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# ScienceAsia 27 (2001)

FORECASTING METHODS

Steps 1, 2, and 3 of the proposed forecasting and planning process are discussed in detail in this section. Firstly, the aggregate demand forecasts of eight product groups throughout the planning horizon of 12 months will be determined. Secondly, the demand forecasts of the product groups will be disaggregated into those of individual product. Thirdly, the safety stocks of individual product will be calculated based on the forecast error.

# Aggregate Demand Forecasts of Product Groups

The typical demand pattern of each product group is seasonal. As an example, Fig. 3 shows the demand pattern of Product Group 3. Thus, three forecasting models that are suitable for making seasonal demand forecasts are considered. They are Winter’s, decomposition and Auto-Regressive Inte- grated Moving Average (ARIMA) models.2-5 Because of their simplicity, the Winter’s and decomposition models are initially used to forecast the aggregate demand of each product group. If the Winter’s and decomposition models are inadequate (ie, the forecast errors are not random), the ARIMA model which is more complicated and perhaps more efficient will be applied.

The Winter’s model has three smoothing parameters that significantly affect the accuracy of the forecasts. These parameters are varied at many levels using a computer program to determine a set of parameters that give the least forecast errors. There are two types of the decomposition model, namely, multiplicative and additive types. The former is selected since the demand pattern shows that the trend and seasonal components are dependent. The forecast errors of the Winter’s and decomposition models are presented in Table 1.

Based on the calculated mean square error (MSE) and the mean absolute percentage error (MAPE), it is seen that the decomposition model has lower

## Original Series

(x 1000) 16

16

demand 3

8

4

0

• 0

10

20

30 time index

40

50

60

Fig 3. Actual demand of Group 3.

273

forecast errors in all product groups than the Winter’s model. Thus, it is reasonable to conclude that the decomposition model provides better demand forecasts than the other.

One way to check whether the forecasting model is adequate is to evaluate the randomness of the forecast errors. The auto-correlation coefficient func- tions (ACFs) of the errors from the decomposition model for several time lags at the significant level of 0.05 of each product group are determined. The ACFs of Groups 1 and 3 are presented as examples in Fig. 4 and 5, respectively. The ACFs of Groups 4, 5, 6, 7, and 8 are similar to those of Group 1 in

Table 1. Forecast errors of the Winter’s and decom- position models.

# Products

MSE Winter’s Decomposition

MAPE (%) Winter’s Decomposition

coefficient

Group 1

16,855,149

9,879,330

Group 2

8,485,892

4,363,290

Group 3

5,433,666

2,227,592

Group 4

6,035,466

4,507,990

Group 5

23,030,657

10,039,690

Group 6

1,690,763

574,108

Group 7

2,034,917

636,755

Group 8

1,884,353

883,811

1

36.14

26.97

48.94

31.86

24.25

15.97

30.08

23.24

18.80

13.14

53.86

34.80

61.99

34.45

46.52

28.76

1

0.5

0

• -

0.5

## Estimated Autocorrelations

Fig 4. ACFs of the residuals from the decomposition model for Group 1.

• -

1

• 0

4

20

16

8

lag

12

0.5

coefficient

0

• -

0.5

• -

1

• 0

4

8

12

16

20

lag

Fig 5. ACFs of the residuals from the decomposition model for Group 3.

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