# Forecasting Lost Sales- The Carlson Department Store Case Solution Sample

QUESTION

Case Study : Forecasting Lost Sales

The Carlson Department Store suffered heavy damage when a hurricane struck on August 31, 2003. The store was closed for four months (Sept – Dec 2003) and Carlson is now involved in a dispute with its insurance company concerning the amount of lost sales during the time the store was closed. Two key issues must be resolved:

1. The amount of sales Carlson would have made if the hurricane had not struck; and
2. Whether Carlson is entitled to any compensation for excess sales from increased business activity after the storm

More than \$8 billion in federal disaster relief and insurance money came into the county, resulting in increased sales at department stores and numerous other businesses.

The table below shows the sales data for the 48 months preceding the storm. The following table reports total sales for the 48 months preceding the storm for all department stores in the county, as well as the total sales in the county for the four months the Carlson Department Store was closed. Management asks you to analyze this data and develop estimates of the lost sales at the Carlson Department Store for the months of September through December 2003. Management also wants to determine whether a case can be made for excess storm-related sales during the same period. If such a case can be made, Carlson is entitled to compensation for excess sales it would have earned in addition to ordinary sales.

Table 1 – Sales for Carlson Department Store, Sept ’99 through Aug ‘03

 Month 1999 2000 2001 2002 2003 January 1.45 2.31 2.31 2.56 February 1.8 1.89 1.99 2.28 March 2.03 2.02 2.42 2.69 April 1.99 2.23 2.45 2.48 May 2.32 2.39 2.57 2.73 June 2.2 2.14 2.42 2.37 July 2.13 2.27 2.4 2.31 August 2.43 2.21 2.5 2.23 September 1.71 1.9 1.89 2.09 October 1.90 2.13 2.29 2.54 November 2.74 2.56 2.83 2.97 December 4.20 4.16 4.04 4.35

Table 2 – Department Store Sales for the County, Sept ’99 through Dec ‘03

 Month 1999 2000 2001 2002 2003 January 46.8 46.8 43.8 48 February 48 48.6 45.6 51.6 March 60 59.4 57.6 57.6 April 57.6 58.2 53.4 58.2 May 61.8 60.6 56.4 60 June 58.2 55.2 52.8 57 July 56.4 51 54 57.6 August 63 58.8 60.6 61.8 September 55.8 57.6 49.8 47.4 69 October 56.4 53.4 54.6 54.6 75 November 71.4 71.4 65.4 67.8 85.2 December 117.6 114 102 100.2 121.8

Managerial Repoert

Prepare a report for the management of the Carlson department store that summarizes your findings, forecasts and recommendations. Include the following:

1. An estimate of the sales had there been no hurricane.

Hint: Remember to graph this time series data over the 48-month period to help you determine the type of approach to use to determine the forecast sales for the final 4 months of 2003 for Carlson department store. Is there a trend in the data (growth or decline)? Is there seasonality in the data (this is a department store … Christmas time and beginning of school are normally big sales periods)? Is there both trend and seasonality?

1. An estimate of the countywide department store sales had there been no hurricane.

Hint: By comparing the forecast of county-wide department store sales with actual sales, one can determine whether or not there are excess storm-related sales. By computing what is known as a “lift factor” – the ratio of actual sales to forecast sales – you have a measure of the magnitude of excess sales, if these do indeed exist

1. Your final estimate of lost sales for the Carlson Department store for Sept – Dec 2003.

Case Analysis

1) An estimate of sales had there been no hurricane

Plotting the 48 months data in excel sheet

From the above graph we can easily conclude that there is trend and seasonality present in the sales pattern over the 48 months. The slope and intercept given by the trend line equation is

Slope= 0.0092

Intercept= 2.2089

Now to find the seasonality index by average method

 1999 2000 2001 2002 Average SI September 1.71 1.9 1.89 2.09 1.8975 0.779661 October 1.9 2.13 2.29 2.54 2.215 0.910118 November 2.74 2.56 2.83 2.97 2.775 1.140216 December 4.2 4.16 4.04 4.35 4.1875 1.720596 Total 10.55 10.75 11.05 11.95 Average 2.6375 2.6875 2.7625 2.9875

Now as we know the September month will start from 57th data in the sheet (refer the excel sheet attached)

By putting the value in the trend equation and multiplying with seasonality index

For example, for the month of September Trend component forecast = 0.0092*57+2.2089= 2.7333

Forecast with seasonality = 2.7333*0.78= 2.13

Similarly calculating for others we get-

 Trend Forecast with seasonality September 2.7333 2.13 October 2.7425 2.50 November 2.7517 3.14 December 2.7609 4.75

b) Forecast of sales of countrywide departmental stores

Trend equation= 0.1278x+59.244

Seasonality index calculation

 Average SI Forecast September 55.8 57.6 49.8 47.4 69 55.92 0.750403 49.92323 October 56.4 53.4 54.6 54.6 75 58.8 0.78905 52.59523 November 71.4 71.4 65.4 67.8 85.2 72.24 0.969404 64.74088 December 117.6 114 102 100.2 121.8 111.12 1.491143 99.77538

 Month Actual Forecast Lift Factor September 69 49.92323 1.382122 October 75 52.59523 1.425985 November 85.2 64.74088 1.316015 December 121.8 99.77538 1.220742

c) Final estimate of lost sales

Final estimate would be = Forecast x Lift Factor

 Month Forecast Lift Factor Actual September 2.13 1.382122 2.946648 October 2.50 1.425985 3.558795 November 3.14 1.316015 4.128259 December 4.75 1.220742 5.796996

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