Krishna Murthy Dasari February 26, 2010 29
Defining fulltime staffing levels for a service desk is very difficult without a definitive way to predict the demand for service. Workload forecasting is the basis of any good staffing plan. While there are many forecasting techniques available, one that is simple, easy to implement and can be applied to any size service desk is the best place to start.
The forecasting process is a combination of using judgment and application of mathematics. The mathematical process takes past history and uses it to predict future events. Both these components should be used in order to come out with an accurate forecast. A working knowledge of the statistical techniques discussed here will make the process understandable. Even for organizations which use time series analysis software, it is critical to understand these calculations as it helps in correctly interpreting results and verifying the accuracy of the results generated by the software.
There are two main approaches to forecasting. One is the explanatory method which is based on an analysis of factors which are believed to influence the call volume; the other is the exploration method where the prediction is based on an inferred study of past general call volume behavior over time. Even for a modest degree of accuracy the former method is more difficult to implement and validate than the latter approach. For this reason, the focus here is on the exploration or time series approach to forecasting.
This approach is scientifically valid yet easy to follow and implement.
For an IT service desk whose primary purpose is to coordinate and resolve incidents as quickly as possible, an optimum level of staff numbers is required. A forecast of volume of calls helps the service desk in computing the optimum number of staff numbers. As a first step the forecast requires the past data of call volume. Table 1 gives the data for the years 2004, 2005 and 2006. In this case, it is believed that the recent three years reflect the current business situation and it is expected these patterns to continue into 2007.
This data is adjusted for variation to eliminate certain spurious differences which are caused by peculiarities of the calendar. For example, the call volume for the month of February may be less not because of any real drop in activity but because of the fact that February has fewer days. The data is plotted in Figure 1. The red line represents the original call volume. Within each year a decline in call volume is observed in the beginning and an increase in the middle of the year and again a decline during the end of the year. Between the given years call volume seems to generally increase overall.
Table 1: Call Volume for 2004, 2005 and 2006  
Month 
2004 
2005 
2006 
January 
57,776 
71,328 
85,637 
February 
61,866 
73,650 
86,128 
March 
52,993 
70,658 
90,530 
April 
53,096 
66,371 
80,283 
May 
67,789 
79,350 
94,169 
June 
75,203 
87,445 
99,654 
July 
62,831 
78,539 
95,303 
August 
75,547 
87,846 
99,880 
September 
76,905 
83,774 
90,153 
October 
70,446 
82,878 
96,010 
November 
71,952 
79,947 
89,092 
December 
62,712 
65,325 
67,517 
Data in this table is adjusted for calendar variation. Method: Divide each month’s data by number of days in the month to find the daily average. Multiply daily averages by 30.4167 (average number of days in a month) to obtain monthly data. 
General analysis of the Figure 1 time series plot shows that a variety of things are likely influencing the call volume. It is important that these influences be decomposed out of the raw call volume data shown in Table 1. Generally there are four types of patterns, movements or components of time series. They are:
To be able to make a proper call volume forecast, one must know to what extent each of the above components is present in the data. To understand and measure these components, the forecast procedure involves initially removing the component effects from the original data. This is called decomposition. After the effects are measured, making a call volume forecast involves putting back the components on new call volume estimate. This is called as recomposition.
This step explains the removal of seasonal effects in the data. Without deseasonalizing the original call volume, one may incorrectly infer that the observed growth patterns will continue indefinitely when actually the increase is just because of the time of the year. To measure seasonal effects, a series of seasonal indexes should be calculated. A practical and widely used method to compute these indexes is the ratio to moving average approach. These indexes quantitatively measure how far above or below a given period stands in comparison to the expected call volume.
Procedure for calculation of seasonal indexes is:
The computation is shown in Tables 2 and 3.
The removal of seasonality from the original data is depicted in Figure 1 by the blue line. Note that the deseasonalized call volumes do not oscillate as widely as the original call levels. The remaining up and down movement must therefore be due to trend, cyclic and irregular effects.
Table 2: Ratio to Moving Average Calculations for Selected Months  
Month in 2004 
Call 
12Month 
Ratio to Moving 
January 
57,776 

February 
61,866 

March 
52,993 

April 
53,096 

May 
67,789 

June 
75,203 

July 
62,831 
66,324 
94.73 
August 
75,547 
67,380 
112.12 
September 
76,905 
68,607 
112.09 
October 
70,446 
69,896 
100.79 
November 
71,952 
70,931 
101.44 
December 
62,712 
71,923 
87.19 
Table 3: Seasonal Index and Deseasonalized Call Volume for Selected Periods  

Seasonal 






{Calculated 
Month 
Original 
Deseasonalized 
Jan 
97.59 
100.45 
99.02 
Jan 
57,776 
58,348 

Feb 
99.19 
95.57 
97.38 
Feb 
61,866 
63,531 

Mar 
94.14 
99.61 
96.88 
Mar 
52,993 
54,702 

Apr 
87.49 
91.19 
89.34 
Apr 
53,096 
59,430 

May 
103.44 
105.85 
104.65 
May 
67,789 
64,779 

Jun 
113.34 
111.42 
112.38 
Jun 
75,203 
66,917 

Jul 
94.73 
100.88 
97.81 
Jul 
62,831 
64,241 

Aug 
112.12 
111.24 
111.68 
Aug 
75,547 
67,647 

Sep 
112.09 
104.30 
108.20 
Sep 
76,905 
71,078 

Oct 
100.79 
101.41 
101.10 
Oct 
70,446 
69,681 

Nov 
101.44 
96.41 
98.92 
Nov 
71,952 
72,734 

Dec 
87.19 
77.72 
82.46 
Dec 
62,712 
76,054 

* Total of Seasonal Index % is 1199.81 which is very close to 1200. No correction factor is required. 
Measurement of trend component is done by fitting a line to the data given in Table 1. This fitted line is calculated by the method of least squares which represents the overall linear growth over time. The trend line equation is:
Y = A + BX
Where Y = Predicted call volume occurring in the period X due to the trend effect
A = Vertical intercept of the trend line equation
B = Call volume growth rate per month, i.e., the slope of the trend line equation
The trend line parameters are calculated by use of mathematical formulas or Excel. The trend line equation for this case is found to be:
Y = 77,516 + 946(X)
To illustrate how the above equation is used, suppose the organization’s interest is in the predicted call volume accorded by trend for January of 2006. This period corresponds in the equation to X = 6.5. Thus the predicted call volume for January 2006 is 83,665.
The trend line is depicted in Figure 1 by the blue line.
To measure how the general business cycle affects call volume, a series of cyclic indexes are calculated. The deseasonalized data still contains trend, cyclic and irregular components. Also the predicted call volume using the trend equation do represent pure trend effects. Thus, it stands to reason that the ratio of the deseasonalized call volume and the call volume derived from the trend line equation should provide an index which reflects cyclic and irregular components only. The cyclic index calculations are shown in Table 4.
Table 4: Cyclic Index and Smoothed Cyclic Index for Selected Months  
Month in 2004 
Deseasonalized 
Predicted Call 
Cyclic Index 
ThreePeriod 
January 
58,348 
60,961 
95.71 

February 
63,531 
61,907 
102.62 
95.12 
March 
54,702 
62,853 
87.03 
94.27 
April 
59,430 
63,799 
93.15 
93.41 
May 
64,779 
64,745 
100.05 
98.36 
June 
66,917 
65,691 
101.87 
99.44 
July 
64,241 
66,637 
96.40 
99.45 
August  
September  
October  
November  
December  
* Calculated similar to Table 3. ** Calculated by using trend line equation. 
The business cycle is longer than the seasonal cycle and it should be understood that cyclic analysis is not as accurate as seasonal analysis due to complexity of general economic factors over long periods of time. Thus a general approximation of the cyclic factor is what is required to forecast the call volume. To study the general cyclic movement rather than precise cyclic changes, the cyclic plot must be smoothed out by replacing each index calculation with a centered threeperiod moving average. This is shown in Table 4. Both the cyclic index and the smoothed cyclic index are depicted in Figure 2.
In Figure 2, it can be noted that cyclic peaks occurring in Periods 11 and 27, and Periods 5 and 24 are approximately of the same magnitude and may thus be parts of different business cycles. From this, it can be infer that the cyclic length, i.e., the elapsed time before the cycle repeats is approximately 20 months. In order to make call volume forecasts, the approximate continuation of this cycle curve is projected into the next few months of 2007 in the figure.
At this point of time, the study of the past data to understand the different components of the time series analysis is completed. Now an attempt can be made to forecast volumes for the first two months of 2007. The procedure is:
Step 1: Compute the future call volume trend level using the trend line equation
Step 2: Multiply the call volume trend level from Step 1 by the period seasonal
Step 3: Multiply the result of Step 2 by the projected cyclic index to include cyclic
effects and get the final forecast result
Table 5: Call Volume Forecast Calculations for January and February 2007  
Year 2007 
Predicted Call 
Seasonal 
Estimated Call 
Projected 
Call Volume 
Forecast Adjusted 
January 
95,017 
0.99 
94,085.8334 
0.99 
93,145 
94,931 
February 
95,963 
0.97 
93,448.7694 
1.01 
94,383 
86,884 
* From trend line equation Y = 77516+946(X). X values for January and February are 18.5 and 19.5 respectively. ** From Column (D) of Table 3. *** Estimated by inspection of cyclic projection in Figure 2. 
The actual call volumes for January and February 2007 were 94,530 and 87,224 respectively.
This call volume forecasting procedure can be applied to any service desk which has data for the past few years. The advantage of the procedure is that it is simple to understand and implement and at the same time a fairly accurate. An effective combination of the mathematical calculations with management’s firsthand knowledge of the situation is required to achieve accurate forecasts. There are other more complex forecasting techniques, but organizations should go through an evolutionary progression in adopting them. Start with a simple forecasting method, gain knowledge and move towards more sophisticated methods if necessary.


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Comments
could you please tell me how do you calsulate table no 2
I see people are struggling with the calculation of the moving averages. The reason that the moving average starts in July is that the calculation uses a full year’s data. In fact it uses 13 months of data. The formula for the July average is [ (January 2004 + January 2005 values) / 2 + (the sum of February 2004 through December 2004 ) ] / 12. Applying this formula to the other months will produce all of the data in table 2.
How do you calc the 3 period index smoothed values in table 4?
How did you get a YIntercept of 77,516?
Note that the author says January 2006 corresponds to x=6.5. This would imply that Decemember 2005 corresponds to x =5.5 and November 2005 corresponds to x=4.5 and so on. You can put these points in next to the raw data and then use the TREND() formula in excel to calculate the trend points for each month. If you plug in 0 for the “new x” value in Excel, you’ll get a yintercept of 77,516. The y intercept really isn’t that important though. What matters more is the slope. You can get this just by subtracting two of the adjacent outputs from each other. So Trend( Feb 2004) Trend( Jan 2004) = 964.
Hi Drew,
I tried using the formula Trend( Feb 2004) Trend( Jan 2004) = 964, but I got 4090. It simply subtracts Feb to Jan 2004 volume. Appreciate your help.
Article’s very helpful. May I ask though where could have i erred? The Feb and Mar Ratio to Moving Ave and Seasonal Index I got were: 99.62, 103.79, and 99.40 and 98.97, respectively.
Dino,
I got exactly the same results you did for Feb and Mar ratio to Moving Average and Seasonal Index. Where did I go wrong????
Thanks,
Eric
Already got where i erred. Have another query. What if the total seasonal index is not close to 1200? What adjustment is needed if this is the case? Is there an acceptable margin? Thanks in advance.
To normalize values you can do this. Add up all the seasonal averages. It should be close to 1200. Then multiply each seasonal index percentage by 1200 / the sum of the seasonal averages. This will normalize your averages making sure that they add to 1200 and that you don’t lose (or gain) any calls by applying this adjustment.
What exactly were the steps for calculating the 12 month moving average? I’m confusedfor Table 2 I see the numbers for Moving Average beginning in July, but why are we beginning in July & not January?
You can see the formula used for the 12 month moving average in a comment posted above. In general though, an X month moving average uses (X1)/2 months prior to the target month and (X1)/2 month after the target month in order to “smooth” the data. So you wouldn’t expect to be able to calculate the 12 month moving average until July 2004, since data only goes back to January 2004.
@dino – I got the same seasonal index values for 2006. I rechecked everything three times and I’m concluding that something is wrong with above data.
See my answers above.
i also have problems with the moving average, have recomputed several times, i even googled how to compute the moving average and couldn’t get the same values on table 2.
Ongkee,
Greetings from Atlanta. I also tried replicated this recently and came up with questions for Feb and Mar as well. I can help answer questions for the values in table 2. I can send you my spreadsheet if you are interested.
Eric
erichughes@bellsouth.net
See my answers above.
Hi,
I tried to follow the steps laid out in this article but had some difficulties. I had the following queries:
1. Are the moving averages shown here correct? The moving averages in Table 3 for Feb 06 & Mar 06 appear to be incorrect; values on calculation in excel come to 99.62 and 103.79 – did anyone else get these values?
2. How did you get a trendline equation with A = 77,516? In excel the value of A is coming as 60,015. Can someone help me understand the difference?
3. How is predicted call volume in Table 4 calculated? i.e. how do you determine the value for x (why is Jan ’06 = 6.5)?
4. How do you get the value of cyclic projection from the trendline?
Any help would be greatly appreciated! Tried to create my own model for forecasting, but ran into the road blocks mentioned above.
Regards
Sandy,
Greetings from Atlanta. I also tried replicated this recently and came up with questions for Feb and Mar as well. I can help answer questions 2&3 but have the same question on your 4th question. I can send you my spreadsheet if you are interested.
Eric
erichughes@bellsouth.net
1. When I replicated the example, I spotted the same errors with Feb and Mar 2006 ratio to moving averages in Table 3. I got the same results you did there.
2 & 3. See my post above about how this value of A was acheived. Basically January 2006 was given the value of X=6.5. So December 05 would be 5.5 months, November 05 would be 4.5 months, etc. I believe this was assigned rather arbitrarily. The Y intercept is also arbitrary, as you can choose to use whatever numbers you want for your months. It looks like you numbered your months differently, starting with month 1 = January 04.
Hi Drew,
I am getting the same errors as Sandy for Feb and March Data. Mine is: (Feb – 97.38, Mar – 96.88). May you please provide your calculations. I am currently working on a forecast template for my project.
Your 4th question is answered by the paragraph right before the table. In order to calculate the cyclic effects, the author posits that the deseasonalized data contains trend effects, cyclic effects, and irregular variation. Thus to get the cyclic effects the author first divides the deseasonalized data by the trend data, removing the trend effect. So now the data has only cyclic effects and irregular variation. In order to reduce the noise of the irregular variation, the author applies a 3 month moving average to “smooth” the data and thus reduce the irregular variation.
Can I use the forecast in such a way to determine how many more resources are needed to improve a KPI like ASA? For example, based on volume, time of day, day of week, how many resources are needed to reduce ASA from 2 mins to 1.5 mins?
I am confused on the moving averages i used the formula that you indicated in your reply but i am not getting the same answer that is indicating in the chart, is there something that i am missing
Good day,
Eric would you be able to share your spreadsheet?
any way it can be added to this forum as an attachment?
I had the same problem with the moving average and I took some time to figure it out.
The formula should be =(sum(january 2004,january 2005)/2+sum(february thru december))/12
Need help as to how to calculate three period index smoothing value in table 4 please?
This approach was also posted in 1985: http://home.ubalt.edu/ntsbarsh/Businessstat/statdata/DecomposePaper.pdf – I wonder if there are any new methods out there.
i am having trouble calculating table 5, on the part of the projected cyclic Index, how is that obtained?