Chapter 6 – Case Problem Set B. Arizona Crystal is a distributor of feldspar,
amethyst and other mystically powerful types of crystals. The owner of Arizona ...
Chapter 6 – Case Problem Set B Arizona Crystal is a distributor of feldspar, amethyst and other mystically powerful types of crystals. The owner of Arizona Crystal, Geri Moonbeam, is proud to be a part of the movement that is contributing to the higher spirituality of the world. Geri buys crystals from local collectors and then ships them out to wholesalers throughout the country. Geri pays cash for the crystals, but she extends credit to the wholesalers. As the business has grown, problems have arisen. When Geri buys more crystals than she can sell, inventory increases and cash flow problems arise. When Geri doesn't buy enough crystals, then she can't fill orders and that creates problems with her customers. She needs to base her buying decisions on accurate forecasts of the demand for crystals so she can avoid these problems. After consulting her tarot cards, Geri visits a friend from El Paso, Texas, who channels for a Wall Street tycoon who didn't survive the crash of 1929. He recommends that, since she only has twelve months of data, she should try using a moving average or exponential smoothing forecasting model. So Geri contacts you. She provides you with data on the number of crystals (in thousands) ordered during each of the past twelve months and asks you to help her develop a forecasting model. To do so, solve Problems 7 through 11 below.
Managerial Economics in a Global Economy, 7th Edition
7.
Use a three period moving average model to forecast the demand in January of 1993. Also calculate the RMSE for this model. Use the table below.
Month
Demand (A) Demand (F)
Jan-92
25.6
Feb-92
24.7
Mar-92
21.3
Apr-92
13.9
May-92
12.6
Jun-92
18.0
Jul-92
21.5
Aug-92
22.3
Sep-92
30.7
Oct-92
15.0
Nov-92
13.8
Dec-92
22.6
2
(A-F)
Managerial Economics in a Global Economy, 7th Edition
8.
Use a five period moving average model to forecast the demand in January of 1993. Also calculate the RMSE for this model. Use the table below to carry out your calculations. How does this model compare with the three period model?
Month
Demand (A) Demand (F)
Jan-92
25.6
Feb-92
24.7
Mar-92
21.3
Apr-92
13.9
May-92
12.6
Jun-92
18.0
Jul-92
21.5
Aug-92
22.3
Sep-92
30.7
Oct-92
15.0
Nov-92
13.8
Dec-92
22.6
2
(A-F)
Managerial Economics in a Global Economy, 7th Edition
9.
Use an exponential smoothing model with a weight of 0.6 to forecast demand in January of 1993. Also calculate the RMSE for this model. Use the mean value of 20.2 as your initial estimate. Use the table below to carry out your calculations. How does this model compare with the moving average models?
Month
Demand (A) Demand (F)
Jan-92
25.6
Feb-92
24.7
Mar-92
21.3
Apr-92
13.9
May-92
12.6
Jun-92
18.0
Jul-92
21.5
Aug-92
22.3
Sep-92
30.7
Oct-92
15.0
Nov-92
13.8
Dec-92
22.6
2
(A-F)
Managerial Economics in a Global Economy, 7th Edition
10.
Use an exponential smoothing model with a weight of 0.1 to forecast the demand in January of 1993. Also calculate the RMSE for this model. Use the mean value of 20.2 as your initial estimate. Use the table below to carry out your calculations. How does this model compare with the moving average models and with the previously estimated moving average model?
Month
Demand (A) Demand (F)
Jan-92
25.6
Feb-92
24.7
Mar-92
21.3
Apr-92
13.9
May-92
12.6
Jun-92
18.0
Jul-92
21.5
Aug-92
22.3
Sep-92
30.7
Oct-92
15.0
Nov-92
13.8
Dec-92
22.6
2
(A-F)
Managerial Economics in a Global Economy, 7th Edition
11.
Recall that the degree of smoothing associated with a moving average model is a function of the number of periods used to calculate the average. Recall also that the degree of smoothing associated with an exponential smoothing model is a function of the weight used to calculate the estimate. What is the moving average forecast of demand for January of 1993 when the maximum possible smoothing is applied? What is the exponential smoothing forecast for January of 1993 when the maximum possible smoothing is applied? What is the weight used to obtain the maximum possible smoothing? Use this weight to fill in the table below and calculate the RMSE. What is your conclusion regarding the best forecasting model?
Month
Demand (A) Demand (F)
Jan-92
25.6
Feb-92
24.7
Mar-92
21.3
Apr-92
13.9
May-92
12.6
Jun-92
18.0
Jul-92
21.5
Aug-92
22.3
Sep-92
30.7
Oct-92
15.0
Nov-92
13.8
Dec-92
22.6
2
(A-F)
Managerial Economics in a Global Economy, 7th Edition
12.
Continuing in the same vein as Problem 11, what is the moving average forecast of demand for January of 1993 when the minimum possible smoothing is applied? What is the exponential smoothing forecast for January of 1993 when the minimum possible smoothing is applied? What is the weight used to obtain the minimum possible smoothing? Use this weight to fill in the table below and calculate the RMSE. Now what is your conclusion regarding the best forecasting model?
Month
Demand (A) Demand (F)
Jan-92
25.6
Feb-92
24.7
Mar-92
21.3
Apr-92
13.9
May-92
12.6
Jun-92
18.0
Jul-92
21.5
Aug-92
22.3
Sep-92
30.7
Oct-92
15.0
Nov-92
13.8
Dec-92
22.6
2
(A-F)
Managerial Economics in a Global Economy, 7th Edition
