Question

1. National Scan, Inc sells radio frequency inventory tags. Monthly sales for a seven-month period were as follows:

Month Sales (000 units)

Feb.       21

Mar.      20

Apr.       17

May       22

Jun.       20

Jul.         24

Aug.       22

1. Plot the monthly data on a sheet of graph paper.
2. Forecast September sales volume using each of the following:

(1) The naive approach

(2) A five month moving average

(3) A weighted average using .60 for August, .30 for July, and .10 for June

(4) Exponential smoothing with a smoothing constant equal to .20, assuming a a March ­forecast of 19(000)

(5) A linear trend equation

3. Which method seems least appropriate? Why? (Hint: Refer to your plot from part a.)
4. What does use of the term sales rather than demand presume?

PLEASE LIST ALL STEPS

Answer 1

(a)

Graph:

(b)

Forecast

1) Naive Approach - In this, forecast is equal to actual value of previous period which is Aug Sales.

Hence, Sep = 22

2) Five month moving average = Average of last 5 months = Average (Apr,May,Jun,Jul,Aug) = (17+22+20+24+22)/5 = 21.00

3) Weighted average = 0.6*22 + 0.3*24 + 0.1*20 = 22.40

4) Exponential smoothing:

Apr = Mar forecast + 0.2*(March actual - March forecast) = 19 + 0.2*(20-19) = 19.2

May = 19.2 + 0.2*(17-19.2) = 18.76

Jun = 18.76 + 0.2*(22-18.76) = 19.41

Jul = 19.41 + 0.2*(20-19.41) = 19.53

Aug = 19.53 + 0.2*(24-19.53) = 20.42

Sep = 20.42 + 0.2*(22-20.42) = 20.74

(c)

The least appropriate method is the naïve approach. Naïve approach assumes that the next period demand is the same as pervious period. In such case, we should get a flat line on the graph sheet. However, we see that it is not the case. Thus the least appropriate method is the naïve approach.

(d)

Sales and demands are similar. However sales presumes that these numbers will be sold irrespective of the demand. This means the demand could be more than this values but the numbers of sales will be achieved.

ALTERNATIVE METHODS FOR (a) and (b)

a) The graphical plot of the actual data is shown below. Use the grids to create the label and mark the intervals. Then plot the points. The image on your graph sheet should look similar to the image below.

b) Forecast for the various methods are shown below

• Naïve approach takes the value of the previous period.
• The five month moving average takes the average of the previous five periods as the forecast value for current period
• The weighted average value is obtained by multiplying the respective weights against the previous months
• The exponential smoothing uses the formula
• F(t) = alpha*actual(t-1) + (1 – alpha)*forecast(t-1)
• In order to calculate linear trend we need to use linear regression. And use Y=b + aX to forecast the data. Here we have used the regression option from data analysis to find the value of b = 18.85 and a = 0.5.

The formulas for each of them are shown below