Question

Your manager is trying to determine what forecasting method to use. Based upon the following historical data, calculate the following forecast and specify what procedure you would utilize.

Month	Actual demand
1	62
2	65
3	67
4	68
5	71
6	73
7	76
8	78
9	78
10	80
11	84
12	85

a. Calculate the simple three-month moving average forecast for periods 4–12.

b. Calculate the weighted three-month moving average using weights of 0.50, 0.30, and 0.20 for periods 4–12.

c. Calculate the single exponential smoothing forecast for periods 2–12 using an initial (F1) of 61 and an$\alpha$of 0.30.

d. Calculate the exponential smoothing with trend component forecast for periods 2– 12 using an initial trend forecast (T1) of 1.8, an initial exponential smoothing forecast (F1) of 60, and $\alpha$of 0.30 and$\delta$of 0.30.

e. Calculate the mean absolute deviation (MAD) for the forecasts made by each technique in periods 4–12. Which forecasting method do you prefer?

Short answer

The solutions of (a), (b), (c), (d), and (e) are explained in the steps shown below.

Step-by-step solution

(a) Simple three-month moving average forecast for periods 4–12

A moving average could be a calculation to investigate data points by creating a series of averages of various subsets of the complete data set. It's also called a moving mean.

The calculation of 3-month moving average is calculated by using the following formula:

$\text{Simple moving average}=\frac{\left({\text{A}}_1+{\mathrm{A}}_2+..........+{\mathrm{A}}_{\text{n}}\right)}{\text{n}}$

$$\begin{gathered} =\frac{62+65+67}{3} \\ =\frac{194}{3} \\ =64.67 \end{gathered}$$

(b) Weighted three-month moving average using weights of 0.50, 0.30, and 0.20 for periods 4–12

The weighted moving average is an indicator that is accustomed generates trade directions and making a buy or sells decision. It assigns greater weighting to recent data and less weighting to past data. The weighted moving average is calculated by multiplying each observation within the information set by a predetermined weighting factor.

$\text{Weighted moving average}=\left({\text{A}}_1*{\text{W}}_1+{\text{A}}_2*{\text{W}}_{2+}.........+{\text{A}}_{\text{n}}*{\text{W}}_{\text{n}}\right)$

The calculation of 3 months weighted moving average is done in column 5 by using the above formula:

(c) Forecast for periods 2–12 using an initial (F1) of 61 and an a α of 0.30(Single exponential smoothing)

Single exponential smoothing is the most employed in all forecasting techniques. It’s an integral part of all electronic forecasting programs, and it's widely employed in ordering inventory in retail businesses, manufacturing units, and repair agencies.

The calculation of the forecast for the period 2-12 is done in the table shown below by using the following formula:

${\text{F}}_{t+1}={\text{F}}_t+\alpha \left({\text{A}}_t-{\text{F}}_t\right),\alpha =.30$

(d) The calculation of the exponential smoothing with trend component forecast for periods 2– 12

Exponential smoothing with the trend is a forecasting method of time-series for univariate data which is further extended to support the data with the trend or seasonal constituent. It is the most powerful forecasting technique of forecasting.

The exponential smoothing with the trend is calculated by using the following formula in the table shown below:

${\text{F}}_{\text{t}}={\text{F}}_{\text{t}-1}+\alpha ({\mathrm{A}}_{\text{t}-1}-{\text{F}}_{\text{t}-1})$

(e) MAD calculation

The mean absolute deviation is defined as the average distance between each data point and therefore the mean. It gives us a plan for the variability in an exceeding data set. Mean’ refers to the average of the observations and deviation implies departure or variation from a preset standard. When putting together, we can define deviation because of the distance of every observation from the mean of the information.

$\text{MAD}=\frac{\text{Sum of absolute value of each deviation}}{\text{Number of deviations}}$

By using the above formula the calculation of MAD is done as shown in the table below:

On the basis of MAD, the exponential smoothing with a trend component appears to be the best method. This should not be a surprise given the apparent upward trend.