Chapter 6 – Case Problem Set A. In 1974, Vanguard World Xpress was founded
by Yanos Zarkov, a second generation immigrant from Eastern Europe.
Chapter 6 – Case Problem Set A In 1974, Vanguard World Xpress was founded by Yanos Zarkov, a second generation immigrant from Eastern Europe. The company produces custom crates, boxes, and other packaging materials that are used by exporters of delicate scientific devices. The success of the company is the result of a commitment to quality and service to the customer. Recently, it has become more difficult for Yanos to provide dependable service while, at the same time, containing costs. One of the tradeoffs faced by VWX is between inventory costs and production backlogs. Inventory costs result from the storage of raw and finished packaging materials. Production backlogs occur if there is not sufficient inventory to fill an order, and they result in unsatisfied customers. Yanos feels that accurate demand forecasts would allow the company to contain inventory costs and eliminate production backlogs. The local university recently instituted an intern program, so Yanos contacted the director of the program and agreed to hire a student. It turns out to be you. He asks his accountant to obtain accurate quarterly sales data for the past three years, in millions of dollars, and hands it to you. The data are listed below. With the guidance of your crusty old economics adviser you begin to develop a forecasting model for VWX. Your adviser's recommendations are given as Problems 1 through 6 below. Period Sales Period Sales
1.
1990.1 6.2 1991.3 12.8
1990.2 8.6 1991.4 12.4
1990.3 8.8 1992.1 9.4
1990.4 9 1992.2 14.9
1991.1 5.2 1992.3 13.8
1991.2 10 1992.4 13.9
Plot the data on the graph below. Do you see evidence of a secular trend? Seasonal variation? Cyclical variation? Comment on each of these time-series components and on the methods that can be used to estimate them.
Managerial Economics in a Global Economy, 7th Edition
Period
Managerial Economics in a Global Economy, 7th Edition
.4 92 19
.3 92 19
.2 92 19
.1 92 19
.4 19
91
.3 91 19
.2 91 19
.1 91 19
.4 90 19
.3 90 19
.2 90 19
.1 90 19
Salse
16 15 14 13 12 11 10 9 8 7 6 5 4
2.
Estimate the linear trend using regression analysis. Use the estimated trend equation to fill in the blanks in the table that follows. Note that A is the actual value and F is the forecast value of sales. Plot a line based on the forecast values of sales on the graph for Problem 1. Plot the forecast errors (A-F) on the graph below. What time-series components give rise to these forecast errors? Calculate the RMSE and comment on the accuracy of the forecasts that are derived using this method. Can the RMSE be calculated directly from the regression output?
Period
Trend
Sales (A) Sales (F)
1990.1
1
6.2
1990.2
2
8.6
1990.3
3
8.8
1990.4
4
9
1991.1
5
5.2
1991.2
6
10
1991.3
7
12.8
1991.4
8
12.4
1992.1
9
9.4
1992.2
10
14.9
1992.3
11
13.8
1992.4
12
13.9
(A-F)
(A-F)2
Managerial Economics in a Global Economy, 7th Edition
Period
Managerial Economics in a Global Economy, 7th Edition .4
92
19
.3
92
19
.2
92
19
.1
92
19
.4
91
19
.3
91
19
.2
91
19
.1
91
19
.4
90
19
.3
90
19
.2
90
19
.1
90
19
Forecast Errors 2
1
0
-1
-2
-3
-4
-5
3.
Estimate the log-linear trend using regression analysis. Calculate the growth rate that is implied by the estimated slope coefficient. Use the log-linear trend equation to fill in the blanks in the table that follows. Note that lnF is the forecast natural logarithm of sales and the F is the antilog of this value. Calculate the RMSE and comment on the accuracy of the forecasts yielded by this method. Can the RMSE be calculated directly from the regression output? Compare these forecasts with the ones you calculated for Problem 2.
Period
Sales (A) Sales (lnF)
1990.1
6.2
1990.2
8.6
1990.3
8.8
1990.4
9
1991.1
5.2
1991.2
10
1991.3
12.8
1991.4
12.4
1992.1
9.4
1992.2
14.9
1992.3
13.8
1992.4
13.9
Sales (F)
(A-F)
(A-F)2
Managerial Economics in a Global Economy, 7th Edition
4.
Estimate a seasonally adjusted linear trend equation using regression analysis with dummy variables. Use the equation to fill in the blanks in the table below. Plot the forecast errors on the graph that follows. Compare this graph with that from Problem 2. Calculate the RMSE and comment on the accuracy of the forecasts yielded by this method. Compare these forecasts with those you calculated previously.
Period
Trend
Sales (A)
1990.1
1
6.2
1990.2
2
8.6
1990.3
3
8.8
1990.4
4
9
1991.1
5
5.2
1991.2
6
10
1991.3
7
12.8
1991.4
8
12.4
1992.1
9
9.4
1992.2
10
14.9
1992.3
11
13.8
1992.4
12
13.9
Sales (F)
(A-F)
2
(A-F)
Managerial Economics in a Global Economy, 7th Edition
Period
Managerial Economics in a Global Economy, 7th Edition .4
92
19
.3
92
19
.2
92
19
.1
92
19
.4
91
19
.3
91
19
.2
91
19
.1
91
19
.4
90
19
.3
90
19
.2
90
19
.1
90
19
Forecast Errors 2
1.5 1
0.5
0
-0.5
-1
-1.5
-2
5.
Use the trend equation that was estimated in Problem 2 to calculate ratio-to-trend seasonal adjustment factors. Fill in the blanks in the table below. Note that (A/F) is actual sales divided by the trend forecast and SF is the seasonally adjusted trend forecast. Calculate the RMSE. Comment on the accuracy of the forecasts yielded by this method and compare them with the forecasts you calculated previously.
Period
Sales (A) Sales (F)
1990.1
6.2
1990.2
8.6
1990.3
8.8
1990.4
9
1991.1
5.2
1991.2
10
1991.3
12.8
1991.4
12.4
1992.1
9.4
1992.2
14.9
1992.3
13.8
1992.4
13.9
(A/F)
(SF)
2
(A-SF)
Managerial Economics in a Global Economy, 7th Edition
6.
Enter the RMSE and the forecasts for the next four quarters into the table below for each of the four forecasting models estimated in this problem. Use the information in the table to compare the models. Which would you recommend to Yanos Zarkov?
Model
Constant Linear Trend Growth Rate
Seasonal Dummy Variables
Ratio-ToTrend
RMSE 1993.1 1993.2 1993.3 1993.4
Managerial Economics in a Global Economy, 7th Edition
