National Scan Inc. sells radio frequency inventory tags. Monthly sales for a seven-month period were as follows:
Month Sales (000) UnitsFeb 19Mar 18Apr 15May 20Jun 18Jul 22Aug 20a. Forecast September sales volume using each of the following:(1) Thenaiveapproach.(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) Alineartrendequation.

Answer / Explanation:

The data provided in the problem statement is:

Month Sales ('000 units) 1 Feb 19 2 Mar 18 3 Apr 15 4 May 20 5 Jun 18 6 Jul 22 7 Aug 20 a. Now to forecast September sales volume using each of the following: (1) A linear trend equation . Let the linear trend equation be of the form:

Here, In the given data, the "Sno." column represents the x-values and the sales values represents the y-values.

Substituting these values in the formula, we get the following equation:

y = 0.5 x + 16.857

Using, x = 8 (for September), y = 20.857 Hence, the forecast for September = 20,857 units

(2) A five-month moving average. Five month moving average means that the forecast of a month is equal to the average of the sales of the previous 5 months.

Hence, forecast of September is equal to the average of the sales of April, May, June, July and August. Forecast for September = (15000 + 20000 + 18000 + 22000 + 20000) / 5 = 19,000 units

(3) Exponential smoothing with a smoothing constant equal to .20, assuming a March forecast of 19(000). The formula for exponential smoothing is : = Ft=Ft−1+α( At − 1 − Ft − 1).

Here, Ft = Forecast for period t Ft − 1 = Forecast for period t-1 At−1 = Actual sales for period t - 1 α = Smoothing constant Using this formula.

We can populate the following table and get the forecast for September: Sno. Month Sales ('000 units) Forecast ('000 units) 1 Feb 19 2 Mar 18 19 3 Apr 15 18.800 4 May 20 18.040 5 Jun 18...

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