| | | | | Closed on Sundays | Closed on Sundays — Develop forecasts using regressions sales each the series rain respectively Calculate MFE
Mathematics & StatisticsGeneralWorked Solution
1. Develop forecasts using regressions of sales on each of the series of rain forecasts respectively. Calculate the MFE (bias), MAD, and MAPE for the two forecasting models. Which rain forecast seems to be better at predicting Rachel’s daily sales, the 5 day forecast or the 2 day forecast?
2. How can Rachel make use of the rain forecasts to improve her forecasts of total sales each day? What other changes to her business would she need to make in order to capitalize on this information?
3. How are order lead time and forecasting accuracy related to each other in this case?
4. Plot and visually inspect the sales data. What other suggestions would you give Rachel for improving her sales forecasts? What type of time series model would be appropriate? Why?
SOLUTION
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1. The tables and plots below indicate that the 2-day forecast provides better predictions of Rachel’s daily sales. This is to be expected. Nearer term forecasts are usually more accurate (i.e., 2-day forecast is better than 5-day forecast). If rain actually does affect sales, then a better prediction of rain would provide a better prediction of sales.
2-day forecast
Closed on Sundays
Closed on Sundays
Rachel's Bakery
Rachel's Bakery
17.73
4542.8
Day
Probability of Rain (%) 2 day forecast
Total Sales
day regess fcst
err
abs err
ape
Monday
40
5520
5252
268
268
4.86%
Tuesday
30
4320
5074.7
-754.7
754.7
17.47%
Wednesday
10
4212
4720.1
-508.1
508.1
12.06%
Thursday
40
4987
5252
-265
265
5.31%
Friday
80
5545
5961.2
-416.2
416.2
7.51%
Saturday
90
6023
6138.5
-115.5
115.5
1.92%
Monday
30
4590
5074.7
-484.7
484.7
10.56%
Tuesday
30
4733
5074.7
-341.7
341.7
7.22%
Wednesday
30
4923
5074.7
-151.7
151.7
3.08%
Thursday
50
4687
5429.3
-742.3
742.3
15.84%
Friday
100
5988
6315.8
-327.8
327.8
5.47%
Saturday
70
6132
5783.9
348.1
348.1
5.68%
Monday
10
5324
4720.1
603.9
603.9
11.34%
Tuesday
10
4526
4720.1
-194.1
194.1
4.29%
Wednesday
10
5232
4720.1
511.9
511.9
9.78%
Thursday
50
5684
5429.3
254.7
254.7
4.48%
Friday
70
5911
5783.9
127.1
127.1
2.15%
Saturday
60
6328
5606.6
721.4
721.4
11.40%
Monday
20
4932
4897.4
34.6
34.6
0.70%
Tuesday
15
5235
4808.75
426.25
426.25
8.14%
Wednesday
50
5862
5429.3
432.7
432.7
7.38%
Thursday
20
4862
4897.4
-35.4
35.4
0.73%
Friday
80
6100
5961.2
138.8
138.8
2.28%
Saturday
70
6255
5783.9
471.1
471.1
7.53%
0.05625
361.4895833
6.97%
MFE (bias)
MAD
MAPE
5-day forecast
CONTINUE TO NEXT PAGE.
Rachel's Bakery
Rachel's Bakery
1.7638
5255.4
Day
Probability of Rain (%) 5 day forecast
Total Sales
day regess fcst
err
abs err
Ape
Monday
10
5520
4720.1
799.9
799.9
14.49%
Tuesday
20
4320
4897.4
-577.4
577.4
13.37%
Wednesday
30
4212
5074.7
-862.7
862.7
20.48%
Thursday
50
4987
5429.3
-442.3
442.3
8.87%
Friday
80
5545
5961.2
-416.2
416.2
7.51%
Saturday
90
6023
6138.5
-115.5
115.5
1.92%
Monday
60
4590
5606.6
-1016.6
1016.6
22.15%
Tuesday
70
4733
5783.9
-1050.9
1050.9
22.20%
Wednesday
90
4923
6138.5
-1215.5
1215.5
24.69%
Thursday
100
4687
6315.8
-1628.8
1628.8
34.75%
Friday
100
5988
6315.8
-327.8
327.8
5.47%
Saturday
20
6132
4897.4
1234.6
1234.6
20.13%
Monday
10
5324
4720.1
603.9
603.9
11.34%
Tuesday
10
4526
4720.1
-194.1
194.1
4.29%
Wednesday
10
5232
4720.1
511.9
511.9
9.78%
Thursday
50
5684
5429.3
254.7
254.7
4.48%
Friday
20
5911
4897.4
1013.6
1013.6
17.15%
Saturday
60
6328
5606.6
721.4
721.4
11.40%
Monday
20
4932
4897.4
34.6
34.6
0.70%
Tuesday
15
5235
4808.75
426.25
426.25
8.14%
Wednesday
20
5862
4897.4
964.6
964.6
16.46%
Thursday
20
4862
4897.4
-35.4
35.4
0.73%
Friday
10
6100
4720.1
1379.9
1379.9
22.62%
Saturday
60
6255
5606.6
648.4
648.4
10.37%
29.60625
686.5395833
13.06%
MFE (bias)
MAD
MAPE
2.
She can use the 5 day forecast to improve her forecasting of demand and needed supplies, and place orders in the same manner as she currently does. However, if she wants to take advantage of the better forecast quality of the 2 day forecast, she would need to work with her supplier to see if a 2 day delivery lead time is possible.
3.
This is a good simple example of how supply lead time dictates the time horizon for forecasting. Rachel must forecast at least as far in advance as the supply lead time dictates. If we can reduce lead time, we can reduce the planning horizon, and most probably improve forecast accuracy.
4.
If we plot the data over time, as shown below, it becomes clear that there is strong seasonality in the sales. Rachel could improve her forecasts tremendously by incorporating a seasonal factor into the model.