# Forecasting & Smoothing Methods

**Forecasting & Smoothing Methods**

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Solved Problem #1: see text book

Solved Problem #2: see textbook (manual example using seasonal relatives)

Solved Problem #3: see textbook

Solved Problem #4: see textbook (you do not have to do this problem manually, use the template and notice how the template answers differ slightly from the seasonal relatives provided in the manual example)

To avoid manually entering the data into the templates it can be copied and pasted from Data Sets on the Lesson Page. Use **“copy, paste special, values”** to transfer the data to the template.

#1: A commercial bakery has recorded sales (in dozens) for three products, as shown below.

Day |
Blueberry |
Cinnamon |
Cupcakes |
||||||

Muffins |
buns |
||||||||

1 | 30 | 18 | 45 | ||||||

2 | 34 | 17 | 26 | ||||||

3 | 32 | 19 | 27 | ||||||

4 | 34 | 19 | 23 | ||||||

5 | 35 | 22 | 22 | ||||||

6 | 30 | 23 | 48 | ||||||

7 | 34 | 23 | 29 | ||||||

8 | 36 | 25 | 20 | ||||||

9 | 29 | 24 | 14 | ||||||

10 | 31 | 26 | 18 | ||||||

11 | 35 | 27 | 47 | ||||||

12 | 31 | 28 | 26 | ||||||

13 | 37 | 29 | 27 | ||||||

14 | 34 | 31 | 24 | ||||||

15 | 33 | 33 | 22 | ||||||

a. Determine the Naïve forecast for day 16. |

b. What does the use of sales data rather than demand data imply?

#2: National Scan, Inc., sells radio frequency inventory tags. Monthly sales ($000) for a seven-month period were as follows:

Month |
Sales |

Feb | 19 |

Mar | 18 |

Apr | 15 |

May | 20 |

Jun | 18 |

Jul | 22 |

Aug | 20 |

- Plot the monthly data.

- Forecast September sales volume in thousands of dollars using the following methods: Show your answers in the space provided.

1. Naïve

2. Five-month moving average

3. Weighted moving average using .60 for August, .30 for July, and .10 for June

4. Exponential smoothing with a smoothing constant of .20

5. Linear trend equation.

#3: A cosmetics manufacturer’s marketing department has developed a linear trend equation that can be used to predict annual sales of its popular Hand & Foot Cream.

*F*_{t}* *=80+15*t where*

*F ** _{t}*=

*annual sales*(000

*bottles*)

*t *= 0*corresponds to*1990

* *

- Indicate how much the sales are increasing or decreasing?

- Predict sales for the year 2006 using the equation? This is a manual problem!

#4: Freight car loadings over a 12-year period at a busy port are as follows: The units are in thousands of tons.

Year |
Loadings |

1 | 220 |

2 | 245 |

3 | 280 |

4 | 275 |

5 | 300 |

6 | 310 |

7 | 350 |

8 | 360 |

9 | 400 |

10 | 380 |

11 | 420 |

12 | 450 |

13 | 460 |

14 | 475 |

15 | 500 |

16 | 510 |

17 | 525 |

18 | 541 |

- Determine the linear trend equation for the freight car loadings.

- What is the slope? Interpret it.

#5: A manager of a store that sells and installs spas wants to prepare a forecast for January, February and March of next year. Her forecasts are a combination of trend and seasonality.

The linear trend equation is

*F*_{t}* *=70+5*t where*

*t *=0* corresponds to June of last year*

The seasonal relatives are 1.10 for January, 1.02 for February, and .95 for March.

- What demand should she predict for January, February and March of next year? This is a manual problem! If you need some hints on this problem, refer to solved problem #2 in the textbook.

#6: Obtain estimates of daily relatives for the number of customers at a restaurant for the evening meal given the past 4 weeks of historical data. Day 1 is day 1 of week 1, day 8 is day 1 of week 2, etc.

Day |
Served |

1 | 80 |

2 | 75 |

3 | 78 |

4 | 95 |

5 | 130 |

6 | 136 |

7 | 40 |

8 | 82 |

9 | 77 |

10 | 80 |

11 | 94 |

12 | 125 |

13 | 135 |

14 | 42 |

15 | 84 |

16 | 77 |

17 | 83 |

18 | 96 |

19 | 135 |

20 | 140 |

21 | 37 |

22 | 87 |

23 | 82 |

24 | 98 |

25 | 103 |

26 | 144 |

27 | 144 |

28 | 48 |

a. Construct a graph that will enable you to visualize the daily variation in meals served.

b. What are the daily adjusted seasonal relatives?

c. Plot the adjusted seasonal relatives on a graph for each day of the week?

- Determine the forecast for meals to be served for the next 7 days.

- Plot historical demand with forecast on the same graph.

#7: A farming cooperative manager wants to estimate quarterly relatives for grain shipments, based on the 5 years of data shown below (quantities are in metric tons). You will have to enter this data into the template manually.

QUARTER |
||||

Year |
1 |
2 |
3 |
4 |

1 | 200 | 250 | 210 | 340 |

2 | 210 | 252 | 212 | 360 |

3 | 215 | 260 | 220 | 358 |

4 | 225 | 272 | 233 | 372 |

5 | 232 | 284 | 240 | 381 |

a. Calculate the quarterly adjusted seasonal relatives.

b. Use the adjusted seasonal relative to determine what percentage shipments in quarter 4 are greater than shipments quarter 3.