Question

TOMBOW is a small manufacturer of pencils and has had the following sales record for the most recent five months: Month 1. Units sold (000) 2 3 4 250 245 260 280 320 a. Forecast demand for months 4 and 5 using a three-month moving average. b. Repeat (a) using a three-month weighted moving average, the weights are 6,3, and 1, where 6 refers to the most recent demand. al smoothing with α -0.6. Assume the forecast demand for month 3 was 247. Based on these limited data, which method do you have more confidence in? What is the forecast for month 6 using the best method? d.

Answer 1

a) 3 Month Moving Average ,

F_t = (D_t-1 + D_t-2 +D_t-3)/3

F₄ = (D₃ + D₂ + D₁)/3 = (260+245+250)/3 = 252

Period	Units Sold (000)	3 MA
1	250
2	245
3	260
4	280	252
5	320	262

b ) 3 Month Weighted Average

Weighted Average Forecast formula

F_t = W_t-1*D_t-1 + W_t-2*D_t-2 + W_t-3*D_t-3

In the given Problem , W_t-1 = 0.6 , W_t-2 = 0.3 & W_t-3 = 0.1

Period	Units Sold (000)	3 MWA
1	250
2	245
3	260
4	280	255
5	320	271

3.

alpha, $\alpha$ = 0.35

Formula for calculating the forecast using exponential smoothing method

F_t+1 = $\alpha$ *A_t + (1- $\alpha$ )*F_t

Where F_t+1 is forecast value for t+1 period

A_t = Actual demand for t period

F_t is forecast value for t period

Period	Units Sold (000)	ES(0.6)
1	250
2	245
3	260	247
4	280	255
5	320	270

d) Calculate MAD for each technique

MAD = Sum of Absolute Error/ Number of Period

Error = F_t - D_t

Absolute Error = Absolute value of (F_t - D_t )

Find Error and Absolute error of each Period for all the forecasting type

Period	Units Sold (000)	3 MA	Absolute(Actual-Forecast)
1	250
2	245
3	260
4	280	252	28.3
5	320	262	58.3
MAD			43.3

Period	Units Sold (000)	3 MWA	Absolute(Actual-Forecast)
1	250
2	245
3	260
4	280	255	25.5
5	320	271	49.5
MAD			37.5

Period	Units Sold (000)	ES(0.6)	Absolute(Actual-Forecast)
1	250
2	245
3	260	247
4	280	255	25.2
5	320	270	50.08
MAD			37.6

Technique with less MAD is better technique . So 3 MWA technique can give more confidence

Period	Units Sold (000)	3 MWA
1	250
2	245
3	260
4	280	255
5	320	271
6		302

F₆ = 302