The Saki motorcycle dealer in the MinneapolisSt. Paul area wants to make an accurate forecast of demand for the Saki Super TXII motorcycle during the next month. Because the manufacturer is in Japan, it is difficult to send motorcycles back or reorder if the proper number is not ordered a month ahead. From sales records, the dealer has accumulated the following data for the past year:
The manager of the Carpet City outlet needs to make an accurate forecast of the demand for Soft Shag carpet (its biggest seller). If the manager does not order enough carpet from the carpet mill, customers will buy their carpet from one of Carpet City's many competitors . The manager has collected the following demand data for the past 8 months:
The Fastgro Fertilizer Company distributes fertilizer to various lawn and garden shops . The company must base its quarterly production schedule on a forecast of how many tons of fertilizer will be demanded from it. The company has gathered the following data for the past 3 years from its sales records:
Graph the demand data in Problem 3. Can you identify any trends, cycles, or seasonal patterns?
The chairperson of the department of management at State University wants to forecast the number of students who will enroll in production and operations management (POM) next semester, in order to determine how many sections to schedule. The chair has accumulated the following enrollment data for the past eight semesters:
The manager of the Petroco Service Station wants to forecast the demand for unleaded gasoline next month so that the proper number of gallons can be ordered from the distributor. The owner has accumulated the following data on demand for unleaded gasoline from sales during the past 10 months:
The Victory Plus Mutual Fund of growth stocks has had the following average monthly price for the past 10 months:
Compute the exponentially smoothed forecast with a = .40, the adjusted exponential smoothing forecast with a = .40 and b = .30, and the linear trend line forecast. Compare the accuracy of the three forecasts, using cumulative error and MAD , and indicate which forecast appears to be most accurate.
The Bayside Fountain Hotel is adjacent to County Coliseum, a 24,000-seat arena that is home to the city's professional basketball and ice hockey teams and that hosts a variety of concerts, trade shows, and conventions throughout the year. The hotel has experienced the following occupancy rates for the past 9 years, since the coliseum opened:
Compute an exponential smoothing forecast with a = .20, an adjusted exponential smoothing forecast with a = .20 and b = .20, and a linear trend line forecast. Compare the three forecasts, using MAD and average error ( ), and indicate which seems to be most accurate.
Emily Andrews has invested in a science and technology mutual fund. Now she is considering liquidating and investing in another fund. She would like to forecast the price of the science and technology fund for the next month before making a decision. She has collected the following data on the average price of the fund during the past 20 months:
Eurotronics manufactures components for use in small electronic products such as computers, CD players, and radios at plants in Belgium, Germany, and France. The parts are transported by truck to Hamburg, where they are shipped overseas to customers in Mexico, South America, the United States, and the Pacific Rim. The company has to reserve space on ships months and sometimes years in advance. This requires an accurate forecasting model. Following are the number of cubic feet of container space the company has used in each of the past 18 months:
Develop a forecasting model that you believe would provide the company with relatively accurate forecasts for the next year and indicate the forecasted shipping space required for the next 3 months.
The Whistle Stop Cafe in Weems, Georgia, is well known for its popular homemade ice cream, made in a small plant in back of the cafe. People drive all the way from Atlanta and Macon to buy the ice cream. The two women who own the cafe want to develop a forecasting model so they can plan their ice cream production operation and determine the number of employees they need to sell ice cream in the cafe. They have accumulated the following sales records for their ice cream for the past 12 quarters:
Develop an adjusted exponential smoothing model with a = .50 and b = .50 to forecast demand and assess its accuracy using cumulative error ( E ) and average error ( ). Does there appear to be any bias in the forecast?
For the demand data in Problem 11, develop a seasonally adjusted forecast for 2004. (Use a linear trend line model to develop a forecast estimate for 2006.) Which forecast model do you perceive to be more accurate: the exponential smoothing model from Problem 11 or the seasonally adjusted forecast?
Develop a seasonally adjusted forecast for the demand data for fertilizer found in Problem 3. Then use a linear trend line model to compute a forecast estimate for demand in year 4.
Monaghan's Pizza delivery service has randomly selected 8 weekdays during the past month and recorded orders for pizza at four different time periods per day:
Develop a seasonally adjusted forecasting model for daily pizza demand and forecast demand for each of the time periods for a single upcoming day.
The Cat Creek Mining Company mines and ships coal. It has experienced the following demand for coal during the past 8 years:
Develop an adjusted exponential smoothing model ( a = .30, b = .20) and a linear trend line model and compare the forecast accuracy of the two by using MAD . Indicate which forecast seems to be more accurate.
The Northwoods Outdoor Company is a catalog sales operation that specializes in outdoor recreational clothing. Demand for its items is very seasonal, peaking during the Christmas season and during the spring. It has accumulated the following data for orders per season (quarter) during the past 5 years:
Metro Food Vending operates vending machines in office buildings , the airport, bus stations , colleges, and other businesses and agencies around town, and it operates vending trucks for building and construction sites. The company believes its sandwich sales follow a seasonal pattern. It has accumulated the following data for sandwich sales per season during the past 4 years:
Develop a seasonally adjusted forecast model for these sandwich sales data. Forecast demand for each season for 2006 by using a linear trend line estimate for sales in 2006. Do the data appear to have a seasonal pattern?
The emergency room at the new Community Hospital selected every other week during the past 5 months to observe the number of patients during two parts of each weekthe weekend (Friday through Sunday) and weekdays (Monday through Thursday). They typically experience greater patient traffic on weekends than during the week:
Develop a seasonally adjusted forecasting model for the number of patients during each part of the week for week 11.
Aztec Industries has developed a forecasting model that was used to forecast during a 10-month period. The forecasts and actual demand were as follows :
Measure the accuracy of the forecast by using MAD, MAPD , and cumulative error. Does the forecast method appear to be accurate?
RAP Computers assembles personal computers from generic parts it purchases at a discount, and it sells the units via phone orders it receives from customers responding to the company's ads in trade journals. The business has developed an exponential smoothing forecast model to forecast future computer demand. Actual demand for the company's computers for the past 8 months as well as a forecast are shown in the following table:
Develop an exponential smoothing forecast with a = .20 for the demand data in Problem 1. Compare this forecast with the 3-month moving average computed in part (a) of Problem 1, using MAD , and indicate which forecast seems to be more accurate.
The Jersey Dairy Products Company produces cheese, which it sells to supermarkets and food-processing companies. Because of concerns about cholesterol and fat in cheese, the company has seen demand for its products decline during the past decade . It is now considering introducing some alternative low-fat dairy products and wants to determine how much available plant capacity it will have next year. The company has developed an exponential smoothing forecast with a = .40 to forecast cheese. The actual demand and the forecasts from the model are as follows:
Assess the accuracy of the forecast model by using MAD and cumulative error. If the exponential smoothing forecast model does not appear to be accurate, determine whether a linear trend model would provide a more accurate forecast.
The manager of the Ramona Inn Hotel near Cloverleaf Stadium believes that how well the local Blue Sox professional baseball team is playing has an impact on the occupancy rate at the hotel during the summer months. Following are the number of victories for the Blue Sox (in a 162-game schedule) for the past 8 years and the hotel occupancy rates:
Develop a linear regression model for these data and forecast the occupancy rate for next year if the Blue Sox win 88 games .
Carpet City wants to develop a means to forecast its carpet sales. The store manager believes that the store's sales are directly related to the number of new housing starts in town. The manager has gathered data from county records on monthly house construction permits and from store records on monthly sales. These data are as follows:
The manager of Gilley's Ice Cream Parlor needs an accurate forecast of the demand for ice cream. The store orders ice cream from a distributor a week ahead; if the store orders too little, it loses business, and if it orders too much, the extra must be thrown away. The manager believes that a major determinant of ice cream sales is temperature (i.e., the hotter the weather, the more ice cream people buy). Using an almanac, the manager has determined the average daytime temperature for 10 weeks, selected at random, and from store records he has determined the ice cream consumption for the same 10 weeks. These data are summarized as follows:
Compute the coefficient of determination for the data in Problem 25 and explain its meaning.
Administrators at State University believe that decreases in the number of freshman applications that they have experienced are directly related to tuition increases . They have collected the following enrollment and tuition data for the past decade:
Develop a linear trend line model for the freshman applications data at State University in Problem 27.
Explain the numerical value of the slope of the linear regression equation in Problem 25.
Some members of management of the Fairface Cosmetics Firm believe that demand for its products is related to the promotional activities of local department stores where the cosmetics are sold. However, others in management believe that other factors, such as local demographics , are stronger determinants of demand behavior. The following data for local annual promotional expenditures for Fairface products and local annual unit sales for Fairface lip gloss have been collected from 20 stores selected at random from different localities:
Based on these data, does it appear that the strength of the relationship between sales and promotional expenditures is sufficient to warrant using a linear regression forecasting model? Explain your response.
Employees at Precision Engine Parts Company produce parts according to exact design specifications. The employees are paid according to a piece-rate system, wherein the faster they work and the more parts they produce, the greater their chances for monthly bonuses. Management suspects that this method of pay may contribute to an increased number of defective parts. A specific part requires a normal, standard time of 23 minutes to produce. The quality control manager has checked the actual average times to produce this part for 10 different employees during 20 days selected at random during the past month and determined the corresponding percentage of defective parts, as follows.
Develop a linear regression model relating average production time to percentage defects to determine whether a relationship exists and the percentage of defective items that would be expected with a normal production time of 23 minutes.
Apperson and Fitz is a chain of clothing stores that caters to high school and college students. It publishes a quarterly catalog and operates a Web site that features provocatively attired males and females. The Web site is very expensive to maintain, and company executives are not sure whether the number of hits at the site relate to sales (i.e., people may be looking at the site's pictures only). The Web master has accumulated the following data for hits per month and orders placed at the Web site for the past 20 months:
Develop a linear regression model for these data and indicate whether there appears to be a strong relationship between Web site hits and orders. What would be the forecast for orders with 50,000 hits per month?
The Gametime Hat Company manufactures baseball caps that have various team logos in an assortment of designs and colors. The company has had monthly sales for the past 24 months as follows:
Develop a forecast model using the method you believe best and justify your selection by using a measure (or measures) of forecast accuracy.
Infoworks is a large computer discount store that sells computers and ancillary equipment and software in the town where State University is located. Infoworks has collected historical data on computer sales and printer sales for the past 10 years, as follows:
Develop an exponential smoothing model with a = .30 for the data in Problem 34 to forecast printer demand in year 11 and compare its accuracy to the linear trend line forecast developed in (a).
Arrow Air is a regional East Coast airline that has collected data for the percentage available seats occupied on its flights for four quarters(1) JanuaryMarch, (2) AprilJune, (3) JulySeptember, and (4) OctoberDecemberfor the past 5 years. Arrow Air also has collected data for the average percentage fare discount for each of these quarters, as follows:
Develop an adjusted exponential smoothing forecast model ( a = .40 and b = .40) for the data in Problem 36 to forecast seat occupancy and compare its accuracy to the seasonally adjusted model developed in (a).
The consumer loan department at Central Union Bank and Trust wants to develop a forecasting model to help determine its potential loan application volume for the coming year. Because adjustable-rate home mortgages are based on government long- term treasury note rates, the department collected the following data for 3- to 5-year treasury note interest rates for the past 24 years:
Develop an appropriate forecast model for the bank to use to forecast treasury note rates in the future and indicate how accurate it appears to be compared to historical data.
The busiest time of the day at the Taco Town fast-food restaurant is between 11:00 A.M. and 2:00 P.M. Taco Town's service is very labor dependent, and a critical factor for providing quick service is the number of employees on hand during this 3-hour period. To determine the number of employees it needs during each hour of the 3-hour lunch period, Taco Town requires an accurate forecasting model. Following are the number of customers served at Taco Town during each hour of the lunch period for the past 20 weekdays:
Develop a forecast model that you believe will best forecast Taco Town's customer demand for the next day and explain why you selected this model.
The Wellton Fund is a balanced mutual fund that includes a mix of stocks and bonds . Following are the year-end share prices of the fund and Dow Jones Industrial Average (DJIA) for a 20-year period:
Develop a linear regression model for these data and forecast the fund share price for a DJIA of 12,000. Does there appear to be a strong relationship between the fund's share price and the DJIA?
The Valley United Soccer Club has boys' and girls ' travel soccer teams at all age levels up to 18 years. The club has been successful and grown in popularity over the years; however, an obstacle to its continued growth is a shortage of practice and game soccer fields in the area. The club has tried to make a case to the town council and the parks and recreation committee that it needs more soccer fields to accommodate the increasing number of kids who want to play on club teams. The number of kids who have played soccer on club teams and the town's population for the past 15 years are as follows:
The soccer club wants to develop a forecasting model to demonstrate to the town council its expected growth in the future.
The Port of Savannah is considering an expansion of its container terminal. The port has experienced the following container throughput during the past 12 years, expressed as TEUs (i.e., 20- foot equivalent units, a standard unit of measure for containers):
The admission data for freshmen at Tech during the past 10 years are as follows:
Tech's admission objective is a class of 5,000 entering freshmen, and Tech wants to forecast the percentage of offers it will likely have to make in order to achieve this objective.
The State of Virginia has instituted a series of standards of learning (SOL) tests in math, history, English, and science that all high school students must pass with a grade of 70 before they are allowed to graduate and receive their diplomas. The school superintendent of Montgomery County believes the tests are unfair because the test scores are closely related to teacher salary and tenure (i.e., the years a teacher has been at a school). The superintendent has sampled 12 other county school systems in the state and accumulated the following data for average teacher salary and average teacher tenure:
Tech administrators believe their freshman applications are influenced by two variables : tuition and the size of the applicant pool of eligible high school seniors in the state. The following data for an 8-year period show the tuition rates (per semester) and the sizes of the applicant pool for each year:
In Problem 34, Infoworks believes its printer sales are also related to the average price of its printers. It has collected historical data on average printer prices for the past 10 years, as follows:
The manager of the Bayville police department motor pool wants to develop a forecast model for annual maintenance on police cars, based on mileage in the past year and age of the cars. The following data have been collected for eight different cars :
The dean of the college of business at Tech has initiated a fund-raising campaign. One of the selling points he plans to use with potential donors is that increasing the college's private endowment will improve its ranking among all business schools , as published each year by the magazine The Global News and Business Report . He would like to demonstrate that there is a relationship between funding and the rankings. He has collected the following data, showing the private endowments ($1,000,000s) and annual budgets ($1,000,000s) from state and private sources for eight of Tech's peer institutions plus Tech, and the ranking of each school: