Hospitality hotels forecasts monthly labor needs

Management Operation Problem FORECASTING

ORECASTING PROBLEMS

Question 2

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Hospitality Hotels forecasts monthly labor needs. (a) Given the following monthly labor figures, make a forecast for June using a three-period moving average and a five-period moving average. (Round answers to 2 decimal places, e.g. 15.25.)

Month

Actual Values

January

36

February

42

March

42

April

45

May

44

3-Period Moving Average

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5-Period Moving Average

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(b) What would be the forecast for June using the naïve method? (Round answers to 2 decimal places, e.g. 15.25.)

Forecast for June

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(c) If the actual labor figure for June turns out to be 45, what would be the forecast for July using each of these models? (Round answers to 2 decimal places, e.g. 15.25.)

3-Period Moving Average

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5-Period Moving Average

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Naïve method

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(d) Compare the accuracy of these models using the mean absolute deviation (MAD). (Round answers to 2 decimal places, e.g. 15.25.)

MAD (3-period)

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MAD (5-period)

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MAD (naïve)

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(e) Compare the accuracy of these models using the mean squared error (MSE). (Round answers to 2 decimal places, e.g. 15.25.)

MSE (3-period)

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MSE (5-period)

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MSE (naïve)

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Question 3

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The manager of a small health clinic would like to use exponential smoothing to forecast demand for laboratory services in the facility. However, she is not sure whether to use a high or low value of. To make her decision, she would like to compare the forecast accuracy of a high and low on historical data. She has decided to use an α=0.7 for the high value and α=0.1 for the low value. Given the following historical data, which do you think would be better to use? (Round answers to 2 decimal place, e.g. 15.25)

Week

Demand (lab requirements)

1

322

2

342

3

326

4

360

5

386

6

342

Forecasts using α = 0.1, MAD

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Forecasts using α = 0.7, MAD

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Using http://edugen.wileyplus.com/edugen/art2/common/pixel.gif provides a better historical fit based on the MAD criterion.

Question 4

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Demand at Nature Trails Ski Resort has a seasonal pattern. Demand is highest during the winter, as this is the peak ski season. However, there is some ski demand in the spring and even fall months. The summer months can also be busy as visitors often come for summer vacation to go hiking on the mountain trails. The owner of Nature Trails would like to make a forecast for each season of the next year. Total annual demand has been estimated at 4,020 visitors. Given the last two years of historical data, what is the forecast for each season of the next year?

Visitors

Season

Year 1

Year 2

Fall

196

225

Winter

1,415

1,616

Spring

504

601

Summer

693

818

(Round your answers to 0 decimal place, the tolerance is +/-1.)

Season

Forecast

Fall

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Winter

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Spring

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Summer

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Question 5

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Rosa's Italian restaurant wants to develop forecasts of daily demand for the next week. The restaurant is closed on Mondays and experiences a seasonal pattern for the other six days of the week. Mario, the manager, has collected information on the number of customers served each day for the past two weeks. If Mario expects total demand for next week to be around 350, what is the forecast for each day of next week? (Round answers to 1 decimal place, e.g. 15.2.)

Day

Number of customers

Week 1

Week 2

Tuesday

52

48

Wednesday

36

32

Thursday

35

30

Friday

89

97

Saturday

98

99

Sunday

65

69

Day

Forecast

Tuesday

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Wednesday

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Thursday

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Friday

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Saturday

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Sunday

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Question 6

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The president of a company was interested in determining whether there is a correlation between sales made by different sales teams and hours spent on employee training. These figures are shown.

Sales (in thousands)

Training Hours

12

8

34

12

29

10

46

15

8

4

a. Compute the correlation coefficient for the data. (Round your answer to 4 decimal places, the tolerance is +/-0.0001.) The correlation coefficient is http://edugen.wileyplus.com/edugen/art2/common/pixel.gif What is your interpretation of this value? (Do not round your intermediate computations to answer this question.) There is http://edugen.wileyplus.com/edugen/art2/common/pixel.gif linear association between sales and training hours.

b. Using the data, what would you expect sales to be if training was increased to eighteen hours? Use the linear regression model. (Round your answer to 2 decimal places, the tolerance is +/-0.01.) Sales = http://edugen.wileyplus.com/edugen/art2/common/pixel.gif (in thousands)

Question 7

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The number of students enrolled at Spring Valley Elementary has been steadily increasing over the past five years. The school board would like to forecast enrollment for years 6 and 7 in order to better plan capacity. Use a linear trend line to forecast enrollment for years 6 and 7. (Round answers to 1 decimal place, e.g. 15.1.)

Year

Enrollment

1

220

2

245

3

256

4

289

5

310

Year 6 forecast

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Year 7 forecast

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Question 8

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Happy Lodge Ski Resorts tries to forecast monthly attendance. The management has noticed a direct relationship between the average monthly temperature and attendance.

Month

Average Temperature

Resort Attendance (in thousands)

1

24

41

2

25

34

3

31

38

4

38

31

5

40

27

a. Given five months of average monthly temperatures and corresponding monthly attendance, compute a linear regression equation of the relationship between the two. Round your answer to 2 decimal places, the tolerance is +/-0.01. For negative amounts use a negative sign preceding the number eg -45. Resort attendance = http://edugen.wileyplus.com/edugen/art2/common/pixel.gif + http://edugen.wileyplus.com/edugen/art2/common/pixel.gif (average temperature) If next month’s average temperature is forecast to be 45 degrees, use your linear regression equation to develop a forecast. (To achieve this answer do not round your interim calculations. Round your answer to 1 decimal place, the tolerance is +/-0.1.) Resort attendance = http://edugen.wileyplus.com/edugen/art2/common/pixel.gif thousand attendees.

b. Compute a correlation coefficient for the data and determine the strength of the linear relationship between average temperature and attendance. How good a predictor is temperature for attendance? (Round your answer to 2 decimal places, the tolerance is +/-0.01.) The correlation coefficient is http://edugen.wileyplus.com/edugen/art2/common/pixel.gif It indicates that the average temperature http://edugen.wileyplus.com/edugen/art2/common/pixel.gif predictor of resort attendance. (Do not round your intermediate computations to answer this question.)

Question 9

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Small Wonder, an amusement park, experiences seasonal attendance. It has collected two years of quarterly attendance data and made a forecast of annual attendance for the coming year. Compute the seasonal indexes for the four quarters and generate quarterly forecasts for the coming year, assuming annual attendance for the coming year to be 1525.

Quarter

Park Attendance (in thousands)

Year 1

Year 2

Fall

352

391

Winter

156

212

Spring

489

518

Summer

314

352

Quarter

Average Seasonal Index

Fall

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Winter

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Spring

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Summer

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Quarter

Forecast of Average Seasonal Demand

Fall

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Winter

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Spring

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Summer

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(For seasonal indices: round your intermediate computations to 2 decimal places and final answers to 3 decimal places, the tolerance is +/- 0.005.) (For forecasts: use average seasonal indices from your previous answers for computations, round your answers to 0 decimal places, the tolerance is +/- 5.)

Question 10

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Given the following data, use exponential smoothing with α = 0.2 and α = 0.5 to generate forecasts for periods 2 through 6. Use MAD and MSE to decide which of the two models produced a better forecast.

Period

Actual

Forecast

1

15

17

2

18

3

14

4

16

5

13

6

16

Period

Actual

Forecast

α = 0.2

α = 0.5

1

15

17

17

2

18

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3

14

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4

16

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5

13

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6

16

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MAD:

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MSE:

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Exponential smoothing using α = http://edugen.wileyplus.com/edugen/art2/common/pixel.gif yields lower MSE.

(Round your answers to 2 decimal places, the tolerance is +/-0.05)

Question 11

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Pumpkin Pies Galore is trying to forecast sales of pies for the month of December. Demand for pies in September, October, and November has been 220, 315, and 396, respectively. Edith, the company’s owner, uses a three-period weighted moving average to forecast sales. Based on her experience, she chooses to weight September as 0.1, October as 0.3, and November as 0.6. (Round your answers to 1 decimal place, the tolerance is +/-0.1.)

a. What would Edith’s forecast for December be? Forecast using a weighted moving average = http://edugen.wileyplus.com/edugen/art2/common/pixel.gif

b. What would her forecast be using the naïve method? Forecast using the naïve approach = http://edugen.wileyplus.com/edugen/art2/common/pixel.gif

c. If actual sales for December turned out to be 439 pies, which method was better (use MAD)? Absolute deviation using a weighted moving average = http://edugen.wileyplus.com/edugen/art2/common/pixel.gif Absolute deviation using naïve method = http://edugen.wileyplus.com/edugen/art2/common/pixel.gif . (For computation use only December data.) The http://edugen.wileyplus.com/edugen/art2/common/pixel.gif approach is better.

Question 12

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A company has used three different methods to forecast sales for the past five months. Use MAD and MSE to evaluate the performance of the three methods.

(a) Which forecasting method performed best?

Period

Actual

Method A

Method B

Method C

1

10

10

9

8

2

8

11

10

11

3

12

12

8

10

4

11

13

12

11

5

12

14

11

12

MAD

MSE

Method A

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Method B

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Method C

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(b) Which of these is actually the naïve method? http://edugen.wileyplus.com/edugen/art2/common/pixel.gif

(Round your answers to 1 decimal place, no tolerance)

44

44.67

43.6

45

43.67