Assignment 2: Problem 1
Given the following data
Month Sales (1000)
Feb
19
Mar
18
Apr
15
May
20
Jun
18
Jul
22
Aug
20
Forecast for Sep
• Using linear regression
• Using 5 period moving average
• Using exponential smoothing.
Alpha is .2 and forecast for
march was 19
• Using Naïve method
• Compute MAD for naïve method
and exponential smoothing.
Which one is preferred? NM or
ES.
(a) Plot the Data
Sales (1000)
19
18
15
20
18
22
20
Monthly Sales
25
Sale (1000)
1
2
3
4
5
6
7
Month
Feb
Mar
Apr
May
Jun
Jul
Aug
20
15
Monthly Sales
10
5
0
0
2
4
Month
6
8
(b-2)Forecast for Sep Using 5 Period Moving Average
t
1
2
3
4
5
6
7
At
19
18
15
20
18
22
20
F8 =MA7= (A7+A6+A5+A4+A3)/5 = (20+22+18+20+15)/5
F8 =MA7= 19
(b-2)Forecast Using 5 Period Moving Average for All Periods
t
1
2
3
4
5
6
7
At
19
18
15
20
18
22
20
Moving Average
MAt
Ft
18
18.6
19
18
18.6
19
(b-3)Forecast for Sep Using Exponential Smoothing α =.2 and F(Mar) = 19
t
1
2
3
4
5
6
7
At
19
18
15
20
18
22
20
F3 = (1-α)F2 + α A2
F3 = (.8)19+ .2(18)
F3 = 18.8
March is period 2
(b-3)Forecast for Sep Using α =.2 and F(Mar) = 19
Using the same formula, we compute F4, F5, F6, F7, and finally F8
which is the demand for Sep.
1
2
3
4
5
6
7
At
19
18
15
20
18
22
20
Ft
19
18.80
18.04
18.43
18.35
19.08
19.26
(b-4)Forecast for Sep Using Naïve Method
F8 =A7
F(t +1) =At
F8 = 20
Forecast for all periods using Naïve Method
t
1
2
3
4
5
6
7
At
19
18
15
20
18
22
20
Ft
19
18
15
20
18
22
20
(c) Which Technique ?
When comparing several methods using MAD, we need to
use the same time horizon for all methods. We need to
have actual as well as forecasts for all methods for all
periods of MAD computations
Here we have
Actual for periods 1 to 7; that is 7 periods.
Regression can provide us with forecast for periods 1 to ∞
On the other hand, five period moving average can only
provide us with forecast for periods 6 and 7; that is 2
periods
Therefore, to compare all these methods, we can compute
MAD only over 2 periods.
But two period is not enough
(c) Naïve Method or Exponential Smoothing ?
Naïve method forecasts for periods 2 to 7; That is
6 periods
Exponential Smoothing for periods 2 to 7; That is 6
periods
We can compare NM and ES over 6 periods.
We may also ignore period 2 because in
exponential smoothing forecast for period 2 is just
the same as actual demand for period 1 and that is
the same for naïve method.
Here we compare NM and ES over a 5 period time
horizon.
From period 3 to period 7
(c) Naïve Method or Exponential Smoothing ?
Period
Actual
Naïve Method
Expo. Smoothing
3
4
5
6
7
15
20
18
22
20
18
15
20
18
22
18.80
18.04
18.43
18.35
19.08
(c) Naïve Method or Exponential Smoothing ?
Period
Actual
Naïve Method
Expo. Smoothing
NM
ES
3
4
5
6
7
15
20
18
22
20
18
15
20
18
22
18.80
18.04
18.43
18.35
19.08
3
5
2
4
2
3.80
1.96
0.43
3.65
0.92
(c) Which Technique ?
Period
Actual
Naïve Method
Expo. Smoothing
NM
ES
3
4
5
6
7
15
20
18
22
20
18
15
20
18
22
18.80
18.04
18.43
18.35
19.08
3
5
2
4
2
3.2
3.80
1.96
0.43
3.65
0.92
2.15
Better
However, we need to keep all methods, because we need more actual data.
A MAD computed just 5 periods is not a reliable measure.
It is better to have all methods for say 10-20 more periods, and then identify the
best method
Regression
t
1
2
3
4
5
6
7
At
19
18
15
20
18
22
20
Ft  16.86  0.5t
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.492518281
R Square
0.242574257
Adjusted R Square
0.091089109
Standard Error
2.090796157
Observations
7
Forecast using simple regression
ANOVA
df
Regression
Residual
Total
Intercept
X Variable 1
SS
1
5
6
MS
F
7
7
21.85714286 4.371428571
28.85714286
Coefficients Standard Error
t Stat
16.85714286
1.767045268 9.539734585
0.5
0.395123334 1.265427671
Significance F
1.60130719
0.261481287
P-value
0.000214193
0.261481287
Lower 95%
Upper 95%
12.31480839 21.39947732
-0.515696865 1.515696865
Assignment 2: Problem 2(a)
Exponential smoothing is being used to forecast demand. The
previous forecast of 66 turned out to be 5 units larger than actual
demand. The next forecast is 65. Compute ?
F(t+1) = Ft +  (At-Ft)
65
66
65 = 66 +  (-5)
5=1
 = 0.2
-+5
5
Assignment 2: Problem 2(b)
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
MA68 = (180+750)/6 = 155
Assignment 2: Problem 2(c)
Tickets numbered from 100 to 200 have been sold. Using
the random number rand() = 0.35 identify the winner.
If the random number is 0 it must become 100.
The only way to transform 0 into a positive number is by
addition.
It is not possible by multiplication
X = 100 +R
But R is greater than or equal to 0 and less than or equal to
1. Therefore X here is between 100 1nd 101.
That is not what we want
X= 100+100R and round it.