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By Krishna Murthy Dasari

Defining full-time 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.

Introduction to the Methodology

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.

Figure 1: Call Volume – Original, Deseasonalized and Trend Effects

Decomposing the Call Volume 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:

1. Seasonal variations: The fluctuations which are repeated from year to year with about the same timing and level of intensity.
2. Secular trend or simply trend: The general tendency of the data to grow or decline over a long period of time.
3. Cyclical variations: Long-term movements that represent consistently recurring rises and declines in activity. These are not caused by seasonal effects.
4. Irregular variations: Variations in business activity which do not repeat in a definite pattern.

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.

Deseasonalizing the Call Volume Data

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:

1. Compute a centered 12-month moving average.
2. Compute the ratio of actual call volume in each month to the moving average.
3. Average the above ratios for Months 1 through 12 for all given years.
4. Correct the averaged ratios from Step 3 for possible round off error to get the 12-month seasonal index set.
5. Divide the original call volume by the seasonal indexes to get the deseasonalized call volumes.

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 Volume (A)	12-Month Moving Average (B)	Ratio to Moving Average (C = A/B)
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
	Ratio to Moving Average			Seasonal Index % (D)	Year 2004
Month	2004 (A)	2005 (B)	2006 (C)	{Calculated by Averaging A, B and C]*	Month	Original Call Volume (E)	Deseasonalized Call Volume (F = E/D)
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.

Measuring the Call Volume Trend

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.

Measuring the Cyclic Effects

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 Call Volumes (A)*	Predicted Call Volume/Trend (B)**	Cyclic Index Percent (C = A/B)	Three-Period Index Smoothing (D)
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 three-period moving average. This is shown in Table 4. Both the cyclic index and the smoothed cyclic index are depicted in Figure 2.

Figure 2: Cyclic Index and Smoothed Cyclic Index Plot

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.

Making the Call Volume Forecast

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 Volume/Trend (A)*	Seasonal Index % (B)**	Estimated Call Volume w/Trend & Seasonal Effects (C = A x B)	Projected Cyclic Index (D)***	Call Volume Forecast (E = C x D)	Forecast Adjusted for Calendar Variation (F = E/30.4167 [Average Number of Days in Month]
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.

Summary: Math and Firsthand Knowledge

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.

About the Author: Krishna Murthy Dasari is a software quality professional with 12 years of experience in quality. He has worked in manufacturing and information technology industries. He has specialized experience in ISO 9000, CMMI, ITIL, Six Sigma and information security management. He is currently working with Satyam Computer Services Ltd. He can be reached at dvkm_dasari@yahoo.com.