1. Moving Average, MAD, Tracking Signal Problems

2. Short Questions and Multiple choices
1. Given the following data, compute 3-period moving average forecast for period 6?
Period
Demand
( )/3 = 68
2. Monthly sales for the past five months were as follows: April (15), May (20), June (18), July (22), August (20). Determine a September forecast, using a 4-period moving average.
A) 16.5
B) 18.75
C) 19.1
D) 20.0
E) none of the above 

3. Short Questions and Multiple choices
3. In order to increase the responsiveness of a forecast (i.e., respond quickly to the data changes) made using the moving average technique, the number of periods in the average should be:
A) decreased
B) increased
C) multiplied by a larger alpha
D) multiplied by a smaller alpha
none of the above
4. Given the following data, Compute MAD and TS at the end of period 4.
Sum |A-F| = 15
MAD = Sum |A-F| /n
=15/4 = 3.75
Sum (A-F) = 9
TS = Sum(A-F)/MAD
TS = 9/3.75 = 2.4

4. Short Questions and Multiple choices
5. Given forecast errors of 4, 8, and - 3, what is the MAD? 
A) 4
B) 3
C) 5
D) 6
E) 12
6. The sum of the forecast errors (SFE) and the mean absolute deviation (MAD) are calculated in each period. The values of SFE and MAD in the last period to be 46 and 21, respectively. Which of the following is the value of tracking signal in the last period?
A) 0.6
B) 1.8
C) 2
D) 2.2
E) 2.5

5. Short Questions and Multiple choices
7. You must choose between two alternative forecasting models. Both models have been used to prepare forecasts for a six-month period. Compute mean absolute deviation (MAD) for the forecasting model 2.
A) 0.33
B) 2.0
C) 5.67
D) 9.51
E) none of the above
8. Which forecasting model would you recommend? What is the MAD for the recommended forecasting model?
A) Model 1 with MAD of 4.67
B) Model 2 with MAD of 0.33
C) Model 1 with MAD of 3.39
D) Model 2 with MAD of 2.0

6. Short Questions and Multiple choices9.
I- to select the best forecasting technique
II- to estimate the standard deviation of the forecast.
III- to see if the forecast is within control limits
IV- to see if the forecast does not show any specific pattern.
A) the main two applications of MAD are I and II. The main two applications of Tracking Signal are III and IV.
B) the main two applications of MAD are I and III. The main two applications of Tracking Signal are II and IV.
C) the main two applications of MAD are I and IV. The main two applications of Tracking Signal are II and III.
D) the main two applications of MAD are II and III. The main two applications of Tracking Signal are I and IV.
E) none of the above

7. Short Questions 17 10. Given the following tracking signal graph
A) the forecasting method overestimates the demand
B) the forecasting method underestimates the demand
C) the demand is very seasonal
D) the forecasting method is moving average
E) the forecasting method is exponential smoothing

8. Short Questions and Multiple choices
11. The 5-period moving average in month 6 was 150 units. Actual demand in month 7 is 180 units. What is 6 period moving average in month 7?
MA56 = (A6+A5+A4+A3+A2)/5
MA67 = (A7+A6+A5+A4+A3+A2)/6
MA56 = (A6+A5+A4+A3+A2)/5 = 150
A6+A5+A4+A3+A2 = 750
A7 = 180
MA67 = ( )/6 = 155

9. Short Questions and Multiple choices
12. Actual demand in month 8 is 160 units. The 4-period moving average in month 7 was 110 units. What is 5-period moving average in month 8?
A) 100
B) 110
C) 120
D) 140
E) 150
MA47 = (A7+A6+A5+A4)/4 = 110
A7+A6+A5+A4 = 440
A8 = 160
MA58 = (A8+ A7+A6+A5+A4)/5
MA58 = ( )/5 = 120

10. Short Questions and Multiple choices
13. Suppose the 5-period moving average in period 20 is equal to 800. Suppose period 16 demand is 850. Also suppose the demand for period 21 is Compute 5-period moving average for period 21.
+A16)/5
MA520 = (A20+A19+A18+A17+A16)/5 =800
MA520 = (A20+A19+A18+A17+A16)/5
= (
= (
+850)/5 =800
+850 =4000
=3150
= (
+A21)/5
MA521 = (A21+ A20+A19+A18+A17)/5 =???
MA521 = (A21+ A20+A19+A18+A17)/5
= (
+900)/5
= (
)/5 =810
MA521 = MA520 +(A21- A16)/5
MA521 = 800 +( ) /5=810

11. Problem 1- Moving Average, t to t+1
Using the following data you can compute 4-period and 7-period moving averages in period 20. t At
( )/7 =
( )/4 =
Now suppose you do not have the actual data.
You only the demand for period 21 to be 800, 4-period moving average in period 20 to be , and 7-period moving average in period 20 to be
Can you compute 7-period moving average and 4 period moving average in period 21 without using the original data?

12. 7-period moving average at periods 20, and 21
Let us first check how do we compute 7-period moving average using all the available data
MA720 = (A14+A15+A16+A17+A18+A19+A20)/7
MA720 = ( )/7 =
MA720 = ( )/7 =
Demand for period 21 is 800
MA721 = ( )/7 =
MA721 = ( )/7 =
MA720 = ( )/7 + (658)/7 =
MA721 = (800 )/7 + ( )/7=844.43
Therefore, we can compute MA721 , in the following simple way
MA721 = MA720 +(A21- A14)/7
MA721 = ( ) /7=844.43

13. Problem 1- Moving Average, t to t+1
Given the same data t At
But suppose you do not have access to all the data.
Suppose you only know that the 4-Period moving average in month 20 is , the actual demand for period 17 is 634, and the demand for period 21 is 800. Can you compute 4-period moving average for period 21 without using other data?

14. 4-period Moving Average at Periods 20 and 21
MA420 = ( )/4 =
MA420 = ( )/4 =
MA420 = ( )/4 =
MA420 = ( )/4 =
Therefore, we can compute MA421 , in the following simple way
MA421 = MA420 +(A21- A17)/4
MA421 = ( ) /4=825.75
In general ( the data of period t minus the data of period t-n) / n
In Moving Average forecasting always
F(t+1) = MAt  F22= MA21

15. Problem 2- MAD and TS
Actual and forecast data are available from period 1 to period 10.
In period 10: MAD = 110 and TS = 2.2, Forecast for period 11 is 1210 (F11=1210) , Actual demand in Period 11 is 1100 (A11=1100).
Compute MAD in period 11.
First Lets look at MAD in Period 10
MAD = Sum |A-F| /n
110 = Sum |A-F| /10
Sum |A-F| = 1100  Sum |A-F| from period 1 to 10 = 1100
In period 11, A-F = = -110
Sum |A-F| from period 1 to 11 = = 1210
MAD in period 11 = Sum |A-F| /11
MAD in period 11 = 1210/11 = 110

16. Problem 2- MAD and TS
Actual and forecast data are available from period 1 to period 10.
In period 10: MAD = 110 and TS = 2.2, Forecast for period 11 is 1210 (F11=1210) , Actual demand in Period 11 is 1100 (A11=1100). MAD in Period 11 = 110. Compute TS in period 11.
First Lets look at TS in Period 10
TS = Sum(A-F)/MAD
2.2 = Sum(A-F)/110  Sum (A-F) from period 1 to 10 = 242
(A-F) in period 11 = = -110
Sum (A-F) from period 1 to 11 = = 132
Sum(A-F) in Period 11 = 132
MAD in Period 11 = 110
TS in Period 11 = 132/110 = 1.2

17. Problem 3- Tracking Signal, UCL and LCL
What are the reasonable values for UCL and LCL in Tracking Signal?
At is Actual and Ft is forecast of a random variable such as demand.
Forecast error (A random Variable) Et =At-Ft has mean of 0.
MAD provides an estimate for the standard deviation of Et. StdDev (Et) = 1.25 MAD. See for example
Et = Normal (0,1.25MAD)
If x = Normal(µ,σ)  Sum (x) = Normal(Nµ, √N σ)
StdDev [Sum(Et)] = √N StdDev (Et)

18. Problem 3- Tracking Signal, UCL and LCL
Et = Normal (0,1.25MAD)
Sum (Et) = Normal (0, √N 1.25MAD)
3 ≥ (Et -0)/N 1.25 MAD ≥ -3.
+ 3n ≥ (Et -0)/MAD ≥ - 3N 1.25.
+ 3.75N ≥ (Et -0)/MAD ≥ N.
Tracking Signal TS= Et/MAD with samples of size N is
distributed normally around 0
with UCL = 3.75N
and LCL =-3.75N