Solved Problem #2: see textbook (manual example using seasonal relatives)
Lesson 05 Forecasting & Smoothing Methods Solutions Solved Problem #1: see text book Solved Problem #2: see textbook (manual example using seasonal re...
Lesson 05 Forecasting & Smoothing Methods Solutions 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.
What does the use of sales data rather than demand data imply? Sales data does not take into account the demand which may have been greater than the actual sales. If the demand was actually greater than sales and the bakery could have met that demand, using sales would cause them to under forecast their full business potential.
1
#2: National Scan, Inc., sells radio frequency inventory tags. Monthly sales ($000) for a seven-month period were as follows: Month Feb Mar Apr May Jun Jul Aug a.
Sales 19 18 15 20 18 22 20
Plot the monthly data. Historical Data
25
20
15
10
5
0 0
1
2
3
4
5
6
7
8
Period Sales
b.
Forecast September sales volume in thousands of dollars using the following methods: Show your answers in the space provided. 1. 2. 3. 4. 5.
Naïve Five-month moving average Weighted moving average using .60 for August, .30 for July, and .10 for June Exponential smoothing with a smoothing constant of .20 Linear trend equation.
Month Sep
Naive 20
MA 19
WMA 20.4
ES 19.26
LT 20.86
2
#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.
Ft = 80 + 15t where F t = annual sales (000 bottles ) t = 0 corresponds to 1990 a.
Indicate how much the sales are increasing or decreasing? Sales are increasing by 15,000 bottles per year
b.
Predict sales for the year 2006 using the equation? This is a manual problem! t = 16 therefore the forecast for the year 2006 = 80 + 16*15 = 320 thousand bottles
#4: Freight car loadings over a 12-year period at a busy port are as follows: The units are in thousands of tons. Year 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 a.
Determine the linear trend equation for the freight car loadings. Forecast = 208.48 + 19 * year
b.
What is the slope? Interpret it. Slope = 19 thousand pounds Interpretation: the freight loadings are increasing 19 thousand pounds per year
3
c.
Use the trend equation to predict the freight loadings for years 20 and 21. Year 20 21
d.
Loadings 588.40 607.40
The manager intends to install new equipment when the loadings exceeds 800 (thousand tons) per year. Assuming the current trend continues the loading volume will reach that level in approximately what year? This is a manual problem! Solving the equation for t yields t = 31.13 years
#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
Ft = 70 + 5t 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. a.
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. January 181.5
February 173.4
March 166.25
4
#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 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Plot historical demand with forecast on the same graph. Historical Data & Seasonally Adjusted Linear Trend
180 160 140 120 100 80 60 40 20 0 0
10
20
30
40 Served
50
60
70
Forecast
#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 5
1 200 210 215 225 232
2 250 252 260 272 284
3 210 212 220 233 240
4 340 360 358 372 381
7
a.
Calculate the quarterly adjusted seasonal relatives.
Use the adjusted seasonal relative to determine what percentage shipments in quarter 4 are greater than shipments quarter 3. Quarter 4 shipments are 62.23% greater than shipments in quarter 3.