The Water Department of the city of Wolf Creek, has to purchase untreated lake water from several administrative entities around the city in order to fulfill the water requirements of its population. Most of the water is treated and pumped at one of two plants – The Wolf Pack Plant and the Half Moon Plant. The Half Moon Plant is located on the southeast side of Fort Worth and is on a higher plain than the west-side Wolf Pack Plant. Both plants are required to operate in order to meet the city’s demand; however, the electrical cost of pumping water out of the Wolf Pack Plant is approximately 15% higher than for the Half Moon Plant because of its lower elevation. Because of the cost differential, the water pumped from the two plants has been slowly approaching a 60-40 split in favor of the Half Moon Plant. For budgetary reasons, the City Manager would like you to forecast the water processed and pumped at the Wolf Pack Plant. He will use your forecasts as a basis for estimating the associated electrical cost. You are informed that water consumption varies from fall to spring and summer to winter. There is also a gradual increase in the water demand at the Wolf Pack Plant because the total demand made by the population has slowly increased. 1. Using the Data in the table, compute the centered moving averages. What is the benefit derived from obtaining these moving averages? 2. Compute the seasonal indexes for each month. When does the Water Department experience the larges seasonal effect? Does this seem reasonable? Does there seem to be a seasonal pattern? 3. Deseasonalize the data and use the deseasonalized time series to determine the linear trend equation. What is the average increase in water use per month? How far into the future do you think the trend could be projected? 4. Assuming a multiplicative model, obtain the cyclical components. Does there seem to be a cyclical pattern? 5. Prepare a forecast of water use in Fort Worth for the last three months of 2006 and the first month of 2007 using only the trend equation. Use the seasonal indexes to adjust the deseasonalized forecasts. 6. In January 2007, the actual water use turned out to be 325.6. Discuss the forecasting error encountered here.
Month 2001 – 2002 2002- 2003 2003 -2004 2004 – 2005 2005 – 2006
Oct 365.5 361.3 429.7 354.6 312.9
Nov 319.9 307.7 331.2 292.2 368.3
Dec 309.6 312.8 291.3 279.2 316.3
Jan 327 294 296.4 268.5 316.3
Feb 285.6 258.2 267.4 251.8 275.2
Mar 358.9 300.2 319.4 287.8 283.3
Apr 326.5 402.3 350.2 336.4 286.2
May 324.6 367.3 447.4 350.6 352.7
Jun 352.5 349.5 476 371.5 512.6
Jul 616.4 469.5 540.3 479.2 529.2
Aug 531.2 628.7 617.5 462.5 488.6
Sep 403.6 428.7 429.9 421 461.4