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Case Analysis: Forecasting Food and Beverage Sales

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CASE ANALYSIS: FORECASTING FOOD AND BEVERAGE SALES Suzanne Michelle Gager QNT 531: Advanced Problems in Statistics and Research Methods Terrance C. Feravich March 20, 2006 Case Analysis: Forecasting Food and Beverage Sales Problem Definition The Vintage Restaurant is on Captiva Island, a resort community near Fort Myers, Florida. The restaurant, which is owned and operated by Karen Payne, has just completed its third year of operation. During that time, Karen has sought to establish a reputation for the restaurant as a high-quality dining establishment that specializes in fresh seafood. The efforts of Karen and her staff have proven successful, and her restaurant has become one of the best and fastest-growing restaurants on the island. Karen has concluded that to plan for the growth of the restaurant in the future, she needs to develop a system that will enable her to forecast food and beverage sales by month for up to one year in advance. Karen has the following data ($1000s) on total food and beverage sales for the three years of operation. Lost Beverage and Food Sales Case Vintage Restaurant Sales MONTH First Year Second Year Third Year January 242 263 282 February 235 238 255 March 232 247 265 April 178 193 205 May 184 193 210 June 140 149 160 July 145 157 166 August 152 161 174 September 110 122 126 October 130 130 148 November 152 167 173 December 206 230 235 The statistical Summary of the data is shown below: Year January February March April May June July August September October November December Total Sales 1 242 235 232 178 184 140 more.


216.94 May 1.043 221.18 June 0.798 169.22 July 0.831 176.22 August 0.865 183.43 September 0.636 134.87 October 0.725 153.74 November 0.874 185.34 December 1.192 252.78 Now assuming that the January sales for the fourth year turn out to be $295,000, the forecast error would be: 42220. Since a forecast error of $42,220 is quite large, Karen might be puzzled about the difference between your forecast and the actual sales value. The cycles can be easily studied if the trend itself is removed. This is done by expressing each actual value in the time series as a percentage of the calculated trend for the same date. The resulting time series has no trend, but oscillates around a central value of 100. A variety of factors are likely influencing data. It is very important in the study that these different influences or components be separated or decomposed out of the 'raw' data levels. Decomposition Analysis is the pattern generated by the time series and not necessarily the individual data values that offers to the manager who is an observer, a planner, or a controller of the system. Therefore, the Decomposition Analysis is used to identify several patterns that appear simultaneously in a time series. In general, there are four types of components in time series analysis: Seasonality, Trend, Cycling and Irregularity. Xt = St . Tt. Ct . I The first three components are deterministic and are called "Signals", while the last component is a random variable, "Noise". To be able to make a proper forecast, we must know to what extent each component is present in the data. more.


Predict Trend Sales for the next 12 months using the regression equation (x=37 to 48 corresponding to Jan of year 4 to Dec of year 4) Year Month Predicted Trend Sales X Y 4 January 37 207.08 =169.4143+1.0181*37 February 38 208.1 =169.4143+1.0181*38 March 39 209.12 =169.4143+1.0181*39 April 40 210.14 May 41 211.16 June 42 212.17 July 43 213.19 August 44 214.21 September 45 215.23 October 46 216.25 November 47 217.27 December 48 218.28 Step 5 Multiply the predicted trend sales by the seasonal index to get the Predicted Sales value for the next 12 months Year Month Seasonal index Predicted Trend Sales Predicted sales= Seasonal index * Trend sales 4 January 144.36% 207.08 299 =207.08*144.36% February 129.97% 208.1 270 =208.1*129.97% March 134.41% 209.12 281 =209.12*134.41% April 104.12% 210.14 219 =210.14*104.12% May 104.94% 211.16 222 =211.16*104.94% June 80.04% 212.17 170 =212.17*80.04% July 82.83% 213.19 177 August 85.30% 214.21 183 September 62.80% 215.23 135 October 70.03% 216.25 151 November 85.28% 217.27 185 December 115.93% 218.28 253 The monthly forecasts for the 12 months of the fourth year are as shown below: Month (yr.4) January February March April May June July August September October November December S. Index 1.398 1.293 1.322 1.023 1.043 0.798 0.831 0.865 0.636 0.725 0.874 1.192 Forecast 296.45755 274.19143 280.3411 216.9357 221.1768 169.2226 176.2205 183.4305 134.8691 153.7423 185.339 252.7735 Suppose the actual January sales for the fourth year turn out to be $295,000. The forecasted January sales are $296,458. Error between actual and forecasted sales = $296,458 - $295,000 = $1458 Percentage Error = This is an extremely small percentage error. Karen does not have to worry about this error and she can be assured that her forecast model is extremely good. more.

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