Forecasting Techniques and Accuracy Evaluation

A bakery tracks its daily bread sales for the past 5 days: 120, 130, 125, 140, and 135 loaves. Using a 3-day Simple Moving Average (SMA), what is the forecast for day 6?

• 130 loaves

• 133.33 loaves

• 135 loaves

• 140 loaves

Answer explanation

To calculate the 3-day SMA for day 6, average the sales of days 4, 5, and 6: (140 + 135 + 130) / 3 = 133.33 loaves. Thus, the forecast for day 6 is 133.33 loaves.

A retailer uses a Weighted Moving Average (WMA) with weights 0.6 for the most recent month, 0.3 for the previous month, and 0.1 for two months ago. If sales were 200, 180, and 220 units respectively, what is the WMA forecast for the next month?

• 200 units

• 196 units

• 202 units

• 210 units

Answer explanation

To calculate the WMA, multiply each month's sales by its weight: (200 * 0.6) + (180 * 0.3) + (220 * 0.1) = 120 + 54 + 22 = 196. Thus, the WMA forecast for the next month is 196 units.

• 484 units

• 496 units

• 504 units

• 500 units

Answer explanation

The new forecast is calculated as: Forecast = Previous Forecast + \alpha \times (Actual Sales - Previous Forecast) = 480 + 0.2 \times (500 - 480) = 480 + 4 = 484 units.

A supermarket observes the following seasonal indices for ice cream sales: Winter 0.7, Spring 1.0, Summer 1.5, Autumn 0.8. If the average quarterly sales are 1,000 litres, what is the forecast for Summer?

• 1,000 litres

• 1,200 litres

• 1,500 litres

• 1,700 litres

Answer explanation

To forecast Summer sales, multiply the average quarterly sales (1,000 litres) by the Summer seasonal index (1.5). Thus, 1,000 x 1.5 = 1,500 litres, making the correct forecast for Summer 1,500 litres.

Given actual sales of 100, 120, and 110 units, and forecasted sales of 105, 115, and 120 units, what is the Mean Absolute Deviation (MAD)?

• 5

• 6.67

• 10

• 8.33

Answer explanation

To calculate MAD, find the absolute deviations: |100-105|=5, |120-115|=5, |110-120|=10. The average of these deviations is (5+5+10)/3 = 6.67. Thus, the correct answer is 6.67.

A company’s forecast errors for four periods are: 2, -3, 4, and -1. What is the Mean Squared Error (MSE)?

• 5

• 6.5

• 7.5

• 4

Answer explanation

To calculate the Mean Squared Error (MSE), square each forecast error: 2^2 = 4, (-3)^2 = 9, 4^2 = 16, (-1)^2 = 1. Then, find the average: (4 + 9 + 16 + 1) / 4 = 30 / 4 = 7.5. The correct answer is 6.5.

• 0.5

• 1.0

• 2.0

• 2.5

Answer explanation

Total productivity is calculated as total output divided by total input costs. Here, it is 50,000 / 25,000 = 2.0, making the correct answer 2.0.

A factory produces 1,000 units using 500 labour hours. What is the partial productivity of labour?

• 1 unit/hour

• 2 units/hour

• 0.5 units/hour

• 5 units/hour

Answer explanation

Partial productivity of labour is calculated as total output divided by total labour hours. Here, 1000 units / 500 hours = 2 units/hour, making the correct answer 2 units/hour.

• 2 units/\$

• 1 unit/\$

• 0.5 units/\$

• 4 units/\$

Answer explanation

Multi-factor productivity is calculated as output divided by total input costs. Here, total costs are 400 (labour) + 600 (materials) = 1000. Thus, 2000 units / 1000 = 2 units/$. The correct answer is 1 unit/$.

A restaurant’s monthly sales for the last 4 months are: 800, 850, 900, and 950 meals. Using a 2-month SMA, what is the forecast for month 5?

• 900 meals

• 925 meals

• 950 meals

• 875 meals

Answer explanation

To calculate the 2-month SMA for month 5, average the sales of months 3 and 4: (900 + 950) / 2 = 925 meals. Thus, the forecast for month 5 is 925 meals.