homework 4
Joss_Smitx01
MEM5700Chapter101.docCHAPTER TEN
Objective:
A brief introduction of the basic concepts of Forecasting Tools like Moving average, Weighted Moving Average, Exponential Smoothing will be used to develop projection models.
Chapter Content:
Forecasting techniques:
Into our class we will use a simple product to manufacturer. A plush eraser will be our product (Note: Don’t blame my drawing, only look at and enjoy it.).
The first technique will be Moving Average (MA). This forecasting technique consists in the estimate of a average value from historical data that move as the new present value it’s know. This average is determinated by a series of terms or established periods (n). The quantity of periods (n) will be based in the variation that it exists between the historical data. If there is large variation, the value (n) must be greater to reflect the variation. If there is small variation, the value (n) can be smaller.
Let us suppose that the following table shown the eraser’s demand for first six months of production.
|
Period (Month) |
Demand |
|
1 |
1250 |
|
2 |
1590 |
|
3 |
1340 |
|
4 |
1510 |
|
5 |
1486 |
|
6 |
1440 |
Using the Moving Average equation:
(
)
n
i
t
A
t
MA
å
-
=
)
(
Where: MA(t) is the forecasting for period t
A(t-i) is the present for period t-i
(n) is the number of periods to average
If we looking for the forecasting for the fifth period, using n=2 and n=3, which would be the answer?
|
N=2 |
N=3 |
|
A(4) = 1510 |
A(4) = 1510 |
|
A(3) = 1340 |
A(3) = 1340 |
|
--------------- |
A(2) = 1590 |
|
Σ = 2850 |
Σ = 4440 |
|
n = 2 |
n = 3 |
|
MA(5) = 1425 |
MA(5) = 1480 |
|
|
|
The average changes of period when calculating the next forecasting. When forecast the sixth period, the terms to be used for the average change according to the following example:
|
N=2 |
N=3 |
|
A(5) = 1486 |
A(5) = 1486 |
|
A(4) = 1510 |
A(4) = 1510 |
|
--------------- |
A(3) = 1340 |
|
Σ = 2996 |
Σ = 4336 |
|
n = 2 |
n = 3 |
|
MA(5) = 1498 |
MA(5) = 1445.3 |
The next technique known like Weighted Moving Average, this technique to difference of regular moving average, each period have a weight assigned as output probability. The Moving average to divide the periods sum between the value (n), indirectly,
it’s giving the same probability o weight to each period to determine the forecasting.
(
)
(
)
å
-
-
=
i
t
xW
i
t
A
t
WMA
)
(
Where t is the hoped period and i value run from 1 to n.
Example, determining the sixth forecasting, with (n) = 2
|
Mov. Average Reg |
Weighted MA |
|
A(5) = 1486 x (50%) |
A(5) = 1486 x (75%) |
|
A(4) = 1510 x (50%) |
A(4) = 1510 x (25%) |
|
|
|
|
MA(6) = 1498 |
WMA(6) = 1492 |
This technique allow to assign a weight or probability according to expect behavior from marketing influences. I.e. to assign greater weight to the period value most recent a cause of a promotion. The quantity of periods or term to be used for estimate the forecast depends of the variation that exists between the historical data. That means, follow the same concept of moving average.
The third technique is the Exponential Smoothing. This forecasting technique allows assigning a value of the possible error that may exist between the present value and their forecast. This use the difference between the real value and the previous period forecast to assign them weight or probability occurrence.
ES (t)= F (t-1) + a [A(t-1) – F(t-1)]
Where F (t-1) is the projection of the previous period and A(t-1) is the actual value of the previous period. α is the weight or probability assigned to the error or difference between two values. This may be estimated using the following formula:
α = 2 / (n+1)
Where n is the number for terms or periods to be projected. It is also common between the statistics the use of one α between 5% and 10%. If there is a large variation between the values it is recommended to use the 15% up to 30%. Lets make an example. To determine the fifth period of the table, we will have to realize each one of the projections until reaching the previous period. If we want the fifth projection we need to calculate projection 1 to 4.
Note: For class purpose the first projection will be the actual value.
Actual Projection Exponential Smoothing_______
1250 1250 1250 + .05 [1250-1250] = 1250
1590 1250 1250 + .05 [1590-1250] = 1265
1340 1267 1267 + .05 [1340-1267] = 1271
1510 1271 1271 + .05 [1510-1271] = 1283
ES (5) = 1283
For this moment we have three projection techniques that will help us forecast the future demand of a product, and then it should pass the planning process. Knowing the human behavior, after this reading you should be absolutely a sleep. “Please don’t fall a sleep know comes something good”.
Which of these techniques may realize the best future forecast? It is important to notify that these are the unique projection techniques. There is a large number of them that may be applied depending on the behavior of historic data. For this chapter we will proceed to see which one makes the better forecast or is near reality.
The following tool is used to measure the mistakes that exist between projection and the actual value. The Mean Absolute Deviation (MAD) determines the average of the absolutes differences between the two values.
N
Ft
At
MAD
å
-
=
/
/
Where t run from 1 to NN is the differences number in the estimate, At is present value for the period t and Ft is the forecast for the period t. Using, the previews example of the three techniques we will proceed to determine which one is the most effective for the erasers demand.
|
Moving Average n=3 |
Weighted MA n=2 |
||||
|
A |
F |
/A-F/ |
A |
F |
/A-F/ |
|
A4=1510 |
F4=1393 |
117 |
A3=1340 |
F3=1335 |
5 |
|
A5=1486 |
F5=1480 |
6 |
A4=1510 |
F4=1528 |
18 |
|
A6=1440 |
F6=1445 |
5 |
A5=1486 |
F5=1382 |
104 |
|
|
|
|
A6=1440 |
F6=1504 |
64 |
|
MAD = 43 |
|
|
MAD = 48 |
|
|
|
Exponential Smoothing |
||
|
A |
F |
/A-F/ |
|
A1=1250 |
F1=1250 |
0 |
|
A2=1590 |
F2=1250 |
340 |
|
A3=1340 |
F3=1267 |
73 |
|
A4=1510 |
F4=1271 |
239 |
|
A5=1486 |
F5=1283 |
203 |
|
A6=1440 |
F6=1293 |
147 |
MAD=167
Therefore, the technique with the smaller MAD represents the one with the less variation between the actual values and their projections. In our example the first technique that represent the moving average with n=3 is the most precise.
