發文作者:Yaowei Fu | 01/25/2011

Croston – 一種預測技巧

最近有位朋友問到關於Croston這個售後服務較常見的預估技巧. 他的問題如下>
The objects of forecast are predicting the consumption at the right moment with right quantity. Croston does try to predict the “right moment”, which apparently more sophisticate than moving average. But, does this really matter?
 
我把我的回答整理如下:
Ok, forecast is crucial to predict future consumption. And Croston indeed provides some benefits in the forecast with timing. But it is also the techniques in following processes, inventory planning and supply planning, to determine whether it is really effective.

Timing of Occurrence

Let me put up a example using Croston to show the “timing”
image
    Firstly, there is an asteroid mark on the calculation of non-zero and zero period.  This is important to know since in Croston, it can using average, single exponential with alpha or some other fancier methods to calculate them. The weight of recently history can be controlled by these methods. It is nothing to do with Croston itself. And actually every vendor does this slightly different (and mostly are configurable). So, the time series forecast will be formed based on these two measures.
    The sample is showing Croston tries to “detect” the cyclic/periodicity of demand pattern. In this case, it suggested a demand could occur possibly after 1.8 (2 after roundup) zero period.  Secondly, if the recent periods are zero periods, it further adjusts the next occurrence from last non-zero period. Here the benefit of timing comparing to other smoothing methold like average could be demostrated. People can start thinking that there may be no need to position something for the first two periods.

Implication to Inventory Planning

The safety level (or inventory position) calculation in inventory planning is based on the demand over risk period and the variance associated the demand within the risk period.

For demand over risk period:

First, If lead time is relatively long, like the case in aerospace, then the timing is not beneficial. Eventually it is a average demand cross the period.  If lead time is short, then timing does seem applicable. But this benefit is also arguable, since we are building a “multiplicative adaptive” system. We are adjusting buffers while we are predicting demand go up and down. This actually could signify bullwhip effect. Think the case when forecast goes from 0 to 5 and then 0, and then the safety level went from 0 to 3 to 0… that means on that particular 2nd period, the requirement go up extra 30%.

For variance associated with risk period:

One common experience about Croston is that a lot of people got frustrated with the high deviation (forecast inaccuracy). This is really because the deviation (or forecast error)measure is not only measuring the amount but also the timing.
For example:
Forecast: 0, 0, 5, 0, 0, 5
Actual: 0, 0, 5, 0, 0, 5
    The forecast error is actually 0. But if actual is 0, 5, 0, 0, 5, 0 then forecast error go up to the roof.  This further exaggerates the problem of bullwhip mentioned in the demand over risk period. Higher variance/error drives up the required buffer thus dramatizes the effect. Average actually is a safer bet here. Of course in general, if demand is low, then the deviation (or forecast error) is not reliable and can be ignored.
In summary here:
High demand Low demand
Long lead time Croston is no applicable Potentially applicable, but arguable with bullwhip effect
Short lead time Croston is no applicable Still arguable due to bullwhip effect. And since lead time is low, there are various management tactic to address the issue rather than rely on Croston.

In inventory planning, I personally think there is no mandatory for Cronston. The value still can be delivered by other forecast methods which handle trend, cycle and smoothing.

Implication to Supply Planning

This is also applicable to distribution planning. The common ordering/replenishing policies are (r,q), (s,S) and (S,S-1).
    I personally really don’t think (r,q) and (r,S) apply here, since they are mostly for high consumption goods (Cronston normally won’t apply on this type of goods)
Note1: (s,s-1) is a ordering policy basically says if the inventory level is one below (s-1), place a order to bring inventory level to s. It is very broadly used in aerospace and long term supply planning. s is generally the safety stock(or ROP  depending on the usage. This could be another chapter)
Note2: (s,s-1) is more popular in long term supply planning while (r,q) and (r,S) are widely used in short term distribution planning.
    But there do have values in (s,s-1) with Croston.  Let’s see an example: In the earlier example, the forecast is 0, 0, 1.8, 0, 0 (while average is 0.36). Under (s,s-1), it will suggest to order 0.36 per month.
    Keep in mind the supply planning is always integer planning. That means system will suggest to order one in first period and sit there while we pretty much can guess there will have no need in first two periods. What a waste! If that unit is a 747 engine and idle there for a quarter, then there will be a strong financial implication.
    This is just showing the disadvantage of average method and the benefit of “timing” in particularly (s,s-1) policy. Of course then there are other tactics to address above issues for average, like carry forward rounding. But I try to convey is this ((s,s-1) with low demand) is pretty much the main area Croston can provide values than average or other smoothing method.

Conclusion

OLYMPUS DIGITAL CAMERA             I personally do see the Croston provides values in certain unique circumstance. And the value is significant. But departing from that circumstance, the benefit of Croston will fade significantly and should be used with caution to avoid adverse implications.
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