question archive The following data represents number of customers arriving at Quick Lube for an oil change between 8 and 11 AM over the past 6 days
The following data represents number of customers arriving at Quick Lube for an oil change between 8 and 11 AM over the past 6 days
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The following data represents number of customers arriving at Quick Lube for an oil change between 8 and 11 AM over the past 6 days. Day 1 2 3 4 5 6 Customers 12 9 11 12 10 13 a) Using the Naïve Method, how many customers would you forecast for Day 7? b) Using 3 day Moving Average, how many customers would you forecast for Day 7? c) Using Exponential Smoothing with alpha = .3, how many customers would you forecast for Day 7? (hint: use Actual Value for period 1 as period 2 forecast) d) If the actual # of customers for period 7 was 12, compute the MAD statistic for each method (parts a, b and c) using periods 4, 5, 6 and 7 as data points. e) Which method produces the best forecasts for Quick Lube? Why?
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a) Using the Naïve Method, how many customers would you forecast for Day 7?
- 13
b) Using 3-day Moving Average, how many customers would you forecast for Day 7?
- 11.67
c) Using Exponential Smoothing with alpha = .3, how many customers would you forecast for Day 7? (hint: use Actual Value for period 1 as period 2 forecast)
- 11.56
d) If the actual # of customers for period 7 was 12, compute the MAD statistic for each method (parts a, b, and c) using periods 4, 5, 6, and 7 as data points. e) Which method produces the best forecasts for Quick Lube? Why?
- The 3-day Moving Average Method produces the best forecasts for Quick Lube as it has the lowest MAD of 1.08 among the other forecasting methods. Having the lowest MAD indicates a way more accurate forecast as the data forecasted are dispersed close to the mean with minimum deviation.
Step-by-step explanation
a) Using the Naïve Method, how many customers would you forecast for Day 7?
- The forecast using the Naïve Method is simply the number of customers in the previous day.
E.g. Forecast on day 2 is equal to the number of customers in day 1.
| Day | Customers | Forecast |
| 1 | 12 | |
| 2 | 9 | 12 |
| 3 | 11 | 9 |
| 4 | 12 | 11 |
| 5 | 10 | 12 |
| 6 | 13 | 10 |
| 7 | 13 |
b) Using 3-day Moving Average, how many customers would you forecast for Day 7?
- To compute the forecast using a? 3-day moving? average, we just need to get the average of the number of customers for the past three days.
| Day | Customers | Forecast |
| 1 | 12 | |
| 2 | 9 | |
| 3 | 11 | |
| 4 | 12 |
= (12 + 9 + 11) / 3 = 10.67 |
| 5 | 10 |
= (9 + 11 + 12) / 3 = 10.67 |
| 6 | 13 |
= (11 + 12 + 10) / 3 = 11 |
| 7 |
= (12 + 10 + 13) / 3 = 11.67 |
c) Using Exponential Smoothing with alpha = .3, how many customers would you forecast for Day 7? (hint: use Actual Value for period 1 as period 2 forecast)
- To compute the forecast using exponential smoothing, we need to use the formula:
Forecast = Forecast for the previous day + α (Number of customers in the previous day - Forecast for the previous day)
Forecast = Forecast for the previous day + 0.3 (Number of customers in the previous day - Forecast for the previous day)
- The forecast on day 2 is equal to the number of customers on day 1.
| Day | Customers | Forecast |
| 1 | 12 | |
| 2 | 9 | 12 |
| 3 | 11 |
= 12 + 0.3 (9 - 12) = 11.1 |
| 4 | 12 |
= 11.1 + 0.3 (11 - 11.1) = 11.07 |
| 5 | 10 |
= 11.07 + 0.3 (12 - 11.07) = 11.349 |
| 6 | 13 |
= 11.349 + 0.3 (10 - 11.349) = 10.9443 |
| 7 |
= 10.9443 + 0.3 (13 - 10.9443) = 11.56101 = 11.56 |
d) If the actual # of customers for period 7 was 12, compute the MAD statistic for each method (parts a, b and c) using periods 4, 5, 6 and 7 as data points. e) Which method produces the best forecasts for Quick Lube? Why?
- To compute the MAD, we first need to compute the absolute error of each month. ?Compute for absolute error using the formula:
Absolute error = | Number of customers - Forecast |
- If the absolute errors were computed, compute the MAD of the forecasting method using the formula:
MAD = Σ of all absolute errors
Number of days
| Naïve Method | |||
| Day | Customers | Forecast | Absolute error |
| 4 | 12 | 11 |
= |12 - 11| = 1 |
| 5 | 10 | 12 |
= |10 - 12| = 2 |
| 6 | 13 | 10 |
= |13 - 10| = 3 |
| 7 | 12 | 13 |
= |12 - 13| = 1 |
MAD (Naive Method) = Σ of all absolute errors
Number of days
MAD (Naive Method) = 1 + 2 + 3 + 1
4
MAD (Naive Method) = 1.75
| 3-day Moving Average | |||
| Day | Customers | Forecast | Absolute error |
| 4 | 12 | 10.667 |
= |12 - 10.667| = 1.333 |
| 5 | 10 | 10.667 |
= |10 - 10.667| = 0.667 |
| 6 | 13 | 11 |
= |13 - 11| = 2 |
| 7 | 12 | 11.667 |
= |12 - 11.667| = 0.333 |
MAD (3-day Moving Average) = Σ of all absolute errors
Number of days
MAD (3-day Moving Average) = 1.333 + 0.667 + 2 + 0.333
4
MAD (3-day Moving Average) = 1.08
| Exponential Smoothing with alpha = 0.3 | |||
| Day | Customers | Forecast | Absolute error |
| 4 | 12 | 11.07 |
= |12 - 11.07| = 0.93 |
| 5 | 10 | 11.349 |
= |10 - 11.349| = 1.349 |
| 6 | 13 | 10.9443 |
= |13 - 10.944| = 2.056 |
| 7 | 12 | 11.56101 |
= |12 - 11.561| = 0.439 |
MAD (Exponential Smoothing) = Σ of all absolute errors
Number of days
MAD (Exponential Smoothing) = 0.93 + 1.349 + 2.056 + 0.439
4
MAD (Exponential Smoothing) = 1.193
The 3-day Moving Average Method produces the best forecasts for Quick Lube as it has the lowest MAD among of 1.08 the other forecasting methods. Having the lowest MAD indicates a way more accurate forecast as the data forecasted are dispersed close to the mean with minimum deviation.
