CALL VOLUME FORECASTING FOR SERVICE DESKS Krishna Murthy Dasari Satyam Computer Services Ltd. This paper discusses the practical role of forecasting for Service Desk call volumes. Although there are many forecasting techniques available, a technique which is simple and easy to implement is described in this paper so that any Service Desk can start using this. The procedure is discussed from a realistic perspective by noting circumstances which do come up in the real world and how to adjust the forecast methodology to account for such situations. INTRODUCTION Defining full-time staffing levels is very difficult without a definitive way to predict the demand for service. Work load forecast is a very important parameter and is the basis of any good staffing plan. A precise forecast of the work to be expected helps to calculate the staff numbers and to create intricate schedule plans. 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 effectively in order to come out with an accurate forecast. A working knowledge of the specialized statistical techniques discussed in this paper will get you through the process. Even for organizations which use time series analysis software, it is critical to understand these calculations as it helps in interpreting the results in the right way and to verify the accuracy of the results generated by the software. The procedure described in this paper can be applied to any size of a service desk. 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 or 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 desired accuracy the former method is more difficult to implement and validate than the latter approach. Because of this reason, this paper focuses on the exploration or time series approach to forecasting. This approach is scientifically valid yet easy to follow and implement. The analysis presented in this paper is 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 to resolve incidents quickly. 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 of 2004, 2005 and 2006 reflect the current business situation and it is expected these patterns to continue into 2007.
This data is adjusted for calendar variation to eliminate certain spurious differences which are caused by peculiarities of our 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. Brown line represents the original call trend. 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 years 2004, 2005 and 2006 Month 2004 2005 2006 January 57776 71328 85637 February 61866 73650 86128 March 52993 70658 90530 April 53096 66371 80283 May 67789 79350 94169 June 75203 87445 99654 July 62831 78539 95303 August 75547 87846 99880 September 76905 83774 90153 October 70446 82878 96010 November 71952 79947 89092 December 62712 65325 67517 * Data is adjusted for calendar variation. Divide each monthly data by number of days in the month to arrive at the daily average. Multiply these values with 30.4167(average number of days in a month) to obtain monthly data. Figure 1: CALL VOLUME Original, Deseasonalized & Trend Effects 120000 100000 Trend Line Number of calls 80000 60000 Deseasonalized call volume Original call volume 2004 2005 2006 40000 Jan-04 Apr-04 Jul-04 Oct-04 Jan-05 Apr-05 Jul-05 Oct-05 Jan-06 Apr-06 Jul-06 Oct-06
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 refer to variations in business activity which do not repeat in a definite pattern. To be able to make a proper call volume forecast, we 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 as 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, we may for example incorrectly infer that the observed growth patterns will continue indefinitely when actually the increase is just because it is that time of the year. To measure seasonal effects, we calculate a series of seasonal indexes. 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: 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 1-12 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 orange line. Note that the deseasonalized call volume 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 Call Volume (a) Jan-04 57776 Feb-04 61866 Mar-04 52993 Apr-04 53096 May-04 67789 Jun-04 75203 12 - Month Moving Average (b) Ratio to Moving Average c = a/b Jul-04 62831 66324 94.73 Aug-04 75547 67380 112.12 Sep-04 76905 68607 112.09 Oct-04 70446 69896 100.79 Nov-04 71952 70931 101.44 Dec-04 62712 71923 87.19 Jan-05 71328.. Feb-05 73650.. Mar-05 70658.. Table 3: Seasonal Index and Deseasonalized Call Volume for Selected Periods Ratio to Moving Average Seasonal Index % (d) = Average of a,b and c * Month 2004 Original Call Volume (e) 2004 Deseasonalized Call Volume f = (e/d) Month 2004 (a) 2005 (b) 2006 (c) Jan 97.59 100.45 99.02 Jan-04 57776 58348 Feb 99.19 95.57 97.38 Feb-04 61866 63531 Mar 94.14 99.61 96.88 Mar-04 52993 54702 Apr 87.49 91.19 89.34 Apr-04 53096 59430 May 103.44 105.85 104.65 May-04 67789 64779 Jun 113.34 111.42 112.38 Jun-04 75203 66917 Jul 94.73 100.88 97.81 Jul-04 62831 64241 Aug 112.12 111.24 111.68 Aug-04 75547 67647 Sep 112.09 104.30 108.20 Sep-04 76905 71078 Oct 100.79 101.41 101.10 Oct-04 70446 69681 Nov 101.44 96.41 98.92 Nov-04 71952 72734 Dec 87.19 77.72 82.46 Dec-04 62712 76054 * 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 of the form 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 Microsoft Excel. The trend line equation for this case if found to be Y = 77516 + 946(X) To illustrate how the above equation is used, suppose we are interested in the predicted call volume accorded by trend for month January of 2006. This period corresponds in the equation to X = 6.5. Thus the predicted call volume for January 2006 is 83665. The trend line is depicted in Figure 1 by the blue color line. MEASURING THE CYCLIC EFFECTS To measure how the general business cycle affects call volume, we calculate a series of cyclic indexes. 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 Deseasonalized Call Volume (a) * Predicted Call Volume(Trend) (b) ** Cyclic Index % ( c) = (a)/(b) 3 Period Index Smoothing (d) Jan-04 58348 60961 95.71 Feb-04 63531 61907 102.62 95.12 Mar-04 54702 62853 87.03 94.27 Apr-04 59430 63799 93.15 93.41 May-04 64779 64745 100.05 98.36 Jun-04 66917 65691 101.87 99.44 Jul-04 64241 66637 96.40 99.45 Aug-04.... Sep-04.... Oct-04.... Nov-04.... Dec-04.... * 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 we smooth out the cyclic plot by replacing each index calculation with a centered 3 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 115 110 Cyclic Indexes Cyclic projection 105 Cyclic Index % 100 95 Cyclic Indexes smoothed for 3 months 90 85 Jan-04 Apr-04 Jul-04 Oct-04 Jan-05 Apr-05 Jul-05 Oct-05 Jan-06 Apr-06 Jul-06 Oct-06 Jan-07 From the above figure it is noted that cyclic peaks occurring in periods 11 & 27, and 5 & 24 are approximately of the same magnitude and may thus be parts of different business cycles. From this we can 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 we project the approximate continuation of this cycle curve into the next few months of 2007 as indicated 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 let s attempt to make forecast for the first two months of 2007. The procedure is given below. 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 gives the calculations of the forecast. Table 5: Call Volume Forecast Calculations for January and February 2007 Year - 2007 Predicted Call Volume (Trend) (a)* Seasonal Index (%) (b) ** Estimated Call Volume with with Trend and Seasonal Effects (c) = (a).(b) Projected Cyclic Index (d) *** Call Volume Forecast (e) = ( c).(d) Call Volume Forecast Adjusted for Calender Variation f = ((e/30.4167)*number of days in the month) **** January 95017 0.99 94085.8334 0.99 93145 94931 February 95963 0.97 93448.7694 1.01 94383 86884 * 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 *** Estimation by inspection of cyclic projection in Figure 2 **** Actual Call Volume for January and February 2007 are 94530 and 87224 respectively.
SUMMARY AND FINAL REMARKS The procedure described in this paper can be applied to any Service Desk which has data for the past few years. The advantage of this procedure is, it is simple to understand and implement and at the same time a fairly accurate forecast can be made. An effective combination of mathematical calculations described in this paper with management s firsthand knowledge of the situation is required to achieve accurate forecasts. There are other relatively complex forecasting techniques, but I recommend the organizations to go through an evolutionary progression in adopting them. Start with a simple forecasting method as described in this paper, gain knowledge and move towards more sophisticated methods. Author Biography: Krishna Murthy Dasari is a Six Sigma Black Belt and a software quality professional with 12 years of experience in quality. He has worked in industries like manufacturing and IT. 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