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

Month | Sales (000 units) |
---|---|

Feb. | 19 |

Mar. | 18 |

Apr. | 15 |

May | 20 |

June | 18 |

July | 22 |

Aug. | 20 |

**Required: Forecast September sales volume using each of the following:**

a. The naive approach

b. A five-month moving average

c. A weighted average using 0.60 for August, 0.30 for July, and 0.10 for June

d. Exponential smoothing with a smoothing constant equal to 0.20, assuming previous forecast of 19(000).

a. The Naive ApproachThe naive approach assumes that the sales for September will be the same as the sales for August.$ForecastforSeptember=SalesinAugust=20\backslash text\{Forecast\; for\; September\}\; =\; \backslash text\{Sales\; in\; August\}\; =\; 20$

b. A Five-Month Moving AverageTo calculate a five-month moving average, we take the average of the sales of the last five months (April through August).$FiveMonthMovingAverage=\frac{SalesinApr+SalesinMay+SalesinJune+SalesinJuly+SalesinAug}{5}\backslash text\{Five\; Month\; Moving\; Average\}\; =\; \backslash frac\{\backslash text\{Sales\; in\; Apr\}\; +\; \backslash text\{Sales\; in\; May\}\; +\; \backslash text\{Sales\; in\; June\}\; +\; \backslash text\{Sales\; in\; July\}\; +\; \backslash text\{Sales\; in\; Aug\}\}\{5\}$

$FiveMonthMovingAverage=\frac{15+20+18+22+20}{5}=\frac{95}{5}=19\backslash text\{Five\; Month\; Moving\; Average\}\; =\; \backslash frac\{15\; +\; 20\; +\; 18\; +\; 22\; +\; 20\}\{5\}\; =\; \backslash frac\{95\}\{5\}\; =\; 19$

c. A Weighted AverageFor the weighted average, we use the given weights: 0.60 for August, 0.30 for July, and 0.10 for June.$WeightedAverage=(0.60\times SalesinAug)+(0.30\times SalesinJuly)+(0.10\times SalesinJune)\backslash text\{Weighted\; Average\}\; =\; (0.60\; \backslash times\; \backslash text\{Sales\; in\; Aug\})\; +\; (0.30\; \backslash times\; \backslash text\{Sales\; in\; July\})\; +\; (0.10\; \backslash times\; \backslash text\{Sales\; in\; June\})$

$WeightedAverage=(0.60\times 20)+(0.30\times 22)+(0.10\times 18)\backslash text\{Weighted\; Average\}\; =\; (0.60\; \backslash times\; 20)\; +\; (0.30\; \backslash times\; 22)\; +\; (0.10\; \backslash times\; 18)$

$WeightedAverage=12+6.6+1.8=20.4\backslash text\{Weighted\; Average\}\; =\; 12\; +\; 6.6\; +\; 1.8\; =\; 20.4$

d. Exponential SmoothingFor exponential smoothing with a smoothing constant of 0.20 and a previous forecast of 19(000):$ForecastforSeptember=\alpha \times \left(SalesinAug\right)+(1-\alpha )\times \left(PreviousForecast\right)\backslash text\{Forecast\; for\; September\}\; =\; \backslash alpha\; \backslash times\; (\backslash text\{Sales\; in\; Aug\})\; +\; (1\; \u2013\; \backslash alpha)\; \backslash times\; (\backslash text\{Previous\; Forecast\})$Forecast for September=α×(Sales in Aug)+(1−α)×(Previous Forecast)

$ForecastforSeptember=0.20\times 20+0.80\times 19\backslash text\{Forecast\; for\; September\}\; =\; 0.20\; \backslash times\; 20\; +\; 0.80\; \backslash times\; 19$

$ForecastforSeptember=4+15.2=19.2\backslash text\{Forecast\; for\; September\}\; =\; 4\; +\; 15.2\; =\; 19.2$

## Summary of Forecasts: