CASE 1 THE SMALL ENGINE DOCTOR 13 The Small Engine Doctor is the name of a business developed by Thomas Brown, who is a mail carrier for the U.S. Postal Service. He had been a tinkerer since childhood, always taking discarded household gadgets apart in order to understand "what made them tick." As Tom grew up and became a typical suburbanite, he acquired numerous items of lawn and garden equipment. When Tom found out about a course in small engine repair offered at a local com- munity college, he jumped at the opportunity. Tom started small engine repair by dismantling his own equipment, overhauling it, and then reassembling it. Soon after completing the course in engine repair, he began to repair lawn mowers, rototillers, snowblow- ers, and other lawn and garden equipment for friends and neighbors. In the process, he acquired various equipment manuals and special tools. It was not long before Tom decided to turn his hobby into a part-time business. He placed an adver- tisement in a suburban shopping circular under the name of the Small Engine Doctor. Over the last two years, the business has grown enough to provide a nice supplement to his regular salary. Although the growth was welcomed, as the business is about to enter its third year of operation there are a number of concerns. The business is operated out of Tom's home. The basement is partitioned into a family room, a workshop, and an office. Originally, the office area was used to handle the advertising, order processing, and bookkeeping. All engine repair was done in the workshop. Tom's policy has been to stock only a lim- ited number of parts, ordering replacement parts as they are needed. This seemed to be the only practical way of dealing with the large variety of parts involved in repairing engines made by the dozen or so manu- facturers of lawn and garden equipment. Spare parts have proved to be the most aggra- vating problem in running the business. Tom started his business by buying parts from equipment dealers. This practice had several disadvantages. First, he had to pay retail for the parts. Second, most of the time the dealer had to back-order one or more parts for any given repair job. Parts ordered from the manu- facturer had lead times of anywhere from 30 to 120 days. As a result, Tom changed his policy and began to order parts directly from the factory. He found that shipping and handling charges ate into his prof- its, even though the part price was only 60% of retail. However, the two most important problems created by the replacement parts were lost sales and storage space. Tom attracted customers because of his qual- ity service and reasonable repair charges, which were possible because of his low overhead. Unfortunately, many potential customers would go to equipment dealers rather than wait several months for repair. The most pressing problem was storage space. While a piece of equipment was waiting for spare parts, it had to be stored on the premises. It did not take long for both his workshop and his one-car garage to overflow with equipment while he was waiting for spare parts. In the second year of operation, Tom actually had to suspend advertising as a tactic to limit customers due to lack of storage space. Tom has considered stocking inventory for his third year of operation. This practice will reduce pur- chasing costs by making it possible to obtain quantity discounts and more favorable shipping terms. He also hopes that it will provide much better turnaround time for the customers, improving both cash flow and sales. The risks in this strategy are uncontrolled inven- tory carrying costs and part obsolescence. Before committing himself to stocking spare parts, Tom wants to have a reliable forecast for busi- ness activity in the forthcoming year. He is confident enough in his knowledge of product mix to use an aggregate forecast of customer repair orders as a basis for selectively ordering spare parts. The fore- cast is complicated by seasonal demand patterns and a trend toward increasing sales. Tom plans to develop a sales forecast for the third year of operation. A sales history for the first two years is given in Table 6. TABLE 6 Small Engine Doctor Sales History 2005 2006 2005 2006 Month (units) (units) Month (units) (units) January February March April 18 May June 580823 21 July 28 46 20 August 20 32 10 29 September 14 27 32 October 8 13 26 44 November 6 11 58 December 26 52 ASSIGNMENT 1. Plot the data on a two-year time horizon from 2005 through 2006. Connect the data points to make a time series plot. 2. Develop a trend-line equation using linear regression and plot the results. 3. Estimate the seasonal adjustment factors for each month by dividing the average demand for corresponding months by the average of the corresponding trend-line forecasts. Plot the fitted values and forecasts for 2007 given by Trend Seasonal. 4. Smooth the time series using Holt's linear expo- nential smoothing with three sets of smoothing constants: (a =.1, B = .1), (a = .25, B = .25), and (a 5, .5). Plot the three sets of smoothed values on the time series graph. Generate forecasts through the end of the third year for each of the trend-adjusted exponential smoothing possibilities considered. 5. Calculate the MAD values for the two models that visually appear to give the best fits (the most accurate one-step-ahead forecasts). 6. If you had to limit your choice to one of the models in Questions 2 and 4, identify the model you would use for your business planning in 2007, and dis- cuss why you selected that model over the others. TABLE P-14 Month 2000 2001 2002 2003 2004 2005 2006 January 154 200 223 346 518 613 628 February 96 118 104 261 404 392 308 March 73 90 107 224 300 273 324 April 49 79 85 141 210 322 248 May 36 78 75 148 196 189 272 June 59 91 99 145 186 257 July 95 167 135 223 247 324 August 169 169 211 272 343 404 September 210 289 335 445 464 677 October 278 347 460 560 680 858 November 298 375 488 612 711 895 December 245 203 326 467 610 664 14. The monthly sales of the Cavanaugh Company, pictured in Figure 1 (bottom), are given in Table P-14. a. Perform a multiplicative decomposition of the Cavanaugh Company sales time series, assuming trend, seasonal, and irregular components. b. Would you use the trend component, the seasonal component, or both to forecast? c. Provide forecasts for the rest of 2006. TABLE P-18 Month 1988 1989 1990 1991 1992 1993 1994 1995 January 113.6 122.5 132.6 130.9 142.1 148.4 154.6 167.0 February 115.0 118.9 127.3 128.6 143.1 145.0 155.8 164.0 March 131.6 141.3 148.3 149.3 154.7 164.6 184.2 192.1 April 130.9 139.8 145.0 148.5 159.1 170.3 181.8 187.5 May 136.0 150.3 154.1 159.8 165.8 176.1 187.2 201.4 June 137.5 149.0 153.5 153.9 164.6 175.7 190.1 202.6 July 134.1 144.6 148.9 154.6 166.0 177.7 185.8 194.9 August 138.7 153.0 157.4 159.9 166.3 177.1 193.8 204.2 September 131.9 144.1 145.6 146.7 160.6 171.1 185.9 192.8 October 133.8 142.3 151.5 152.1 168.7 176.4 189.7 194.0 November 140.2 148.8 156.1 155.6 167.2 180.9 194.7 202.4 December 171.0 176.5 179.7 181.0 204.1 218.3 233.3 238.0 Source: Based on Survey of Current Business, 1989, 1993, 1996. 18. Table P-18 contains data values that represent the monthly sales (in billions of dol- lars) of all retail stores in the United States. Using the data through 1994, perform a decomposition analysis of this series. Comment on all three components of the series. Forecast retail sales for 1995 and compare your results with the actual val- ues provided in the table. TABLE P-19 Adjusted Month Seasonal Index Month Adjusted Seasonal Index January 120 July 153 February 137 August 151 March 100 September 95 April 33 October 60 May 47 November 82 June 125 December 97 Source: Based on Mt. Spokane Resort Hotel records. a. If 600 tourists were at the resort in January 2007, what is a reasonable estimate for February? b. The monthly trend equation is = 140 + 5t where t = 0 represents January 15, 2001. What is the forecast for each month of 2007? c. What is the average number of new tourists per month? 19. The adjusted seasonal indexes presented in Table P-19 reflect the changing volume of business of the Mt. Spokane Resort Hotel, which caters to family tourists in the summer and skiing enthusiasts during the winter months. No sharp cyclical varia- tions are expected during 2007.