Question

Use exponential smoothing with trend adjustment to forecast deliveries for period 10. Let alpha = 0.4, beta = 0.2, and let the initial trend value be 4 and the initial forecast be 200.

Period- Actual Demand
1- 200
2- 212
3- 214
4- 222
5- 236
6- 221
7- 240
8- 244
9- 250
10- 266

Answer 1

To forecast deliveries for period 10 using exponential smoothing with trend adjustment, you can use the formulas for level forecast and trend forecast. Using the given values, the forecasted deliveries for period 10 would be 240.4 units.

Step-by-step explanation:

To forecast deliveries for period 10 using exponential smoothing with trend adjustment, we can use the following formulas:

Level forecast: F_10 = alpha × D_10 + (1 - alpha) × (F_9 + T_9)

Trend forecast: T_10 = beta × (F_10 - F_9) + (1 - beta) × T_9

Given that alpha = 0.4, beta = 0.2, the initial trend value is 4, and the initial forecast is 200:

First, we calculate the level forecast:

F_10 = 0.4 × 266 + 0.6 × (200 + 4) = 240.4

Then, we calculate the trend forecast:

T_10 = 0.2 × (240.4 - 200) + 0.8 × 4 = 2.68

Therefore, the forecasted deliveries for period 10 would be 240.4 units.

Answer 2

254.02

Step-by-step explanation:

Relevant data provided

Forecast delivers for period 10

Alpha = 0.4

Beta = 0.2

Trend value = 4

Initial forecast = 200

For period 10 please look into the spreadsheet which has been attached which contains formulas and values.

Forecast including trends

The smoothed forecast is calculated below:

`F_(t)=\alpha A_(t-1)+(1-\alpha )(F_(t-1)+T_(t-1))`

Smoothed trend formula is shown below:

`T_(t)=\beta (F_(t)-F_(t-1))+(1-\beta )T_(t-1)`

Forecast including trend formula is calculated with the help of below formula:-

`FIT_(t)= F_(t)+T_(t)`