Croston's Method
Croston’s method(CR) is a classic method that specifically dealing with intermittent demand, it was developed base upon the Simple Exponential Smoothing method. When Croston dealing with the intermittent demand, he found out that by using the SES, the level of forecasting in each period’s demand are normally higher than it’s actual value, which lead to a very low accuracy. After a period of times of research, he came out a method that optimize the result of the intermittent demand forecasting.
This method basically decompose the intermittent demand into two parts: the size of non-zero demand and the time interval of those demand occurred, and then apply the simple exponential smoothing on both part. Where the formula is follow:
And finally by combining these forecasts
In the formula
For example, the case in SES section in here will be as below:
Croston’s method converse the intermittent demand time series into a non-zero demand time series and a demand interval time series, many cases show that this method work quite well, but before apply Croston’s method, three assumptions should be made:
- The non-zero demand are independent and obey normal distribution;
- The demand intervals are independent and obey geometric distribution;
- There are mutual independence between the demand size and demand intervals.
According to many real cases show that, Croston’s method is suitable for the situation which the lead time obey normal distribution, for those demand series which contain large amount of zero values, Croston’s method did not shows a outstanding performance, sometimes even worse than SES method.
Additionally, Croston’s method can only provide the average demand for each period, it can not give a forecast of the demand size for each period, it can not forecast which period will occurred a demand, and it also can not come out a probability of whether a period will occurred a demand.
After all, although Croston’s method is a very classic and wide use method, it still has a lots of limitations, but after years of research carried by statisticians and scholars, few variations of Croston’s method were brought up.
Croston’s variations
Croston’s method is the main model used in demand forecasting area, most of the works are based upon this model. However, in 2001 Syntetos and Boylan proposed that Croston’s method is no a unbiased method, while some empirical evidence also showed that the losses in performance which use the Croston’s method (Sani and Kingsman, 1997).
Plenty of further research is done in improving the Croston’s method. Syntetos and Boylan (2005) proposed an approximate unbiased procedure that provide less variance in the result of estimate, which is known as SBA (Syntetos and Boylan Approximate). Recently, Teunter et al. (2011) also proposed a intermittent forecasting method that can deal with obsolescence, which is based on Croston’s method known as TSB method (Teunter, Syntetos and Babai).
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