Using MAD, determine whether the forecast in Problem 5-15 or the forecast in the section concerning Wallace Garden Supply is more accurate. • 5-17 Data collected on the yearly demand for 50-pound bags of fertilizer at Wallace Garden Supply are shown in the following table. Develop a 3-year moving average to forecast sales. Then estimate demand again with a weighted moving average in which sales in the most recent year are given a weight of 2 and sales in the other 2 years are each given a weight of 1. Which method do you think is better?
Case study problems 5.13, 5.14, 5.16, 5.18, 5.20, 5.22, 5.23, 5.28, and case study 1 (Forecasting Monthly Sales). 5-13 Explain what would happen if the smoothing constant in an exponential smoothing model was equal to zero. Explain what would happen if the smoothing constant was equal to one. 5-14 Explain when a CMA (rather than an overall average) should be used in computing a seasonal index. Explain why this is necessary. 5-16 Using MAD, determine whether the forecast in Problem 5-15 or the forecast in the section concerning Wallace Garden Supply is more accurate. • 5-17 Data collected on the yearly demand for 50-pound bags of fertilizer at Wallace Garden Supply are shown in the following table. Develop a 3-year moving average to forecast sales. Then estimate demand again with a weighted moving average in which sales in the most recent year are given a weight of 2 and sales in the other 2 years are each given a weight of 1. Which method do you think is better? 5-18 Develop a trend line for the demand for fertilizer in Problem 5-17, using any computer software. 5-20 Use exponential smoothing with a smoothing constant of 0.3 to forecast the demand for fertilizer given in Problem 5-17. Assume that last period’s forecast for year 1 is 5,000 bags to begin the procedure. Would you prefer to use the exponential smoothing model or the weighted average model developed in Problem 5-17? Explain your answer. YEAR DEMAND FOR FERTILIZER (1,000s OF BAGS) 1 4 2 6 3 4 4 5 5 10 6 8 7 7 8 9 9 12 10 14 11 15 5-22 Sales of Cool-Man air conditioners have grown steadily during the past 5 years: The sales manager had predicted, before the business started, that year 1’s sales would be 410 air conditioners. Using exponential smoothing with a weight of α =0.30, α = 0.30, develop forecasts for years 2 through 6. • 5-23 Using smoothing constants of 0.6 and 0.9, develop forecasts for the sales of Cool-Man air conditioners (see Problem 5-22). YEAR SALES 1 450 2 495 3 518 4 563 5 584 6 ? 5-28 Sales of industrial vacuum cleaners at R. Lowenthal Supply Co. over the past 13 months are as follows: • Using a moving average with three periods, determine the demand for vacuum cleaners for next February. • Using a weighted moving average with three periods, determine the demand for vacuum cleaners for February. Use 3, 2, and 1 for the weights of the most recent, second most recent, and third most recent periods, respectively. For example, if you were forecasting the demand for February, November would have a weight of 1, December would have a weight of 2, and January would have a weight of 3. • Evaluate the accuracy of each of these methods. • What other factors might R. Lowenthal consider in forecasting sales? SALES ($1,000s) MONTH SALES ($1,000s) MONTH 11 January 14 August 14 February 17 September 16 March 12 October 10 April 14 November 15 May 16 December 17 June 11 January 11 July Case Study Forecasting Monthly Sales For years The Glass Slipper restaurant has operated in a resort community near a popular ski area of New Mexico. The restaurant is busiest during the first 3 months of the year, when the ski slopes are crowded and tourists flock to the area. When James and Deena Weltee built The Glass Slipper, they had a vision of the ultimate dining experience. As the view of surrounding mountains was breathtaking, a high priority was placed on having large windows and providing a spectacular view from anywhere inside the restaurant. Special attention was also given to the lighting, colors, and overall ambiance, resulting in a truly magnificent experience for all who came to enjoy gourmet dining. Since its opening, The Glass Slipper has developed and maintained a reputation as one of the “must visit” places in that region of New Mexico. While James loves to ski and truly appreciates the mountains and all that they have to offer, he also shares Deena’s dream of retiring to a tropical paradise and enjoying a more relaxed lifestyle on the beach. After some careful analysis of their financial condition, they knew that retirement was many years away. Nevertheless, they were hatching a plan to bring them closer to their dream. They decided to sell The Glass Slipper and open a bed and breakfast on a beautiful beach in Table 5.13 Monthly Revenue ($1,000s) Mexico. While this would mean that work was still in their future, they could wake up in the morning to the sight of the palm trees blowing in the wind and the waves lapping at the shore. They also knew that hiring the right manager would allow James and Deena the time to begin a semi-retirement in a corner of paradise. To make this happen, James and Deena would have to sell The Glass Slipper for the right price. The price of the business would be based on the value of the property and equipment as well as projections of future income. A forecast of sales for the next year MONTH 2011 2012 2013 January 438 444 450 February 420 425 438 March 414 423 434 April 318 331 338 May 306 318 331 June 240 245 254 July 240 255 264 August 216 223 231 September 198 210 224 October 225 233 243 November 270 278 289 December 315 322 335 is needed to help in the determination of the value of the restaurant. Monthly sales for each of the past 3 years are provided in Table 5.13. Discussion Questions 1. Prepare a graph of the data. On this same graph, plot a 12- month moving average forecast. Discuss any apparent trend and seasonal patterns.
2. Use regression to develop a trend line that could be used to forecast monthly sales for the next year. Is the slope of this line consistent with what you observed in question 1? If not, discuss a possible explanation.
3. Use the multiplicative decomposition model and these data to forecast sales for each month of the next year. Discuss why the slope of the trend equation with this model is so different from that of the trend equation in question 2.