Problems (short) 1-2
1. Given the following data, compute 3-period moving
average forecast for period 6?
Period
1 2 3 4 5
Demand 73 68 65 72 67
(65+72+67)/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
A) 16.5 average.
B) 18.75
C) 19.1
D) 20.0
E) none of the
above
MA, MAD, TS Problems
(20+22+18+20)/4 =
20
Ardavan Asef-Vaziri
Jan-2015
1
Problems (short) 3-4
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
the above
4.E)none
Givenof the
following data, Compute
end of period 4.
MA, MAD, TS Problems
MAD and TS at the
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
Ardavan Asef-Vaziri
Jan-2015
2
Problems (short) 5-6
5. Given forecast errors of 4, 8, and - 3, what is the MAD?
A) 4
B) 3
MAD = (4+8+3)/3 =
C) 5
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
A)
0.6 of tracking signal in the last period?
B) 1.8
TS= SFE/MAD
C) 2
TS= 46/21=
D) 2.2
2.2
E) 2.5
MA, MAD, TS Problems
Ardavan Asef-Vaziri
Jan-2015
3
Problems 7-8
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
MA, MAD,
TS Problems
Ardavan Asef-Vaziri
E) none
of the above
Jan-2015
4
Problem 9
9.
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
MA, MAD, TS Problems
Ardavan Asef-Vaziri
Jan-2015
5
Problem 10
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
MA, MAD, TS Problems
Ardavan Asef-Vaziri
Jan-2015
6
Problem 11
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 = (A7+A6+A5+A4+A3+A2)/6
MA67 = (180+750)/6 = 155
MA, MAD, TS Problems
Ardavan Asef-Vaziri
Jan-2015
7
Problem 12
12. Actual demand in month 8 is 160 units. The 4-period
moving average in month 7 was 110 units. What is 5period moving average in month 8?
A) 100
MA47 = (A7+A6+A5+A4)/4 = 110
B) 110
C) 120
A7+A6+A5+A4 = 440
D) 140
A8 = 160
E) 150
MA58 = (A8+ A7+A6+A5+A4)/5
MA58 = (160+440)/5 = 120
MA, MAD, TS Problems
Ardavan Asef-Vaziri
Jan-2015
8
Problem 13
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 900. Compute 5period moving average for period 21.
MA520 = (A20+A19+A18+A17+A16)/5 =
(
=800
+A16)/5

+850)/5
+850

=800
=4000
MA521 = (A21+A20+A19+A18+A17)/5 =
=???
(
=
+900)/5 = (3150+900)/5
=810
(
MA521 = MA520 +(A21- A16)/5
=315
0
+A21)/5
=(
MA521 = 800 +(900- 850) /5=810
MA, MAD, TS Problems
Ardavan Asef-Vaziri
Jan-2015
9
You may stop here.
Problems 14-16
are advanced
problems.
Problem 17 is the
same as problem
MA, MAD, TS Problems
Ardavan Asef-Vaziri
Jan-2015
10
Problem 14: MAD from t to t+1
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
Compute
in period 11.
11 is 1100MAD
(A11=1100).
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 = 1100 -1210 = -110
Sum |A-F| from period 1 to 11 = 1100 + 110 = 1210
MAD in period 11 = Sum |A-F| /11
MAD in period 11 = 1210/11 = 110
MA, MAD, TS Problems
Ardavan Asef-Vaziri
Jan-2015
11
Problem 15: TS from t to t+1
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.
First Lets look
TS in 11.
Period 10
Compute
TS inat
period
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 = 1100-1210 = -110
Sum (A-F) from period 1 to 11 = 242 -110 = 132
TS = Sum(A-F)/MAD
Sum(A-F) in Period 11 = 132
MAD in Period 11 = 110
TSMAD,
in Period
1.2Asef-Vaziri Jan-2015
MA,
TS Problems11 = 132/110 =
Ardavan
12
Problem 16: TS 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
http://www.estepsoftware.com/papers/madrsquare.pdf
Et  Normal (0,1.25MAD)
If x = Normal(µ,σ)  Sum (x) = Normal(µ, √N σ)
StdDev [Sum(Et)] = √N StdDev (Et)
MA, MAD, TS Problems
Ardavan Asef-Vaziri
Jan-2015
13
Problem 16: TS 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 1.25 ≥ (Et -0)/MAD ≥ - 3N 1.25.
+ 3.75N ≥ (Et -0)/MAD ≥ - 3.75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
MA, MAD, TS Problems
Ardavan Asef-Vaziri
Jan-2015
14
Problem 16: TS 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 1.25 ≥ (Et -0)/MAD ≥ - 3N 1.25.
+ 3.75N ≥ (Et -0)/MAD ≥ - 3.75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
MA, MAD, TS Problems
Ardavan Asef-Vaziri
Jan-2015
15
Problem 17: This Problem is Similar to
Problem
13
Using the following data you can compute 4-period and 7period moving averages in period 20.
t 14 15 16 17 18 19 20
At 658 864 1110 634 855 738 910
(658+864+1110+634+855+738+910)/7 =
824.14
(634+855+738+910)/4 = 784.25
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 784.25, and 7-period
moving average in period 20 to be 824.14.
Can you compute 7-period moving average and 4 period
moving average in period 21 without using the
alternative method described in Problem 13?
MA, MAD, TS Problems
Ardavan Asef-Vaziri
Jan-2015
16
Problem 17: This Problem is Similar to
Problem 13
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
MA 720 = (658+864+1110+634+855+738+910)/7 =
(658+864+1110+634+855+738+910)/7
=
824.14
emand
for period 21 is 800
824.14
(864+1110+634+855+738+910+800)/7 = =
MA721 = (864+1110+634+855+738+910+800)/7
844.43
MA720 = (864+1110+634+855+738 +910)/7 +
=+
824.14
=(658)/7
(800 )/7
( 864+1110+634+855+738+900)/7=844.43
herefore, we can compute MA721 , in the following simple way
MA721 = MA720 +(A21- A14)/7
A721 = 824. 14 +(800- 658) /7=844.43
MA, MAD, TS Problems
Ardavan Asef-Vaziri
Jan-2015
17
Problem 17: This Problem is Similar to
Problem
13 moving average in month 20 is 784.25,
Suppose 4-Period
the actual demand for period 17 is 634, and the demand
for period 21 is 800. Compute 4-period moving average
for period 21 without using other data?
(634+855+738+910)/4 =
= 784.25
784.25
MA420 = (634+855+738+910)/4
MA421 = (855+738+910+800)/4
= 825.75
825.75
(855+738+910+800)/4 =
herefore, we can compute MA421 , in the following simple way
MA421 = MA420 +(A21- A17)/4
A421 = 784.25 +(800 - 634) /4=825.75
general ( the data of period t minus the data of period t-n) /
In Moving Average forecasting
always
FMA,
= MAt  F22= MA21
(t+1)
MAD, TS Problems
Ardavan Asef-Vaziri
Jan-2015
18