Forecasting Case Study 2t6m2d

310 • CHAPTER 8

FORECASTING

25. The following data were collected on the study of the relationship between a company’s retail sales and advertising dollars:

(a) Obtain a linear regression line for the data. (b) Compute a correlation coefficient and determine the strength of the linear relationship. (c) Using the linear regression equation, develop a forecast of retail sales for advertising dollars of $40,000.

CASE: Bram-Wear Lenny Bram, owner and manager of Bram-Wear, was analyzing performance data for the men’s clothing retailer. He was concerned that inventories were high for certain clothing items, meaning that the company would potentially incur losses due to the need for significant markdowns. At the same time, it had run out of stock for other items early in the season. Some customers appeared frustrated by not finding the items they were looking for and needed to go elsewhere. Lenny knew that the problem, though not yet serious, needed to be addressed immediately.

Background Bram-Wear was a retailer that sold clothing catering to young, urban, professional men. It primarily carried upscale, casual attire, as well as a small quantity of outerwear and footwear. Its success did not come from carrying a large product variety, but from a very focused style with an abundance of sizes and colors. Bram-Wear had extremely good financial performance over the past five years. Lenny had attributed the company’s success to a group of excellent buyers. The buyers seemed able to accurately target the style preferences of their customers and correctly forecast product quantities. One challenge was keeping up with customer buying patterns and trends.

The Data To determine the source of the problem, Lenny had requested forecast and sales data by product category. Looking at the sheets of data, it appeared that the problem was not with the specific styles or items carried in stock; rather, the problem appeared to

be with the quantities ordered by the buyers. Specifically, the problem centered on two items: an athletic shoe called Urban Run and the five-pocket cargo jeans. Urban Run was a popular athletic shoe that had been carried by Bram-Wear for the past four years. Quarterly data for the past four years are shown in the table. The company seemed to always be out of stock of this athletic shoe. The model used by buyers to forecast sales for this item had been seasonal exponential smoothing. Looking at the data, Lenny wondered if this was the best method to use. It seemed to work well in the beginning, but now he was not so sure. The data for the five-pocket cargo jean seemed also to point to a forecasting problem. When the product was introduced last year, it was expected to have a large upward trend. The buyers believed the trend would continue and used an exponential smoothing model with trend to forecast sales. However, they seemed to have too much inventory of this product. As with the Urban Run athletic shoe, Lenny wondered if the right forecasting model was being applied to the data. It seemed he would have to dig out his old operations management text to solve this problem.

CASE: THE EMERGENCY ROOM (ER) AT NORTHWEST GENERAL (A) • 311

Case Questions 1. Is seasonal exponential smoothing the best model for forecasting Urban Run athletic wear? Why? 2. Explain what has happened to the data for Urban Run. What are the consequences of continuing to use seasonal exponential smoothing? What model would you use? Generate a forecast for the four quarters of the fourth year using your model. Determine your forecast error and the inventory consequences.

3. Is exponential smoothing with trend the best model for forecasting five-pocket cargo jeans? Why? 4. What method would you use to forecast monthly cargo jean demand for the second year given the previous year’s monthly demand? Explain why you selected your approach. Generate the forecasts for each month of the second year with your method. Determine your forecast error and the inventory consequences.

CASE: The Emergency Room (ER) at Northwest General (A) Jenn Kostich is the new department director for emergency services at Northwest General Hospital. One of her responsibilities is to ensure proper staffing in the emergency room (ER) by scheduling nurses to appropriate shifts. This has historically been a problem for the ER. The former director did not base nurse schedules on forecasts, but used the same fixed schedule week after week. Jenn had recently received her degree in operations management. She knew that schedules needed to be based on forecasts

of demand. She needed to start by analyzing historical data in order to determine the best forecasting method to use. Jenn’s assistant provided her with information on patient arrivals in the ER by hour and day of the week for the previous month, October. October was considered a typical month for the ER, and Jenn thought it was a good starting point. Jenn reviewed the information (shown in the chart) that she had requested and wondered where to begin.

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Internet Homework Problems See our Internet home page, at www.pearsonhighered.com/render, for additional homework problems, Problems 5-42 to 5-50.

Case Study Forecasting Attendance at SWU Football Games Southwestern University (SWU), a large state college in Stephenville, Texas, 30 miles southwest of the Dallas/Fort Worth metroplex, enrolls close to 20,000 students. In a typical town–gown relationship, the school is a dominant force in the small city, with more students during fall and spring than permanent residents. A longtime football powerhouse, SWU is a member of the Big Eleven conference and is usually in the top 20 in college football rankings. To bolster its chances of reaching the elusive and long-desired number-one ranking, in 2005 SWU hired the legendary Bo Pitterno as its head coach. Although the numberone ranking remained out of reach, attendance at the five Saturday home games each year increased. Prior to Pitterno’s arrival, attendance generally averaged 25,000 to 29,000 per game. Season ticket sales bumped up by 10,000 just with the announcement of the new coach’s arrival. Stephenville and SWU were ready to move to the big time! The immediate issue facing SWU, however, was not NCAA ranking. It was capacity. The existing SWU stadium,

built in 1953, has seating for 54,000 fans. The following table indicates attendance at each game for the past six years. One of Pitterno’s demands upon ing SWU had been a stadium expansion, or possibly even a new stadium. With attendance increasing, SWU s began to face the issue head-on. Pitterno had wanted dormitories solely for his athletes in the stadium as an additional feature of any expansion. SWU’s president, Dr. Marty Starr, decided it was time for his vice president of development to forecast when the existing stadium would “max out.” He also sought a revenue projection, assuming an average ticket price of $20 in 2011 and a 5% increase each year in future prices.

Discussion Questions 1. Develop a forecasting model, justify its selection over other techniques, and project attendance through 2012. 2. What revenues are to be expected in 2011 and 2012? 3. Discuss the school’s options.

Southwestern University Football Game Attendance, 2005–2010

GAME

2005 ATTENDEES OPPONENT Baylor

2006 ATTENDEES OPPONENT 36,100

ATTENDEES

OPPONENT

1

34,200

2*

39,800

Texas

40,200

Nebraska

46,500

Texas Tech

3

38,200

LSU

39,100

UCLA

43,100

Alaska

4**

26,900

Arkansas

25,300

Nevada

27,900

Arizona

5

35,100

USC

36,200

Ohio State

39,200

Rice

2008 GAME

ATTENDEES

Oklahoma

2007 35,900

2009 OPPONENT

ATTENDEES

TCU

2010 OPPONENT

ATTENDEES

OPPONENT

1

41,900

Arkansas

42,500

Indiana

46,900

LSU

2*

46,100

Missouri

48,200

North Texas

50,100

Texas

3

43,900

Florida

44,200

Texas A&M

45,900

Prairie View A&M

4**

30,100

Miami

33,900

Southern

36,300

Montana

5

40,500

Duke

47,800

Oklahoma

49,900

Arizona State

*Homecoming games **During the fourth week of each season, Stephenville hosted a hugely popular southwestern crafts festival. This event brought tens of thousands of tourists to the town, especially on weekends, and had an obvious negative impact on game attendance. Source: J. Heizer and B. Render. Operations Management, 6th ed. Upper Saddle River, NJ: Prentice Hall, 2001, p. 126.

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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 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

TABLE 5.14 Monthly Revenue (in $1,000s)

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 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 5.14.

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 on these data. Use this model 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.

MONTH

2008

2009

2010

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

Internet Case Study See our Internet home page, at www.pearsonhighered.com/render, for the additional case study on Akron Zoological Park. This case involves forecasting attendance at Akron’s zoo.

APPENDIX 5.1

FORECASTING WITH QM FOR WINDOWS

191

Bibliography Berenson, Mark L., David M. Levine, and Timothy C. Kriehbiel. Business Statistics: Concepts and Applications, 10th ed. Upper Saddle River, NJ: Prentice Hall, 2006. Billah, Baki, Maxwell L. King Ralph D. Snyder, and Anne B. Koehler. “Exponential Smoothing Model Selection for Forecasting,” International Journal of Forecasting 22, 2, (April–June 2006): 239–247.

Heizer, J., and B. Render. Operations Management, 9th ed. Upper Saddle River, NJ: Prentice Hall, 2008. Hyndman, Rob J. “The Interaction Between Trend and Seasonality,” International Journal of Forecasting 20, 4 (October–December 2004): 561–563.

Black, Ken. Business Statistics: For Contemporary Decision Making, 6th ed. John Wiley & Sons, Inc., 2009.

Hyndman, Rob J., and Anne B. Koehler. “Another Look at Measures of Forecast Accuracy,” International Journal of Forecasting 22, 4 (October 2006): 679–688.

Diebold, F. X. Elements of Forecasting, 2nd ed. Cincinnati: South-Western College Publishing, 2001.

Li, X. “An Intelligent Business Forecaster for Strategic Business Planning,” Journal of Forecasting 18, 3 (May 1999): 181–205.

Gardner, Everette Jr. “Exponential Smoothing: The State of the Art—Part II,” International Journal of Forecasting 22, 4 (October 2006): 637–666.

Meade, Nigel. “Evidence for the Selection of Forecasting Methods,” Journal of Forecasting 19, 6 (November 2000): 515–535.

Granger, Clive W., and J. M. Hashem Pesaran. “Economic and Statistical Measures of Forecast Accuracy,” Journal of Forecasting, 19, 7 (December 2000): 537–560.

Snyder, Ralph D., and Roland G. Shami. “Exponential Smoothing of Seasonal Data: A Comparison,” Journal of Forecasting 20, 3 (April 2001): 197–202.

Hanke, J. E., and D. W. Wichern. Business Forecasting, 9th ed. Upper Saddle River, NJ: Prentice Hall, 2009.

Yurkiewicz, J. “Forecasting Software Survey,” OR/MS Today 35, 3 (August 2008): 54–63.

Appendix 5.1 Forecasting with QM for Windows In this section, we look at our other forecasting software package, QM for Windows. QM for Windows can project moving averages (both simple and weighted), do simple and trendadjusted exponential smoothing, handle least squares trend projection, solve regression problems, and use the decomposition method. To develop forecasts in QM for Windows, select Module on the toolbar and select Forecasting. Then either click the new document icon or click File—New—Time Series Analysis to enter a new time series problem. Specify the number of past observations and enter a title, if desired. To illustrate QM for Windows, we will use the Port of Baltimore data from Table 5.5. The number of past observations was eight in that example. When you enter those data, the screen shown in Program 5.8A opens and allows for data input. Once the data is entered, click the

PROGRAM 5.8A QM for Windows Forecasting Methods

Click the arrow in the Method window to select the desired methods.

Enter the data.

You can change these names by typing over them.

HIGHLINE FINANCIAL SERVICES, LTD.

CASE

Highline Financial Services provides three categories of service to its clients. Managing partner Freddie Mack is getting ready to prepare financial and personnel hiring (or layoff) plans for the coming year. He is a bit perplexed by the following printout he obtained, which seems to show oscillating demand for the three categories of services over the past eight quarters:  

 

Service

or promotion, and competition doesn’t change, predict demand for the services the company offers for the next four quarters. Note that there are not enough data to develop seasonal relatives. Nonetheless, you should be able to make reasonably good, approximate intuitive estimates of demand. What general observations can you make regarding demand? Should Freddie have any concerns? Explain.

Year

Quarter

A

B

C

 

 

1

1

 60

95

93

Year

Quarter

A

B

C

2

1

72

85

102

Service

 

2

 45

85

90

 

3

100

92

110

 

2

51

75

  75

 

4

 75

65

90

 

3

112

85

 110

 

4

85

50

100

Examine the demand that this company has experienced for the three categories of service it offers over the preceding two years. Assuming nothing changes in of advertising

Acar, Yavuc, and Everette S. Gardner, Jr. “Forecasting Method Selection in a Global Supply Chain.” International Journal of Forecasting 28, no. 4 (October– December 2012), 842–48. Bonomo, Charles. “Forecasting from the Center of the Supply Chain.” Journal of Business Forecasting Methods and Systems 22, no. 1 (Spring 2003), p. 3. Byrne, Robert F. “Forecasting Performance for North American Consumer Products.” Journal of Business Forecasting 31, no. 3 (Fall 2012), p. 12.

Hanke, John, and Dean Wichern. Business Forecasting, 9th ed. Upper Saddle River, NJ: Pearson, 2009. Hopp, Wallace J., and Mark I. Spearman. Factory ­Physics, 3rd ed. New York: McGraw-Hill, 2008. Wilson, J. Holton, Barry Keating, and John Galt Solutions. Business Forecasting with ForecastX, 6th ed. New York: McGraw-Hill, 2009.

SELECTED BIBLIOGRAPHY AND FURTHER READINGS

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Chapter 12 • Forecasting a. Using Excel, develop the multiple regression equation for these data. b. What is the coefficient of determination for this regression equation? Do you think the superintendent is correct in his beliefs? c. Montgomery County has an average SOL score of 74 with an average teacher’s salary of $27,500 and an average teacher tenure of 7.8 years. The superintendent

549

has proposed to the school board a salary increase that would raise the average salary to $30,000 and a benefits program with a goal of increasing the average tenure to nine years. He has suggested that if the board es his proposals the average SOL score will increase to 80. Is he correct according to the forecasting model?

CASE PROBLEM 12.1 Forecasting at State University During the past few years the legislature has severely reduced funding for State University. In reaction, the istration at State has significantly raised tuition each year for the past five years. A bargain five years ago, State is now considered an expensive state-ed university. Some parents and students now question the value of a State education, and applications for ission have declined. Since a portion of state educational funding is based on a formula tied to enrollments, State has maintained its enrollment levels by going deeper into its applicant pool and accepting less qualified students. On top of these problems, an increase in the collegeage population is expected in this decade. Key of the state legislature have told the university istration that State will be expected to absorb additional students during this decade. However, because of the

economic outlook and the budget situation, State should not expect any funding increases for additional facilities, classrooms, dormitory rooms, or faculty. The university already has a classroom deficit in excess of 25%, and class sizes are above the average of their peer institutions. The president of the university, Tanisha Lindsey, established several task forces consisting of faculty and s to address these problems. These groups made a number of recommendations, including the implementation of total quality management (TQM) practices and more in-depth, focused planning. Discuss in general how forecasting might be used for planning to address these specific problems and the role of forecasting in initiating a TQM approach. Include in your discussion the types of forecasting methods that might be used.

CASE PROBLEM 12.2 The University Bookstore Student Computer Purchase Program The University Bookstore is owned and operated by State University through an independent corporation with its own board of directors. The bookstore has three locations on or near the State University campus. It stocks a range of items, including textbooks, trade books, logo apparel, drawing and educational supplies, and computers and related products such as printers, modems, and software. The bookstore has a program to sell personal computers to incoming freshmen and other students at a substantial educational discount partly ed on from computer manufacturers. This means that the bookstore just covers computer costs with a very small profit margin remaining. Each summer all incoming freshmen and their parents come to the State campus for a three-day orientation program. The students come in groups of 100

throughout the summer. During their visit the students and their parents are given details about the bookstore’s computer purchase program. Some students place their computer orders for the fall semester at this time, while others wait until later in the summer. The bookstore also receives orders from returning students throughout the summer. This program presents a challenging supply chain management problem for the bookstore. Orders come in throughout the summer, many only a few weeks before school starts in the fall, and the computer suppliers require at least six weeks for delivery. Thus, the bookstore must forecast computer demand to build up inventory to meet student demand in the fall. The student computer program and the forecast of computer demand have repercussions all along the bookstore supply chain. The bookstore has a warehouse near campus where it must store all computers since it has no storage space at (Continued)

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its retail locations. Ordering too many computers not only ties up the bookstore’s cash reserves, but also takes up limited storage space and limits inventories for other bookstore products during the bookstore’s busiest sales period. Since the bookstore has such a low profit margin on computers, its bottom line depends on these other products. As competition for good students has increased, the university has become very quality-conscious and insists that all university facilities provide exemplary student service, which for the bookstore means meeting all student demands for computers when the fall semester starts. The number of computers ordered also affects the number of temporary warehouse and bookstore workers that must be hired for handling and assisting with PC installations. The number of truck trips from the warehouse to the bookstore each day of fall registration is also affected by computer sales. The bookstore student computer purchase program has been in place for 14 years. Although the student population has remained stable during this period, computer

sales have been somewhat volatile. Following is the historical sales data for computers during the first month of fall registration:

Year 1 2 3 4 5 6 7

Computers Sold 518 651 708 921 775 810 856

Year 8 9 10 11 12 13 14

Computers Sold 792 877 693 841 1009 902 1103

Develop an appropriate forecast model for bookstore management to use to forecast computer demand for the next fall semester and indicate how accurate it appears to be. What other forecasts might be useful to the bookstore in managing its supply chain?

CASE PROBLEM 12.3 Cascades Swim Club The Cascades Swim Club has 300 stockholders, each holding one share of stock in the club. A share of club stock allows the shareholder’s family to use the club’s heated outdoor pool during the summer upon payment of annual hip dues of $175. The club has not issued any stock in years, and only a few of the existing shares come up for sale each year. The board of directors isters the sale of all stock. When a shareholder wants to sell, he or she turns the stock into the board, which sells it to the person at the top of the waiting list. For the past few years, the length of the waiting list has remained relatively steady at approximately 20 names. However, during the past winter two events occurred that have suddenly increased the demand for shares in the club. The winter was especially severe, and subzero weather and heavy ice storms caused both the town and the county pools to buckle and crack. The problems were not discovered until maintenance crews began to prepare the pools for the summer, and repairs cannot be completed until the fall. Also during the winter, the manager of the local country club had an argument with her board of directors and one night burned down the clubhouse. Although the pool itself was not damaged, the dressing room facilities, showers, and snack bar were destroyed. As a result of these two events, the Cascades Swim Club was inundated with applications to purchase shares. The

waiting list suddenly grew to 250 people as the summer approached. The board of directors of the swim club had refrained from issuing new shares in the past because there never was a very great demand, and the demand that did exist was usually absorbed within a year by stock turnover. In addition, the board has a real concern about overcrowding. It seemed like the present hip was about right, and there were very few complaints about overcrowding, except on holidays such as Memorial Day and the Fourth of July. However, at a recent board meeting a number of new applicants had attended and asked the board to issue new shares. In addition, a number of current shareholders suggested that this might be an opportunity for the club to raise some capital for needed repairs and to improve some of the existing facilities. This was tempting to the board. Although it had set the share price at $500 in the past, the board could set it at a much higher level now. In addition, an increase in attendance could create a need for more lifeguards. Before the board of directors could make a decision on whether to sell more shares and, if so, how many, the board felt they needed more information. Specifically, they would like a forecast of the average number of people (family , guests, etc.) who might attend the pool each day during the summer with the current number of shares.

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The board of directors has the following daily attendance records for June through August from the previous summer; it thinks the figures would provide accurate estimates for the summer. M-139 T-273 W-172 Th-275 F-337 Sa-402 Su-487

W-380 Th-367 F-359 Sa-463 Su-578 M-287 T-247

F-193 Sa-378 Su-461 M-242 T-177 W-245 Th-390

Su-399 M-197 T-273 W-213 Th-303 F-262 Sa-447

T-177 W-161 Th-308 F-256 Sa-391 Su-400 M-224

Th-238 F-224 Sa-368 Su-541 M-235 T-218 W-271

M-198 T-310 W-347 Th-393 F-421 Sa-595 Su-497 M-341 T-291

W-356 Th-322 F-419 Sa-516 Su-478 M-303 T-223 W-315 Th-258

F-284 Sa-417 Su-474 M-194 T-207 W-215 Th-304 F-331 Sa-407

Su-399 M-275 T-241 W-190 Th-243 F-277 Sa-241 Su-384 M-246

T-239 W-274 Th-205 F-361 Sa-411 Su-419 M-258 T-130 W-195

551

Th-259 F-232 Sa-317 Su-369 M-361

Develop a forecasting model to forecast daily demand during the summer.

CASE PROBLEM 12.4 Forecasting enger Arrivals at the Gotham International Airport Since the terrorist attacks of 9/11 and the ensuing measures by the federal Transportation Security istration (TSA) to increase airline security, airports have faced the problem of long waiting lines and waiting times at security gates. One of the key components of any effort by the TSA to operationally improve airport security procedures while reducing enger waiting times and inconvenience is forecasting enger arrivals at security checkpoints in order to determine how many security checkpoints and staff are needed. At the Gotham International Airport, TSA

Year 1

Year 2

operations analysts would like to forecast enger arrivals for next July, the airport's busiest travel month of the year, for the purpose of determining how many security checkpoints they should staff during the month in order that waiting lines and times will not be excessively long. Demand for airline travel has generally been increasing during the past three years. There are two main concourses at Gotham International, East and West, each serving different airlines. The following table shows enger arrivals at the West concourse for 10 days (selected randomly) in two-hour segments from 4:00 A.M. to 10:00 P.M. for the month of July for the past three years.

Day

4–6 A.M.

6–8 A.M.

8–10 A.M.

10–noon

noon–2 P.M.

2–4 P.M.

4–6 P.M.

6–8 P.M.

8–10 P.M.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

2400 1900 2300 2200 2400 2600 1900 2000 2400 2600 3100 2800 2700 2400 3300 3500 2900 3400

2700 2500 3100 3200 3300 2800 2800 2700 3200 3300 3900 3400 3800 3500 3700 4000 4100 3800

3200 3100 2500 3100 3400 3500 3100 2500 3600 3100 4100 3900 4300 4100 4000 3800 3900 4200

1400 1600 1500 2200 1700 1500 1200 1500 1600 200 2200 1900 2100 2400 2600 2300 2400 2000

1700 1800 1500 1900 2200 1700 1500 2000 2100 2500 2600 2100 2400 3000 2600 2700 3000 2500

1800 2000 1800 2400 2100 1900 2000 2300 2500 2600 2300 2500 2400 3200 2700 3100 3200 3000

1600 1800 1900 2100 2000 1500 1400 1900 1800 2400 2500 2000 2400 2600 2900 3000 2500 2200

800 900 1100 1200 1000 1100 900 1000 1400 1100 1100 1200 1200 1200 1000 900 1100 1000

200 300 200 400 600 300 400 200 200 400 300 300 400 700 300 200 500 300

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Day 19 20 21 22 23 24 25 26 27 28 29 30

4–6 A.M. 3600 3700 4400 4200 4500 4600 4500 4200 4500 4300 4900 4700

6–8 A.M. 3600 3700 4400 4500 4500 4600 4300 4300 4500 4200 4100 4500

8–10 A.M. 4000 4000 4500 4300 4700 4600 4400 4500 5100 4300 4200 4100

10–noon 2300 2200 2600 2500 2700 2500 2900 3000 3300 2800 3100 3000

Develop a forecast for daily enger arrivals at the West concourse at Gotham for each time period for July

noon–2 P.M. 2600 2600 3300 3400 3400 3200 3300 4000 4000 3500 3600 4000

2–4 P.M. 2800 2700 3400 3600 3500 3500 3300 3400 3700 4000 3900 3700

4–6 P.M. 2600 2400 3000 3100 2900 2800 3300 3000 3100 3300 3400 3400

6–8 P.M. 1200 1200 1200 1400 1200 1300 1500 1500 1200 1100 1400 1200

8–10 P.M. 200 200 400 300 300 300 400 600 300 400 500 500

of year 4. Discuss the various forecast model variations that might be used to develop this forecast.

REFERENCES Box, G. E. P., and G. M. Jenkins. Time Series Analysis: Forecasting and Control, 2nd ed. Oakland, CA: Holden-Day, 1976. Brown, R. G. Statistical Forecasting for Inventory Control. New York: McGraw-Hill, 1959. Chambers, J. C., K. M. Satinder, and D. D. Smith. “How to Choose the Right Forecasting Technique.” Harvard Business Review (July–August 1971), pp. 45–74. Gardner, E. S. “Exponential Smoothing: The State of the Art.” Journal of Forecasting 4(1; 1985).

Gardner, E. S., and D. G. Dannenbring. “Forecasting with Exponential Smoothing: Some Guidelines for Model Selection.” Decision Sciences 11(2; 1980), pp. 370–383. Makridakis, S., S. C. Wheelwright, and V. E. McGee. Forecasting: Methods and Applications, 2nd ed. New York: John Wiley, 1983. Tersine, R. J., and W. Riggs. “The Delphi Technique: A LongRange Planning Tool.” Business Horizons 19(2; 1976).