day, Table 2 Raw Data Collected by People Counter Date Hour Traffic in per hour Day total 1/1/17 0: /1/17 1: /1/17 2: /1/17 3: /1/17 4: /1/17 5: /1/17 6: /1/17 7: /1/17 8: /1/17 9: /1/17 10:

4 1/1/17 11: /1/17 12: The output of this system would be a live data file that feeds into a data visualization tool, such as Tableau to calculate and visualize trends over any specified time period. Data Analysis Data analysis can be done in Tableau, a computer software that is generally used to create visualizations of data for practical applications. The data can be aggregated by day, week day, month, week, year, etc. This is an easy way for the synagogue to view their attendance and track changes over any time period. Sample data for the Month of January 2016 is show in the figure below. This depicts the total traffic per day, broken down by hour, shown by a heat map for hourly traffic. The following images include other ways that the tableau software can aggregate the data however is most useful for the synagogue. Figure 1 Total Traffic per Day by Hour 4

5 Figure 2 Total Traffic per Day Figure 3 Average Traffic by Weekday 5

6 Figure 4 Time Series Data 6

7 Predictive Model To predict expected traffic for the future there are a few ways to use existing data. Some common predictive techniques are moving average, and exponential smoothing. Moving average uses traffic data from a set past number of days and averages them to predict the future attendance. The formula for this technique using 7 days: F! =!!!!!!!! 7 Where n is the current day, and A is the attendance on day n. This method takes the past 7 day attendance and finds an average to use as the prediction for the next day. This method is good for calculating predictions over a short period of time, as it only takes into account the most recent week s attendance. This will fall short to show seasonality and trend in attendance over a long period of time, therefore should not be used for predicting more than a few weeks in advance. When used to predict attendance for the month of January, this method was accurate to within 2 people and had an overall error of about 4%. Another method for predicting attendance is exponential smoothing. This method takes into account all historical data, weighting more recent data more heavily by a factor, α. This α can be adjusted to find the value that best fits the set of data. For the purpose of this report there were three α values tested: 0.1, 0.2, and 0.3. The formula for forecasting using exponential smoothing is as follows: F! = αa! + 1 α F!!! Where A is the actual attendance at day n. This weights the most recent day by alpha, and each past day by α-1 so that days become exponentially less weighted. This method is good for forecasting with data that has no trend over time, and may prove useful for attendance forecasting if the overall rate of attendance is not trending up or down over long periods of time. If there is a trend in attendance, this method of forecasting will always lag behind the trend. Calculations for Mean Squared Error (MSE), Mean Absolute Deviation (MAD), and Mean Absolute Percent Error (MAPE) are as follows: A! MSE = 1 n F! A!!!!!! MAD = 1 n F! A!!!!! MAPE = 1! n!!! A! F! A! Where F is the prediction for day n, and A is the actual attendance on day n. 7

8 Table 3 Seven Day Moving Average Date Day total 7 day moving average MSE MA(7) MAD MA(7) MAPE MA(7) 1/1/ /2/ /3/ /4/ /5/ /6/ /7/ /8/ /9/ /10/ /11/ /12/ /13/ /14/ /15/ /16/ /17/ /18/ /19/ /20/ /21/ /22/ /23/ /24/ /25/ /26/ /27/ /28/ /29/ /30/ /31/ Error

9 Table 4 Exponential Smoothing with Alpha = 0.1 Date Day total Exponential Smoothing α=0.1 MSE ES 0.1 MAD ES 0.1 MAPE ES 0.1 1/1/ /10/ /2/ /1/ /3/ /1/ /4/ /8/ /5/ /3/ /6/ /22/ /7/ /15/ /8/ /1/ /9/ /18/ /10/ /6/ /11/ /20/ /12/ /27/ /13/ /28/ /14/ /13/ /15/ /13/ /16/ /23/ /17/ /5/ /18/ /31/ /19/ /24/ /20/ /10/ /21/ /15/ /22/ /19/ /23/ /12/ /24/ /10/ /25/ /14/ /26/ /14/ /27/ /3/ /28/ /9/ /29/ /23/ /30/ /5/ /31/ /24/ Error

10 Table 5 Exponential Smoothing with Alpha = 0.2 Date Day total Exponential Smoothing α=0.2 MSE ES 0.2 MAD ES 0.2 MAPE ES 0.2 1/1/ /10/ /2/ /22/ /3/ /6/ /4/ /13/ /5/ /1/ /6/ /15/ /7/ /7/ /8/ /10/ /9/ /23/ /10/ /2/ /11/ /2/ /12/ /18/ /13/ /23/ /14/ /23/ /15/ /16/ /16/ /23/ /17/ /5/ /18/ /12/ /19/ /21/ /20/ /12/ /21/ /10/ /22/ /24/ /23/ /22/ /24/ /29/ /25/ /20/ /26/ /2/ /27/ /17/ /28/ /9/ /29/ /6/ /30/ /5/ /31/ /16/ Error

11 Table 6 Exponential Smoothing with Alpha = 0.3 Date Day total Exponential Smoothing α=0.3 MSE ES 0.3 MAD ES 0.3 MAPE ES 0.3 1/1/ % 1/2/ % 1/3/ % 1/4/ % 1/5/ % 1/6/ % 1/7/ % 1/8/ % 1/9/ % 1/10/ % 1/11/ % 1/12/ % 1/13/ % 1/14/ % 1/15/ % 1/16/ % 1/17/ % 1/18/ % 1/19/ % 1/20/ % 1/21/ % 1/22/ % 1/23/ % 1/24/ % 1/25/ % 1/26/ % 1/27/ % 1/28/ % 1/29/ % 1/30/ % 1/31/ % Error % 11

12 Given the seasonal nature of the data as seen in the tableau aggregation by day, as seen previously in Figure 3, there should be a better method for predicting attendance following a weekly seasonal factor. This method of season predictive modeling is called Winter s method and is preferable over moving average or exponential smoothing because it can track trend over time, and seasonality, in addition to forecasting week by week. To calculate the forecast using Winter s Method the following equations are used for each time period, t: L! = α A! s! + 1 α L!!! + T!!! T! = β L! L!!! + 1 β T!!! s!!! = γ( A! L! + 1 γ s! F!!! = L! + T! S!!! where A is the actual attendance in time t, L is the level at time t, T is the trend at time t, and s is the seasonal factor for time t. In this case α = 0.15, β = 0.10, γ = This method proves to be more accurate as it predicts attendance within 5% accuracy while finding trends and seasonality in the data. 12

13 Table 7 Winter's Method Date Day total S S value Level Trend Winter's Method MSE Winter's MAD Winter's MAPE Winter's 1/1/ s /2/ s /3/ s /4/ s /5/ s /6/ s /7/ s /8/ s /9/ s /10/ s /11/ s /12/ s /13/ s /14/ s /15/ s /16/ s /17/ s /18/ s /19/ s /20/ s /21/ s /22/ s /23/ s /24/ s /25/ s /26/ s /27/ s /28/ s /29/ s /30/ s /31/ s Error

14 By comparing methods of prediction against the actual attendance records, we see that Winter s method follows the actual attendance most accurately while maintaining both trend and seasonality, which are vital to the synagogue to understand patterns of attendance. This can be seen in the figure below. Table 8 Comparison of Predictive Methods Total Attendance Total Traffic 14

15 Future State The application of data visualization can help synagogues track trends in attendance including seasonality in weekly, monthly, and holiday peak and off peak times. Predictive methods such as moving average, exponential smoothing, and Winter s method can be applied to such data trends to assist synagogues in accommodating crowds throughout the year. These methods can be applied to follow the Jewish calendar, as high holidays do not fall consistently on the Gregorian calendar. Predictive modeling and data visualization are tools which have just begun to be applied to large scale, high risk industries such as healthcare and manufacturing. The technologies and principles shown here will spread to commercial and religious sectors as the software and technology become more refined and user friendly. Data visualization is an efficient way to communicate abstract or discrete trends in information that would otherwise be conveyed anecdotally with little to no ability to be verified. 15

16 Works Cited J. García, A. G. (2012, July 6). Directional People Counter Based on Head Tracking. IEEE Transactions on Industrial Electronics, 60(9),