Tutorial 5 Exercises

Question 1

You are the inventory analyst for a distribution centre that tracks weekly product demand. You are tasked with using four different forecasting methods to predict demand for the upcoming week and evaluate their performance.

Week 1 2 3 4 5 6 7
Demand (Units) 120 130 125 135 140 150 145
  1. Treat Week as the independent variable and Demand as the dependent variable \(Y\).
  2. Calculate the regression equation using the least squares method.
  3. Use the equation to forecast demand for Week 8.
  4. Using a 3-period SMA, compute the forecast for Week 8.
  5. Using a 3-period WMA with weights: 0.5, 0.3, and 0.2 for most recent, middle, and oldest. Compute the forecast for Week 8.
  6. Using SES with smoothing constant 0.4 and initial forecast 120. Compute the forecast for Week 8.
  7. Compute the forecast errors (absolute error) for Weeks 4-7 using SMA, WMA, and SES.
  8. Which method would you recommend for short-term forecasting in this case, and why?

Question 2

A company records the following demand for a product over 12 periods.

Period 1 2 3 4 5 6 7 8 9 10 11 12
Demand 210 205 198 192 188 182 178 170 165 160 155 150

The data shows a downward trend in demand over time.

  1. Forecast demand for the next four periods (13–16) using naive forecasting method, \(F_{t+1} = D_t.\)

  2. Discuss how the naive method performs when demand exhibits a trend.

Question 3

Using a 3-period moving average, compute forecasts for periods 13–16.

\[ F_t = \frac{A_{t-1} + A_{t-2} + A_{t-3}}{3} \]

where \(A_t\) is the actual demand in period \(t\).

Period Demand \(A_t\) Forecast \(F_t\)
1 210
2 205
3 198
4 192
5 188
6 182
7 178
8 170
9 165
10 160
11 155
12 150
13
14
15
16

Comment on whether the moving average method responds quickly to the downward trend.

Question 4

Use exponential smoothing with smoothing constant

\[ \alpha = 0.3 \]

The forecasting equation is

\[ F_{t+1} = F_t + \alpha (A_t - F_t) \]

Assume the initial forecast \(F_1 = A_1\), Compute forecasts for periods 13–16.

Period Demand \(A_t\) Forecast \(F_t\)
1 210
2 205
3 198
4 192
5 188
6 182
7 178
8 170
9 165
10 160
11 155
12 150
13
14
15
16

Question 5

Fit a linear regression model

\[ \hat{Y}_t = a + bt \]

  1. Estimate the parameters \(a\) and \(b\) using the least squares method.
Period \(X\) Demand \(Y\) \(X^2\) \(XY\)
1 1 210
2 2 205
3 3 198
4 4 192
5 5 188
6 6 182
7 7 178
8 8 170
9 9 165
10 10 160
11 11 155
12 12 150
sum 78 2183

\[ a = \frac{\sum Y - b\left(\sum X\right)}{n} \]

\[ b = \frac{n(\sum XY) - (\sum X)(\sum Y)}{n(\sum X^2) - (\sum X)^2} \]

  1. Use the estimated regression equation to forecast demand for periods 13–16.

Question 6

  1. Which forecasting method is most appropriate for data with a downward trend?

  2. Why might moving average forecasts lag behind the actual demand when a trend exists?

  3. What are the advantages of using a trend model for forecasting?