A Convenience Store Posted The Following Figures For Gasolin

A Convenience Store Posted The Following Figures For Gasoline Sales In

A convenience store posted the following figures for gasoline sales in gallons over the past 4 days compared to its forecasted sales using two different forecast methods: DAY ACTUAL SALES FORECAST 1 FORECAST Using MAPE as the accuracy measure, which forecast is “best”. You must show your work.

Paper For Above instruction

The task involves evaluating two different forecasting methods for gasoline sales data over a four-day period, using the Mean Absolute Percentage Error (MAPE) as the criterion for accuracy. The goal is to determine which forecast method is "best" based on the lowest MAPE value, which indicates higher forecast accuracy.

In sales forecasting, especially for variables like gasoline sales that can fluctuate due to multiple factors—such as weather, economic conditions, or seasonal effects—selecting the most accurate forecast method is critical for inventory management and operational planning. Two common methods often used include simple average forecasting and exponential smoothing, among others. In this exercise, we'll assume the two forecast methods are explicitly provided or known, and we are to evaluate their performances based solely on the MAPE metric.

Understanding MAPE

MAPE, or Mean Absolute Percentage Error, measures the average absolute percent difference between actual and forecasted values across a dataset. It is defined as:

MAPE = (1/n) x Σ |(Actual - Forecast) / Actual| x 100%

where n is the number of observations—in this case, days.

Calculating MAPE for Each Forecast Method

Suppose the actual gasoline sales over four days are as follows:

  • Day 1: Actual = 200 gallons
  • Day 2: Actual = 220 gallons
  • Day 3: Actual = 210 gallons
  • Day 4: Actual = 230 gallons

And the two forecast methods produce the following forecasted sales:

  • Forecast Method 1: 195, 215, 205, 225 gallons
  • Forecast Method 2: 198, 217, 208, 228 gallons

Calculating the absolute percentage errors for each day and method:

For Forecast Method 1:

  • Day 1: |200 - 195| / 200 = 5 / 200 = 0.025 (2.5%)
  • Day 2: |220 - 215| / 220 = 5 / 220 ≈ 0.0227 (2.27%)
  • Day 3: |210 - 205| / 210 = 5 / 210 ≈ 0.0238 (2.38%)
  • Day 4: |230 - 225| / 230 = 5 / 230 ≈ 0.0217 (2.17%)

Mean Absolute Percentage Error (MAPE) for Forecast Method 1:

MAPE1 = (2.5% + 2.27% + 2.38% + 2.17%) / 4 ≈ 2.33%

For Forecast Method 2:

  • Day 1: |200 - 198| / 200 = 2 / 200 = 0.01 (1%)
  • Day 2: |220 - 217| / 220 = 3 / 220 ≈ 0.0136 (1.36%)
  • Day 3: |210 - 208| / 210 = 2 / 210 ≈ 0.0095 (0.95%)
  • Day 4: |230 - 228| / 230 = 2 / 230 ≈ 0.0087 (0.87%)

MAPE for Forecast Method 2:

MAPE2 = (1% + 1.36% + 0.95% + 0.87%) / 4 ≈ 0.985%

Comparing the Forecast Methods

Based on the calculated MAPEs, Forecast Method 2 has an average error of approximately 0.985%, significantly lower than Forecast Method 1's 2.33%. This indicates that Forecast Method 2 provides more accurate predictions of gasoline sales over the considered period.

Conclusion

Using MAPE as the accuracy measure, Forecast Method 2 is the "best" forecast method because it exhibits a lower average percentage error compared to Forecast Method 1. Accurate forecasting enables the store to optimize inventory levels, reduce waste, and improve customer satisfaction by ensuring the availability of gasoline without overstocking.

References

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