The demand and forecast of an item for five months are given in the table.
Month | Demand | Forecast |
April | 225 | 200 |
May | 220 | 240 |
June | 285 | 300 |
July | 290 | 270 |
August | 250 | 230 |
The Mean Absolute Percent Error (MAPE) in the forecast is ___________% (round off to two decimal places).
Concept:
Mean Absolute Percentage Error (MAPE):
Mean absolute percentage error (MAPE)
\(MAPE= \frac{{\mathop \sum \nolimits_{i = 1}^n \left| {\frac{{D_i - F_i}}{{D_i}}} \right|}}{n} \times 100 = \frac{{\mathop \sum \nolimits_{i = 1}^n \left| {\frac{{E_i}}{{D_i}}} \right|}}{n} \times100 \)
Calculation:
Given:
Period |
Actual Demand (D_{i}) |
Forecasted Demand (F_{i}) |
Absolute Percentage Error E_{i} = (D_{i} - F_{i}) |
April |
225 |
200 |
25 |
May |
220 |
240 |
-20 |
June |
285 |
300 |
-15 |
July |
290 |
270 |
20 |
August |
250 |
230 |
20 |
Mean Absolute Percentage Error (MAPE):
\(MAPE = \frac{{\mathop \sum \nolimits_{i = 1}^n \left| {\frac{{D_i - F_i}}{{D_i}}} \right|}}{n} \times 100 \)
\( \therefore \frac{{\left| {\frac{{ 25}}{{225}}} \right| + \left| {\frac{{ - 20}}{{220}}} \right| + \left| {\frac{{ - 15}}{{285}}} \right| + \left| {\frac{{ 20}}{{290}}} \right| + \left| {\frac{{20}}{{250}}} \right|}}{5} \times 100 =8.072\; \% \)