Question

Sales of floor cleaners at Lavoie's Flooring Co. over the past 13 months are as follows:

Sales of floor cleaners -Lavoie's Flooring Co.
Month	Sale ($1,000s)	Total 3 Months	3 Months Avg.
January	11
February	14	41	13.66666667
March	16	40	13.33333333
April	10	41	13.66666667
May	15	42	14
June	17	43	14.33333333
July	11	42	14
August	14	42	14
September	17	43	14.33333333
October	12	43	14.33333333
November	14	42	14
December	16	41	13.66666667
January	11	27	9
February	?	11	3.666666667

A. Using a moving average with three periods, determine the demand for floor cleaners for next February.

Answer: When using a moving average with three periods, we can determine the demand for floor cleaner in the next February is 3.6

B. Using a weighted moving average with three periods, determine the demand for floor cleaners for February.

Use 4, 2, and 1 for the weights of the most recent, second most recent, and third most recent periods, respectively. For example, if you were forecasting the demand for February, November would have a weight of 1, December would  have a weight of 2, and January would have a weight of 4.

Answer:

November	14	14*1 = 14	Forcast Fabruary = (14*1)+(16*2)+(11*4) / 4+2+1
December	16	16*2 = 32			90/7=	12.857
January	11	11*4 = 44
February	?

C. Use a trend analysis to forecast the demand for floor cleaners.

Answer: ?

D. Evaluate and compare the accuracy of each of these methods using at least one of the forecast error measures.

Answer: ?

F. Are all of the models used in parts a - c appropriate to use with the data provided? Why?

Answer: ?

Answer 1

a) The formula for moving average forecast is :

Moving average forecast = (Sum of demand in previous n periods)/ n

Here n = 3, we have to develop a 3 month moving average:

(The above table is incorrect)

Using the 3 month average model, the forecasted sale of cleaners for next February is $13,670.

b)

Using weighted average with 3 periods and Using 4, 2, and 1 for the weights of the most recent, second most recent, and third most recent periods, respectively. the sum of weights being 7, we have the following table:

For Februrary sale = (14+2*16+4*11)/6 = 90/7 = 12.857

The forecasted sale of cleaners for next Febrauary is $12,857.

c)

Using trend forecasting we use the method of least squares to find the line of best fit which comes out to be:

ŷ = 0.04945X + 13.34615

Substituting X=14 we get

ŷ = 0.04945 * 14 + 13.34615

= 14.03846

Here are the calculations for the same:

Sum of X = 91
Sum of Y = 178
Mean X = 7
Mean Y = 13.6923
Sum of squares (SS_X) = 182
Sum of products (SP) = 9
Regression Equation = ŷ = bX + a
b = SP/SS_X = 9/182 = 0.04945
a = M_Y - bM_X = 13.69 - (0.05*7) = 13.34615
ŷ = 0.04945X + 13.34615

d)

We use criterion MAD, the sum of absolute errors to compare the models, Computing the absolute error using the formula :

where n is the number of forecasted results

Using the same we get the forecasted error for the 3 models as given below:

MAD for the three models are :

1. 3 month MA MAD = 22/10 = 2.2

2. Weighted MA MAD = 28.857/10 = 2.8857

3. Forecast Method MAD = 24.82965/13 = 1.90997

e)

No all models provided are not appropriate. Model b-c i.e. 3 month MA and Weighted MA seems appropriate, but using trend analysis for the given data is not appropriate.